Class 11 Medical Chemistry - Structure Of Atom

Atoms of two elements $$P$$ and $$Q$$ have $$5$$ electrons in $${2}^{nd}$$ shell and $${3}^{rd}$$ shell respectively. What could be the geometric representations of $$P$$ and $$Q$$? What will be the atomic numbers of these elements?

Electronic configuration of an element is $$2^n$$ where n is the number of orbit hence

1st orbit can not have more than 2 electrons $$2^1=2$$

2nd orbit can not have more than 8 electrons $$2^2 = 8$$

Electronic configuration of an elements can be $$ P = 2,5 = 7$$ and $$Q = 2,8,5 = 15$$

A dipositive ion has an electronic arrangement $$2, 8, 8$$. Find out the number of electrons, protons and neutrons in that element if its mass number is $$40$$.

Electronic configuration of dipositive ion is $$2, 8, 8$$ hence its neutral atom will have configuration as $$2, 8, 8, 2$$, which shows total number of electrons/protnes = $$20. $$

Mass = proton + nutron i.e. $$40 = 20 + 20$$

The number of electrons, protons and neutrons in that element = $$20, 20,20.$$

Write the two postulates Bohr's atomic model.

1) An electron can revolve around the nucleus in certain fixed orbits of definite energy without emission of any radiant energy. Such orbits are called stationary orbits.

2)Only those orbits are allowed for which the angular momentum of the electron is an integral multiple of $$\dfrac{nh}{2\pi}$$

Thus,$$L = \dfrac{nh}{2\pi}$$ where $$n=1,2,3........$$

Name two processes which provide the best evidence for the motion of particles in matter.

(i) Brownian movement:

It is the random movement of the particles which is called as Brownian Movement.

This movement occurs because of the bombardment by other moving particles. Larger particles can be moved by light, fast moving molecules.

(ii) Diffusion:

Diffusion is a process in which the molecules move from high concentration to lower concentration.

Find the radius of nucleus of an atom having atomic mass number equal to$$\left( Take\ { R }_{ 0 }\ =\ 1.3\times { 10 }^{ -15 }m \right)$$

The formula for calculating radius of nucleus

$$R=R_{0} \times A^{(1/3)}$$

where A =atomic mass

$$R=(1.3\times10^{-15})(125)^{(1/3)}$$

=$$1.3\times 10^{-15}\times 5$$

$$R=6.5\times10^{-15}m$$

$$Therefore,the\quad radius\quad of\quad nucleus\quad of \quad an\quad atom\quad is \quad6.5\times10^{-15}$$.

Represent each of the following in terms of its symbols:
i) a proton ii) an electron
iii) a neutron

1)Protons are positively charged and are often represented by $$p^+$$ or$$H^+$$

2)Electrons are negatively charged and are often represented as $$ e$$ or $$e^-$$

3)Neutrons do not have any charge and are often represented as $$n$$ or $$n^0$$

Out of 6s and 4f orbitals, which is filled first and why?

Lowest energy orbitals fill first. Thus, the filling pattern is 1s, 2s, 2p, 3s, 3p, 4s, 3d, etc. Since the orbitals within a subshell are degenerate (of equal energy), the entire subshell of a particular orbital type is filled before moving to the next subshell of higher energy.
The orbitals are filled according to (n+l) rule i.e. the orbitals having more (n+l) value will be filled before even if the value of n of that particular orbit is more.
Here, (n+l) of 6s orbital is 6 and that of a 4f orbital is 7 and hence 4f orbital is filled before 6s orbital.

If number of electrons in an atom is 8 and number of protons is also 8, then (i) what is the atomic number of the atom ? and (II) what is the charge on the atom?

(i) The atomic number is equal to the number of protons. Therefore, the atomic number of the atom is 8.

(ii) Since the number of both electrons and protons is equal, therefore, the charge on the atom is 0.

Calculate energy of electron which is moving in the orbit that has its radius. sixteen times the radius of first Bohr orbit for $$H-atom$$

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The atomic numbers of two elements A and B are 11 and 12 respectively. Which element exhibits highest metallic property ? Write the molecular formula of the compounds formed when theses elements combine with the element 'Z' having atomic number 8.

Atomic no 11 will have the highest metallic property which is sodium.

Atomic no 8 is oxyzen

When sodium reacts with Oxyzen it will form. $$Na_{2}O$$

An element belonging to 3d series of modern periodic table has spin magnetic moment =5.92 B.M.in +3 oxidation state. Determine the atomic number of element.

Answer is Fe Iron
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"The atomic number and mass number of sodium are $$11$$ and $$23$$ respectively".What information does this statement convey?

The atomic number and mass number of sodium are $$11$$ and $$23$$ respectively.

This suggests that number of proton in sodium $$=11$$ and number of nucleons i.e. proton and neutrons in sodium $$=23.$$ Thus, number of neutrons $$=12$$ and also Since no. of protons $$=$$ no. of electrons $$= 11$$

So, they are similar.

What is meant by the statement that "the atomic number of sodium is eleven"?

Atomic number of sodium is $$11$$ means, the number of protons present in sodium atom $$=11.$$

Also Since number of electrons $$=$$ number of protons.

So, number of electrons are also $$11.$$

A hydrogen atom in ground state is heated by a photon exciting the electron to the $$3rd$$ excite state. The electron then drop to the $$2nd$$ orbit what is the frequency of radiation emitted and absorbed in the process.

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The energy required to excite an electron of H-atom from first orbit to second orbit is

1308775_1336121_ans_b2ac4156aa7f49ca8879968bb23a1f14.PNG

Name the three constituent of an atom and state their mass and charge of each. How are they distributed in an atom?

Three constituent of an atom are:

Electrons:mass is $$9.2\times{10}^{-31}$$kg,Charge is $$-1.6\times{10}^{-19}$$C

Neutron:mass is $$1.6749\times{10}^{-27}$$kg,charge is zero.

Protons:mass is $$1.6726\times{10}^{-27}$$kg,charge is $$+1.6\times{10}^{-19}$$C

Define 'atomic number' and 'mass number'.

Atomic Number - The number of protons in the atom of an element is called the atomic number of the element. For example - The atomic number of sodium $$(_{11}Na)$$ is $$11$$ as it has $$11$$ protons in the nucleus of its atom.

All atoms of a given element have the same number of protons.

Atoms of different elements have different numbers of protons. For example - The number of protons in one atom of $$Na$$ is $$11$$, but the number of protons in one atom of chlorine $$(_{17}Cl)$$ is $$17$$, as sodium and chlorine are two different elements.

Mass Number - The mass number of an atom is the total number of protons and neutrons present in the nucleus of the atom.

Mass number $$(A)$$= Number of protons $$+$$ Number of neutrons

Atoms of different elements usually have different mass numbers but they can be the same. For example, the mass number of argon atoms and calcium atoms can both be $$40$$.

What are the postulates of Bohr's model of an atom?

Postulates of the Bohr Atomic Model:

Electrons revolve around the nucleus in a fixed circular path termed “orbits” or “shells” or “energy level.”

The orbits are termed as “stationary orbit.”

Every circular orbit will have a certain amount of fixed energy and these circular orbits were termed orbital shells. The electrons will not radiate energy as long as they continue to revolve around the nucleus in the fixed orbital shells.

The different energy levels are denoted by integers such as n=1 or n=2 or n=3 and so on. These are called as quantum numbers. The range of quantum number may vary and begin from the lowest energy level (nucleus side n=1) to highest energy level.

The different energy levels or orbits are represented in two ways such as 1, 2, 3, 4… or K, L, M, N….. shells. The lowest energy level of the electron is called the ground state.

The change in energy occurs when the electrons jump from one energy level to other. In an atom, the electrons move from lower to higher energy level by acquiring the required energy. However, when an electron loses energy it moves from higher to lower energy level.

If number of electrons in an atom is $$8$$ and number of protons is also $$8$$, then:
(i) What is the atomic number of an atom?
(ii) What is the charge on the atom?
(iii) Why does moon have very cold and very hot temperature even though it is present at the same distance from the sun as the earth is?

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Mass of single atom of silver is $$1.794\times{10}^{-22}$$. What is atomic mass of silver.

1.794 X 10^-22

The electronic spectrum is characteristic of an element.
If true then enter 1, if false enter 0.

Electronic transitions involve exciting an electron from one principle quantum state to another. Only by absorbing energy, can an electron be excited. Once it is in the excited state, it will relax back to it's original more energetically stable state, and in the process, release energy as photons. As different elements have different electronic configurations and the different set of quantum numbers, thus the electronic spectrum is characteristic of an element.

What do you mean by the dual nature of an electron?

Electrons possess both wave and particle nature.

An atom of an element has one electron in the valence shell and the two inner shells have 8 electrons each. Find the atomic number of that element.

Valence shell has 1 electron and 2 inner shells have 8 electrons, thus the valence electron is in 'N' shell.

The electronic configuration is 2, 8, 8, 1 and atomic number is 19.

The highest number of unpaired electrons are in $$ Fe^{3+},Fe^{2+},Fe^{+}$$ :

The atomic number of iron = $$26$$

The electronic configuration of $$Fe^{+}$$ = $$1s^22s^22p^63s^23p^64s^13d^6$$

has 5 unpaired electrons.

The electronic configuration of $$Fe^{2+}$$ = $$1s^22s^22p^63s^23p^63d^64s^0$$

It has 4 unpaired electrons

The electronic configuration of $$Fe^{3+}$$ = $$1s^22s^22p^63s^23p^63d^54s^0$$

It has 5 unpaired electrons.

So the highest number of unpaired electrons are present in $$Fe^{3+}$$.

Define Isotopes.

An neutral atom has the same number of ......... as electrons.

An atom has same number of protons and electrons.

An atom is made up of protons, neutrons and ..........

An atom is a fundamental unit of the every substance. It is made up of electron, proton and neutron. Proton and neutron is present inside the nucleus and electron revolve around it.

An atom of the element is $$^{35}_{17}Cl$$. Complete the following table.
Element Mass number Atomic number No. of protons No. of electrons
No. of neutrons

Element	Mass number	Atomic number	No. of protons	No. of electrons	No. of neutrons
Chlorine	35	17	17	17	35 - 17 = 18

Match column I with column II and select the correct option from the codes given below:

A. Electron are negatively charged particles and balances the positive charge discovered by Thomson
B. Protons are positive charge particles discovered by Goldstein
C. Nucleus is the center of an atom discovered by Rutherford
D. Neutrons are the subatomic particle with no net charge discovered by Chadwick

Which of the following is (are) matter?
Chair, air, love, smell, hate, almonds, thought, cold, cold-drink, the smell of perfume.

The matter is something that has weight and occupies space. Matter can be solid, liquid, or gases. So according to the definition,

matter: Chair, air, almonds, cold-drink.

Compare the properties of protons, electrons and neutrons.

Protons	Electrons	Neutrons
They are positively charged particles.	They are negatively charged particles.	They are neutral particles.
Charge on protons is +1. Mass of protons is $$1.6727\times10^{-27}kg$$.	Charge on electrons is -1. Mass of electrons is $$9.1\times 10^{-31}\ kg$$.	They have no charge. Mass of neutrons is $$1.675\times 10^{-27}\ kg$$.
Protons are present inside the nucleus.	Electrons are present outside the nucleus. They revolve around the nucleus.	Neutrons are present inside the nucleus.

What are the characteristics of the particles of matter?

Hint: Matter exists in three forms mostly solid, liquid, and gas.

Explanation of answer:

All matter has mass and occupies space. All physical objects are made of matter. Matter itself is composed of tiny building blocks known as particles or atom.

The characteristics of the particles of matter are:

They have spaces between them.
The particles of matter are continuously moving.
The particles of matter attract each other.
Particles of matter are very tiny in size which can exist independently.

What are the limitations of J. J. Thomson's model of the atom?

According to this model, the atom consists of positively charged sphere and the electrons are embedded in it. The charges are equal in magnitude but opposite in sign, so the atom is neutral.

The limitations of J. J. Thomson's model of the atom are:

It could not explain the alpha scattering experiment done by Rutherford.
There was no experimental evidence of the model proposed by J. J. Thomson.

Describe Bohr's model of the atom.

According to Bohr Atomic model, a small positively charged nucleus is surrounded by revolving negatively charged electrons in fixed orbits. He concluded that electron will have more energy if it is located away from the nucleus whereas the electrons will have less energy if it located near the nucleus.

The postulates given by Neils Bohr are:

Electrons revolve around the nucleus in a fixed circular path termed “orbits” or “shells” or “energy level.”
The orbits are termed as “stationary orbit.”
Every circular orbit will have a certain amount of fixed energy and these circular orbits were termed orbital shells. The electrons will not radiate energy as long as they continue to revolve around the nucleus in the fixed orbital shells.
The different energy levels are denoted by integers such as n=1 or n=2 or n=3 and so on. These are called quantum numbers. The range of quantum number may vary and begin from the lowest energy level (nucleus side n=1) to the highest energy level. Learn the concept of an Atomic number here.
The different energy levels or orbits are represented in two ways such as 1, 2, 3, 4… or K, L, M, N….. shells. The lowest energy level of the electron is called the ground state. Learn the concept of Valency here in detail

State Bohr's postulate of hydrogen atom which successfully explains the emission lines in the spectrum of hydrogen atom.
Use Rydberg formula to determine the wavelength of $$H_{\alpha}$$ line.
[Given: Rydberg constant $$R = 1.03 10^7 m^{-1}$$]

Bohr's third postulate successfully explains emission lines. It states that "Whenever ever an electron jumps from one of its specified non-radiating orbit to another such orbit, it emits or absorbs a photon whose energy is equal to energy difference between the initial and final states".

Thus,

$$E_i-E_f=hv=\frac{hc}{\lambda}$$

The Rydberg formula for the Balmer series is given as,

$$\frac{1}{\lambda}=R(\frac{1}{n_f^2}- \frac{1}{n_i^2})$$

$$'R'$$ is a constant called the Rydberg constant and its value is $$1.03$$ X

$$10^7 m^{-1}$$.

The $$H_\alpha$$ line of the Balmer series is obtained when an electron jumps to the second orbit ($$n_f=2$$) from the third orbit ($$n_i=3$$).

$$\frac{1}{\lambda}=1.03$$ X $$10^7 (\frac{1}{2^2}-\frac{1}{3^2})$$

$$\frac{1}{\lambda}=1.03$$ X $$10^7 (\frac14- \frac 19)$$

$$\frac{1}{\lambda}=1.03$$ X $$10^7(\frac{9-4}{9*4})$$

$$\frac{1}{\lambda}=1.03$$ X $$10^7(\frac{5}{36})$$

$$\lambda=6.99$$ X $$10^-7$$

$$\lambda=699$$ X $$10^{-2}$$ X $$10^{-7}$$

$$\lambda=699nm$$

The value of $$\lambda$$ lies in the visible region.

Column-I Column-II

Thomson's atomic model is also called the plum pudding model.
Rutherford's atomic model resembles the planetary model.
Bohr's atomic theory proposed definite circular orbits of electrons.
According to Dalton's atomic theory, an atom is indivisible.

Hence, correct matches are A-3, B-4, C-1, D-2.

According to Bohr's atomic model, electrons revolve in _______ orbits.

According to Bohr's atomic model, electrons revolve in fixed circular paths called orbits or shells or energy levels which are indicated by $$K, L, M, N…$$ or $$1,2,3,4…$$

Three elements 'X', 'Y' and 'Z' have atomic numbers $$7, 8,$$ and $$9$$ respectively. Write the formula of the compound formed when 'X' combines with 'Z'.

The elements $$X,\ Y$$ and $$Z$$ are nitrogen, oxygen and fluorine respectively. The valency of nitrogen is $$3$$ and that of fluorine is $$1$$.

$$N$$ $$F$$

$$3$$ $$1$$ ( by Criss cross method )

$$XZ_3$$ or $$NF_3$$ is the formula of the compound formed when $$X$$ combines with $$Z$$.

On what basis did Bohr assume the concept of stationary orbits for an electron?

Bohr postulated that as long as an electron revolves in a particular orbit energy neither lost nor gains it remains constant (stationary). So the orbit is considered as stationary orbit.

ACROSS
1 Maximum number of electrons in $$L$$ shell
5 $${H}^{+}$$ ion
8 Negatively charged fundamental particles
9 Atoms of different elements with different mass numbers, but same number of neutrons
10 Atoms of different elements having same atomic numbers

DOWN
2 Atoms of same element having different mass number
3 Number of protons in an atoms
4 Proposed planetary model
6 Fundamental particle with no charge
7 Number of protons and neutrons

An atom of an element has one electron in the valence shell and the two inner shells have $$8$$ electrons each. Find the atomic number of that element.

Electronic configuration of an element is $$2^n$$ where n is the number of orbit hence

1st orbit can not have more than 2 electrons $$2^1=2$$

2nd orbit can not have more than 8 electrons $$2^2 = 8$$

Electronic configuration of an element can be $$2,8,8,1 = 19$$

True or False
The radius of energy of Bohr's orbit is equal to integral multiples of 0.529.

According to bohr model, the attraction force between electron and nucleus is balanced by centrifugal force of electron which is due to motion of electron and tend to take electron away from nucleus. He proposed the formula that:

$$r_n= \dfrac{n^2}{Z}*0.529 A^{\circ} $$

___________ elements have same number of protons.

The atoms of a chemical element can exist in different types. These are called isotopes. They have the same number of protons and electrons, but different numbers of neutrons. Different isotopes of the same element have different masses.

Filling the blanks.
................ can be classified chemically into pure substances and mixtures.

Matter can be classified into two basic categories. Matter is either a mixture or it is a pure substance. We can classify mixtures into two categories - Homogeneous mixtures and heterogeneous mixtures. We can also classify pure substances into two categories - Elements and compounds

Fill in the blanks
According to Bohr's atomic model , electrons revolve around the nucleus in _________ orbits.

According to Neils Bohr, the electrons could revolve around the nucleus in only certain orbits at various energy levels, each orbit having a different radius.

Electrons revolve round the nucleus with definite velocities in concentric circular orbits situated at definite distances from the nucleus. The energy of an electron in a certain orbit remains constant. As long as it remains in that orbit, it neither emits nor absorbs energy. These are termed stationary states or main energy states.

Shadow is not a matter because it has no mass and does not occupy _______.

Shadow is not a matter because it has no mass and does not occupy space.

Fill in the blanks with suitable words:
The particle of an atom that has no charge is ________.

The proton is positively charged, electron is negatively charged and neutron has no charge.

James Chadwick in 1932 bombarded a thin foil of beryllium with fast-moving alpha particles and observed that highly penetrating rays consisting of neutral particles were formed. These neutral particles were found to have a mass which is equal to that of a hydrogen atom. Neutrons are present in the nucleus.

Correct the following statements.
a) Water boils at $$100^0\ C$$ under atmospheric pressure.
b) The liquid evaporates above its boiling point.
c) Solids have the largest interparticle space.
d) Gases have the strongest interparticle forces.

a) Water boils at $$100^0 C$$ at 1 atmospheric pressure.

b) a liquid evaporates at its boiling point and evaporation also occurs at below boiling point.

c) solids have the lowest inter-particle space.

d) gases have the weakest inter-particle forces.

Which rule is violated in the electronic configuration $$1s^0 2s^2 2p^4$$?

Aufbau Principle is violated as the orbital having lower energy must be filled first. So $$1s$$ could not be vacant in $$1s^{ 0 }2s^{ 2 }2p^{ 4 }$$.

An electron having the lowest value of $$(n+l)$$ will be filled first.

State Aufbau principle.

"In the ground state of the atoms, the orbitals are filled with electrons in order of increasing energies."

Electrons enters the orbitals according to following $$(n+l)$$ rules.

a) Orbitals are filled in order of increasing value of $$(n+l)$$.

Thus, 4s orbital is filled before 3d orbital. For 4s orbital, $$(n+l)=4+0=4$$. For 3d orbital, $$(n+l)=3+2=5$$.

b) If two orbitals have same value of $$(n+l)$$ then the orbital with lower value of n will be filled first.

Thus, 3d orbital is filled before 4p orbital. For 3d orbital, $$(n+l)=3+2=5$$. For 4p orbital, $$(n+l)=4+1=5$$. 3d orbital has lower value of n than 4p orbital.

Fill in the blanks with suitable words:
The fundamental particle not present in a normal hydrogen atom is ________.

The atomic mass as well as the atomic number of hydrogen is 1 u. The atomic mass is the sum of the number of protons and neutrons present in the nucleus. The atomic number is the number of protons. Therefore the normal hydrogen doesn't consist of neutron.

The isotopes of hydrogen that deuterium and tritium consist of 1 and 2 neutrons respectively.

Give the main postulates of Bohr's model of an atom.

Main postulates of Bohr's model of an atom are:

1. In an atom, the electrons revolve around the nucleus in certain definite circular paths called orbits, or shells.

2. Each shell or orbit corresponds to a definite energy. Therefore, these circular orbits are also known as energy levels or energy shells.

3. The orbits or energy levels are characterized by an integer not, where, n can have values 1, 2, 3, 4……. The integer not (= 1, 2, 3…) is called the quantum number of respective orbit. The orbits are numbered as 1, 2, 3, 4………… etc., starting from the nucleus side. Thus, the orbit for which n=1 is the lowest energy level.

The orbits corresponding to n = 1,2,3,4…..etc., are also designated as K,L,M,N……….etc., shells. When the electron is in the lowest energy level, it is said to be in the ground state.

Since, electronics can be present only in these orbits, hence, these electrons can only have energies corresponding to these energy levels, i.e., electrons in an atom can have only certain permissible energies .

4. The electrons present in an atom can move from a lower energy level (Elower) to a level of higher energy (Ehigher) by absorbing the appropriate energy. Similarly, an electron can jump from a higher energy level (Ehigher) to a lower energy level (Elower) by losing the appropriate energy.

The energy absorbed or lost is equal to the difference between the energies of the two energy levels, i.e.,

ΔE= E (higher) - E (lower)

State the postulate of Bohr's theory regarding angular momentum of an electron.

Electrons can revolve only in those orbits in which their angular momentum is an integral multiple of $$\dfrac {h}{2\pi}$$, where $$h$$ is Planck's constant. According to this postulate
$$mvr = \dfrac {nh}{2\pi}$$

State the postulate of Bohr's theory regarding emission off a photon.

When the atom receives energy from outside, then one of its outer electron leaves its orbit and goes to some higher orbit. This state of atom is called excited state. The electron in the higher orbit stays for $$10^{-8} sec$$ and then returns back to the lower orbit, while returning back it radiates out energy. The energy of emitted photon is $$hv$$.
$$hv = E_{2} - E_{1}$$

Write Bohr's any two postulates for hydrogen atom.

1. The electrons revolve round the nucleus only in certain selected circular paths called orbits. These orbits are associated with definite energies and are called energy shells or energy levels or quantum levels. These are numbered as 1, 2, 3, 4 ….. etc. (starting from the nucleus) are designated as K, L, M, N ….etc.

2. As long as an electron remains in a particular orbit, it does not lose or gain energy. This means that energy of an electron in a particular path remains constant. Therefore, these orbits are also called stationary states.

The energy levels of an atom of a certain element are shown in the given figureWhich one of the transitions A, B, C, D or E will result in the emission of photons of electromagnetic radiation of wavelength 618.75 nm?
Support your answer with mathematical calculations.

$$\Delta E = \dfrac{hc}{\lambda}$$
$$= \dfrac{6.6 \times 10^{-34} \times 3 \times 10^8}{618.75 \times 10^{-9}} = 3.2 \times 10^{-19} J = 2eV$$
This corresponds to the transition D for which
$$\Delta E = (-1) - (-3 eV) = 2eV$$

Write the statement of Bohr's Second postulate of quantisation. Determine the wavelength of first spectral line in the Lyman series of the hydrogen spectrum.[Rydberg constant R$$=1.097\times 10^7m^{-1}$$].

Bohr's second postulate states that allowed electric motion are only in those orbits in which the angular momentum of an electron is an integral multiple of $$\dfrac{h}{2\pi}$$.

First spectral line of Lyman series of hydrogen atom is given by transition $$(2\rightarrow 1)$$

$$\dfrac{1}{\lambda}=R(\dfrac{1}{n_1^2}-\dfrac{1}{n_2^2})$$

$$=1.097\times 10^7(\dfrac{1}{1^2}-\dfrac{1}{2^2})m^{-1}$$

$$=8227500m^{-1}$$

$$\implies \lambda=121.5nm$$

Total energy of an electron orbiting around the nucleus of an atom is always negative. What is the significance of this?

The negative sign shows that the electron is attracted towards the nucleus by electrostatic force and to remove the electron energy must be supplied. The energy needed to remove the electron in the first orbit is $$+ 13.6\ eV$$ and this is called ionising energy of hydrogen.

a. What are Isotopes?
b. Write any three applications of Avogadros law?

a) Isotopes are the atoms of the same element having same atomic number but different atomic masses. For example: $$_{17} Cl^{35} $$ and $$_{17} Cl^{37} $$ is a pair of isotopes.

b) Applications are:

It determines the atomicity of the gas.
It determines the molecular formula of a gas.
Explains Gay Lussac's Law.
It determines the relation between molecular weight and vapour density.

What is meant by 'Quantization of charge'?

Quantization of charge implies that charge can assume only certain discrete values. That is to say the observed value of electric charge (q) of a particle will be integral multiples of (e) $$1.6\times10^{-19}$$ coulombs.
i.e.
$$q=ne$$ where $$n=0,1,2,....$$ (both positive and negative integers)
The charge cannot assume any value between the integers.

Write three postulates of Bohr. Mention two limitations of Bohr model.

Three postulates of Bohr are

1. An atom has a number of stable orbits in which an electron can reside without the emission of radiant energy. Each orbit corresponds, to a certain energy level.

2. An electron may jump spontaneously from one orbit (energy level $$E_1$$) to the other orbit (energy level $$E_2$$) ($$E_2 > E_1$$); then the energy change $$A_E$$ in the electron jump is given by Planck’s equation.

3.The motion of an electron in a circular orbit is restricted in such a manner that its angular momentum is an integral multiple of $$h/2 \pi$$.

Limitations of Bohr model :

1. It is in violation of the Heisenberg Uncertainty Principle. The Bohr Model considers electrons to have both a known radius and orbit, which is impossible according to Heisenberg.

2. The Bohr Model is very limited in terms of size. Poor spectral predictions are obtained when larger atoms are in question.

Derive an expression for potential and kinetic energy of an electron in any orbit of a hydrogen atom according to Bohr's atomic model.

Let an electron revolves with a constant speed $$v$$ around the nucleus in a stationary orbit of radius $$r$$. The electrostatic force acting on the electron is balanced by the centrifugal force i.e. $$F_c = F_e$$

$$\therefore$$ $$\dfrac{mv^2}{r} = \dfrac{ke^2}{r^2}$$ where $$k = \dfrac{1}{4\pi\epsilon_o}$$

OR $$mv^2 = \dfrac{ke^2}{r}$$ ......(1)

Thus kinetic energy of electron $$K = \dfrac{1}{2}mv^2 = \dfrac{ke^2}{2r}$$ ......(2)

Potential energy of electron $$U = \dfrac{-ke^2}{r}$$

$$\implies$$ $$U = -2K$$ (using (2))

State the basic postulates of Bohr's theory of atomic spectra.

Determine the number of revolutions made by an electron in one second in the $$2$$nd Bohr orbit of $$H$$-atom.

$$n$$=number of revolution per second=$$\dfrac { velocity\quad of\quad { e }^{ - } }{ circumference\quad of\quad orbit } $$

$${ V }_{ n }=2.188\times { 10 }^{ 6 }\times \frac { z }{ n } \quad { \mu }_{ n }=0.529{ A }^{ \bullet }\times \frac { { n }^{ 2 } }{ z } $$

Putting $$z=1$$ and $$n=2$$

$${ V }_{ 2 }=2.188\times { 10 }^{ 6 }\times \dfrac { 1 }{ 2 } \quad { \mu }_{ 2 }=0.529\times 4\times { 10 }^{ -10 }=2.116\times { 10 }^{ -10 }m\\ n=\dfrac { 1.094\times { 10 }^{ 6 } }{ 2\times 3.14{ \times 2.116\times 10 }^{ -10 } } \\ =0.082\times { 10 }^{ 16 }=8.2\times { 10 }^{ 14 }revolution/sec$$

According to Bohr, 'Angular momentum of an orbiting electron is quantised'. What is meant by this statement?

Bohr never assumed stable electronic orbits with the electronic angular momentum quantized as $$l=mvr=\dfrac { nh }{ 2\pi } $$ Quantization of angular momentum means that the radius of the orbit and the energy will be quantized as well. Bohr assumed that the discrete lines seen in the spectrum of the hydrogen atom were due to transitions of an electron from one allowed orbit/energy to another.

Match the List 1 and List 2.

1 amu (atomic mass unit ) = 931.5 MeV

Proton = Positively charged

Neutron = 1.66×10$$^{−27}$$

Alpha particle -Heaviest Particle

Thus, A $$\to$$ 3, B $$\to$$ 4, C $$\to$$ 2, D $$\to$$ 1

Write two limitations of Bohr's model.

The Limitations of Bohr's model are,

1) The Bohr atomic model theory made correct predictions for smaller sized atoms like hydrogen, but poor spectral predictions are obtained when larger atoms are considered.

2) It failed to explain the Zeeman effect when the spectral line is split into several components in the presence of a magnetic field.

The approximate radius of a $$H-atom$$ is $$0.05\ nm$$, and that of a proton is $$1.5\times 10^{-15}m$$. Assuming both the hydrogen atom and the proton to be spherical, calculate a fraction of the space in an atom of hydrogen that is occupied by the nucleus.

Radius of $$H-$$atom = 0.05nm = $$0.05\times10^{-9}$$

Radius of a proton = $$1.5\times10^{-15}m $$

The volume behave like the third power of the raddi

$$\dfrac{volume \ of \ H atom}{volume\ of\ a\ proton}$$ = $$[\dfrac{0.05\times10^-9}{1.5\times10^-15m}]^3$$

$$ = \dfrac{1}{0.000 000 000 000 027}$$

$$=\dfrac{1}{2.7\times10^{-14}} $$

(a) State Bohr's postulate to define stable orbits in hydrogen atom. How does de Broglie's hypothesis explain the stability of these orbits?
(b) A hydrogen atom initially in the ground state absorbs a photon which excites it to the $$n = 4$$ level. Estimate the frequency of the photon.

A) Bohr's Postulates

1. An atom has a number of stable orbits in which an electron can reside without the emission of radiant energy. Each orbit corresponds, to a certain energy level.

2. An electron may jump spontaneously from one orbit (energy level $$E_{1}$$) to the other orbit (energy level $$E_{2}$$)($$E_{2} > E_{1}$$); then the energy change AE in the electron jump is given by Planck's equation

$$\Delta E = E_{2} - E_{1} = hv$$

3. The motion of an electron in a circular orbit is restricted in such a manner that its angular momentum is an integral multiple of $$\dfrac{h}{2\pi}$$

4. A special surface around the nucleus which contained orbits of equal energy and radius was called the shell. These shells are numbered from inside to outwards as 1, 2, 3, 4 etc. and called K, L, M, N respectively.

B. $$\dfrac{1}{\lambda} = R_{H} [ \dfrac{1}{1^{2}} - \dfrac{1}{4^{2}}]$$

$$\lambda = \dfrac{16}{15 R_{H}}$$

$$ Frequency = \dfrac{c}{\lambda}$$

so $$f = 2.8 \times 10^{15} Hz$$

Find out the wavelength of the electron orbiting in the ground state of hydrogen atom.

Radius of ground state of hydrogen atom

$$=0.53 \dot{A} = 0.53×10 ^{-10} m $$

According to de Brogile relation

$$2\pi r = n\lambda $$

For ground state $$n = 1$$

$$2×3.14×0.53×10^{-10}=1×\lambda $$

$$\therefore \lambda =3.32×10 ^{-10}m$$

$$ =3.32\dot{A} $$

Write the postulates of Bohr's atomic model. What is the relationship between the radii of the $$n$$th and first bohr orbit of hydrogen atom?

1) An electron can revolve around the nucleus in certain fixed orbits of definite energy without emission of any radiant energy. Such orbits are called stationary orbits.

2) An electron can make a transition from a stationary state of higher energy $$E_2$$ to a state of lower energy $$E_1$$ and in doing so, it emits a single photon of frequency,

$$v=\dfrac{E_2-E_1}{h}$$ where $$h$$ is the plank constant.

Conversely, on absorbing an energy, $$E_2-E_1$$ when the electron is at energy $$E_1$$, the electron can take transition from $$E_1$$ to $$E_2$$.

3) Only those orbits are allowed for which the angular momentum of the electron is an integral multiple of $$\dfrac{h}{2\pi }$$.

thus $$L=\dfrac{nh}{2\pi}$$ where $$n=1,2,3...$$

If radius of first bohr orbit is $$r_1$$ and radius of $$n^{th}$$ bohr orbit is $$r_n$$ then relation between them is given by,

$$r_n=n^2 r_1$$

State whether True or False.
(a) J.J. Thomson proposed that the nucleus of an atom contains only nucleons.
(b) A neutron is formed by an electron and a proton combining. Therefore, it is neutral.
(c) The mass of an electron is about $$\displaystyle \frac{1}{2000}$$ times that of a proton.

(a) False. It was not proposed by J. J. Thompson. Thompson discovered the electron but not the nucleus.

(b) False. Because neutron is an independent sub-atomic particle.

Calculate the shortest and longest wavelength of Balmer series of $$H_2$$ spectrum. Given $$R=1.097\times 10^7$$ $$m^{-1}$$.

$$For\quad shortest\quad wavelength,\\ { n }_{ 1 }=1\quad \& \quad { n }_{ 2 }=\infty \\ Now,\quad \dfrac { 1 }{ \lambda } \quad =\quad R[\dfrac { 1 }{ { ({ n }_{ 1 }) }^{ 2 } } -\frac { 1 }{ { { (n }_{ 2 }) }^{ 2 } } ]\\ \dfrac { 1 }{ \lambda } \quad =\quad 1.097\times { 10 }^{ 7 }[\dfrac { 1 }{ { 1 }^{ 2 } } -\dfrac { 1 }{ { \infty }^{ 2 } } ]\\ \dfrac { 1 }{ \lambda } \quad =\quad 1.097\times { 10 }^{ 7 }\\ \lambda \quad =\quad 911.6\quad \mathring { A } \\ For\quad longest\quad wavelength,\\ { n }_{ 1 }=1\quad \& \quad { n }_{ 2 }=2\\ So,\quad \dfrac { 1 }{ \lambda } \quad =\quad 1.097\times { 10 }^{ 7 }[\dfrac { 1 }{ { 1 }^{ 2 } } -\dfrac { 1 }{ { 2 }^{ 2 } } ]\\ \dfrac { 1 }{ \lambda } \quad =\quad 1.097\times { 10 }^{ 7 }\times \dfrac { 3 }{ 4 } \\ d\frac { 1 }{ \lambda } \quad =\quad 0.823\times { 10 }^{ 7 }\\ \lambda \quad =\quad 1215.06\quad \mathring { A }$$

Give any two postulates of Bohr's theory of atomic model.

Postulates of Bohr's theory of atomic model:

1) Only certain special orbits known as discrete orbits of electrons, are allowed inside the atom.

2) While revolving in discrete orbits the electrons do not radiate energy.

A hydrogen like atom (described by the Bohrs model) is observed to emit six wavelengths originating from all possible transitions between a graph of levels having energies between $$0.85\ eV$$ and $$-0.544\ eV$$ (including both these values).
(i) Find the atomic number of the atom.
(ii) Calculate the smallest and longest wavelength emitted in these transitions.
(Take $$hc=1240\ eV-nm$$ and ground state energy of $$H-atom=-13.6\ eV$$)

1416486_1013957_ans_10515b6f6419488ea9a54e82f59ddae6.jpg

Write Bohr's postulates for the hydrogen atom model.

First Postulate: Electron revolves round the nucleus in discrete circular orbits called stationary orbits without emission of radiant energy. These orbits are called stable orbits or non-radiating orbits.

Second Postulate: Electrons revolve around the nucleus only in orbits in which their angular momentum is an integral multiple of $$h/2\pi$$.

Third Postulate: When an electron makes a transition from one of its non-radiating orbits to another of lower energy, a photon is emitted having energy equal to the energy difference between the two states. The frequency of the emitted photon is then given by, $$v=\dfrac{{E}_{i}-{E}_{f}}{h}$$

Calculate no. of ions, atoms, protons, electrons in $$3g$$ $$CO^{2-}_3$$.

$$3$$g of $${ CO }_{ 3 }^{ 2- }\equiv \frac { 3g }{ 60g{ mol }^{ -1 } } =0.05$$ mole

$$\therefore$$ no. of ions $$=0.05\times 6.023\times { 10 }^{ 23 }=0.3\times { 10 }^{ 23 }$$

no. of atoms $$=0.3\times { 10 }^{ 23 }\times 4=1.2\times { 10 }^{ 23 }$$

no. of protons $$=0.3\times { 10 }^{ 23 }\times \left( 12+3\times 16 \right) $$

$$=18\times { 10 }^{ 23 }$$

no. of electrons $$=0.3\times { 10 }^{ 23 }\times \left( 12+3\times 16+2 \right) $$

$$=18.6\times { 10 }^{ 23 }$$

Define matter.

The matter is anything that occupies some space and possesses some mass.

It is made up of tiny particles. Matter is of $$3$$ types $$ \to $$ gas, liquid and solid.

One mole of an element contains $$4.2\times 10^{24}$$ electrons. What is the atomic number of the element?

According to the problem

Atomic Number =$$x$$

Electron is one mole=$$a \times 6.023 \times {10^{23}}$$

$$x = \frac{{4.2 \times 1024}}{{6.023 \times {{10}^{23}}}}$$

$$x = 7$$

Hence the atomic number is $$7$$.

Calculate the radius of Bohr's 3rd orbit in $$Li^{2+}$$ ion

Radius of the Bohr's orbit is given by,

$$r=\dfrac{n^2h^2}{4\pi^2 mZ e^2}$$

Substituting values of $$h, m,$$ $$Z=4$$ and $$n=3$$ for lithium and $$e$$ the electronic charge $$r$$ may be calculated as,

$$r=1.07A^0$$

A binary compound between an unknown element $$E$$ and hydrogen contains $$91.27$$% $$E$$ and $$8.73$$%$$H$$ by mass. If the formula of the compound is $${E}_{3}{H}_{8}$$. Calculate the atomic mass of $$E$$.

Given formula of the compound $${ E }_{ 3 }H_{ 8 }$$

Moles of E present in the compound is 3

$$No.\quad of\quad moles=\dfrac { Given\ mass }{ Molar\ mass\ of\ the\quad compound } $$

$$3=\dfrac { 91.27 }{ Molar\ mass\ of\ the\ compound } $$

Molar mass of the compound=30

$$3\times E+8\times 1=30\\ E=7.3$$

Atomic mass of E is 7.3

Write electronic configurations of the elements (number in the brackets indicate atomic numbers)
oxygen $$(8)$$

Oxygen is the eighth element with a total of 8 electrons. In writing the electron configuration for oxygen the first two electrons will go in the 1s orbital. Since $$1s$$ can only hold two electrons the next 2 electrons for $$O$$ go in the $$2s$$ orbital. The remaining four electrons will go in the $$2p$$ orbital. Therefore the O electron configuration will be $$1s^{ 2 }\quad 2s^{ 2 }\quad 2p^{ 4 }$$.

What are the draw backs of Bohrs atomic model? Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit.

1. Bohr treated electrons as particles where according to de Broglie's hypothesis, having a very low mass, electron also exhibits wave nature.

2. Bohr's model was acceptable only for nucleus having only one electron e.g. Hydrogen, $$He^{+1}$$, $$Li^{+2}$$ etc. Bohr's model could not explain the spectra of multi-electronic atoms.

3. Bohr's model was two-dimensional where an atom is three-dimensional.

4. Bohr's model could not explain the effect electric field and magnetic field on spectra. (Stark effect and Zeeman effect)

5. Using a better spectrometer, the spectra showed very fine lines. Bohr's model could not explain the origin of those fine lines.

For angular momentum of an electron

$$mvr=\cfrac { nh }{ 2\Pi } \rightarrow (1)\\$$

then debroglie equation,

$$ \lambda =\cfrac { h }{ mv }$$

$$ \\ mv=\frac { h }{ v } \rightarrow (2)\\$$

Putting the value of 1 and 2

$$2\Pi r\quad =n\left( \frac { h }{ mv } \right) \\ 2\Pi r\quad =\quad n\lambda \\ hence,\ 2\Pi r\ represents\ here,\ circumference\ of\ the\ Bohr\ orbit\ (r)$$\\

What is the energy of electron in an orbit which $$n=\infty$$

It is the amount of energy that an electron gains when subjected to a potential of 1 volt; 1 eV = 1.602 × 10^–19 J. Using the Bohr model, determine the energy, in electron volts, of the photon produced when an electron in a hydrogen atom moves from the orbit with n = 5 to the orbit with n = 2.

In the Bohr's model, for unielectronic species following symbols are used.
$$K_{n, z} \rightarrow $$ Kinetic energy electron in $$n^{th}$$ orbit with atomic number "z".
Calculate z in all cases.

Kinetic energy of $$n^{th}$$ orbit

$$K.E=\cfrac {mv^2}{2}=\cfrac {mz^2e^4}{8 E_o^2h^2n^2}$$

Identify the following elements.
a) $$_{25}X^{55}$$
b) $$_{17}X^{35}$$
c) $$_{20}X^{40}$$

$$a) _{25}X^{65}$$ Atomic number $$=25,$$ Element $$=$$Manganese.

$$b) _{17}X^{35}$$ Atomic number $$=17,$$ Element $$=$$Chlorine.

$$c) _{20}X^{40}$$ Atomic number $$=20,$$ Element $$=$$Calcium.

In the Bohr's model, for unielectronic species following symbols are used.
$$r_{n, z} \rightarrow $$ Radius of $$n^{th}$$ orbit with atomic number "z".
Calculate z in all cases.

Radius of $$n^{th}$$ orbit in Bohr's model

$$r= \cfrac {n^2h^2}{4 \pi^2mc^2}\times \cfrac {1}{z}$$ $$n$$= principal quantum number ; $$z$$= atomic number

$$=\cfrac {n^2}{z^2}\times 52.49 m$$

How does the ionization energy of an atom vary along a period and a group of the periodic table?

It is considered a measure of the tendency of an atom or ion to surrender an electron or the strength of the electron binding. The greater the ionization energy, the more difficult it is to remove an electron.

Ionization energy increases from left to right in a period and decreases from top to bottom in a group.

Isotopes are the atoms of element having the atomic number but mass number.

Isotopes are the atoms of same element having the same atomic number but different mass number

Suppose the elements $$X$$ and $$Y$$ combine to form two compounds $$XY_2$$ and $$X_3Y_2$$. When $$0.1$$ mole of $$XY_2$$ weighs $$10$$g and $$0.05$$ mole of $$X_3Y_2$$ weighs $$9$$g, the atomic weights of $$X$$ and $$Y$$ are:

Let $$x$$ and $$y$$ be the atomic weights of $$X$$ and $$Y$$

Given $$0.1$$ mole of $$XY_2$$ weighs $$10g$$

$$\Rightarrow x+2y=\cfrac {10}{0.1}=100 \longrightarrow (1)$$

$$0.05$$ mole of $$X_3Y_2$$ weighs $$9g$$

$$\Rightarrow 3x+2y=\cfrac {9}{0.05}=180 \longrightarrow (2)$$

$$(1) \Rightarrow x= 100-2y$$

Substituting for $$x$$ in Equation (2)

$$\Rightarrow 3(100-2y)+2y=180$$

$$\Rightarrow 300-6y+2y=180$$

$$\Rightarrow y=30$$

Hence $$x=100-2(30)=40$$

If radius of the nucleus is $$3.5\times^{-15}\ m$$ then find the space or volume occupied by the nucleus.

Nucleus of atom is spherical in shape

So volume occupied by nucleus $$ = 4/3$$ $$\pi r^3$$

$$ = 4/3 \times 3.5\times10^{-15}m$$

$$ = 4.67\times 10^{-15}m$$

Write the symbols of the first ten elements in the periodic table with the atomic numbers.

$$Hydrogen\longrightarrow _1H\quad\quad Carbon\longrightarrow _6C\\ Helium\longrightarrow _2He\quad\quad Nitrogen\longrightarrow _7N\\Lithium\longrightarrow _3Li\quad\quad Oxygen\longrightarrow _8O\\Beryllium\longrightarrow _4Be\quad\quad Fluorine\longrightarrow _9F\\Boron\longrightarrow _5B\quad\quad Neon\longrightarrow _{10}N$$

Consider Bohr theory for hydrogen atom. The magnitude of angular momentum, orbit radius and velocity of the electron in $${ n }^{ th }$$ energy state in a hydrogen atom are $$l , \ r$$ and $$v$$ respectively. Find out the value of $$x$$ if product of $$v,\ r$$ and $$l$$ is directly proportional to $${ n }^{ x }$$.

Angular momentum, radius and velocity of $$H$$ atom is given by ,

$$l$$ $$\alpha$$ $$n$$,

$$r$$ $$\alpha$$ $$n^2$$,

$$v$$ $$\alpha$$ $$\dfrac{1}{n}$$

$$vrl$$ $$\alpha$$ $$n^x$$ (given)

Substituting values of $$v$$, $$r$$ and $$l$$

$$vrl$$ $$\alpha$$ $$n^2$$

Therefore comparing with the given equation $$x=2$$

Difference between atomic number and mass number.

The atomic number is the number of electrons present in an atom. It is equal to the number of protons in a neutral atom. It is denoted by symbol $$z$$.

The mass number, also called atomic mass number or nucleon number, is the total number of protons and neutrons in an atomic nucleus.

It is represented by A.

$$\therefore A-Z$$ represents the number of neutrons.

The kinetic energy of the $$e^{-}$$ in the $$2^{nd}$$ Bohr orbit of a hydrogen atom is:
(as in Bohr's radius)

Kinetic energy in $$n^{th}$$ orbit is,

$$K_n=\dfrac{me^4}{8\epsilon_0^2 n^2 h^2}$$

Now substituting values of $$e,h,m,\epsilon_0$$ and $$n=2$$

$${K.E}_2=3.40eV$$

The mass number of an atom is slightly less than the actual atomic mass. Give reasons.

The mass number is not equal to the atomic mass because of isotopes.

Mass number is simply the number of protons and neutrons.

The actual atomic mass of an atom is the weighted average of all existing atoms & isotopes per element. The isotopes have a different number of neutrons than protons.

Drawbacks of Bohr's atomic model :

i) It is valid only for one electron atoms, eg: H, $$He^{+},Li^{+2},Na^{+1}$$ etc.

ii) Orbits were taken as circular but according to Sommerfiled these are elliptical.

iii) Intensity of spectral lies could not be explained.

iv) Nucleus was taken as stationary but it also rotates on its own axis.

v) It could not be explained the minute structure in spectrum line.

vi) This does not explain the Zeeman effect (splitting up of spectral lines in magnetic filed) and Stark effect (splitting up in electric filed)

vii) This does not explain the doublets in the spectrum of some of the atoms.

Find the mass of $$1.5055\times10^{25}$$ number of molecule of aluminium oxide.

Molucullar weight of $$Al_2O_3= 102\,g$$

$$6.022\times 10^{23}$$ molecules are present in 102 g $$Al_2O_3$$

So $$1.5055\times 10^{25}$$ molecules will present in $$\dfrac{102}{6.022\times 10^{23}}\times 1.5055\times 10^{25}$$ g $$Al_2O_3$$

$$=2.55\times 10^{3}$$ g

The wavelength of $$\beta$$-line of the Balmer series is $$4815 \overset{o}A$$ . What is the wavelength of $$\alpha$$-line of the Balmer series of the same atom?

The wavelength of the visible line in blue- green region corresponds to $$H_{\beta}$$, the balmer's formula is,

$$\dfrac{1}{\lambda}=R(\dfrac{1}{2^2} -\dfrac{1}{n^2})$$

$$R$$=Rydberg's constant=$$1.097\times 10^7m^{-1}$$

For $$H_{\beta}$$ $$ n=3$$

$$\dfrac{1}{\lambda}=1.097\times 10^7m^{-1}(\dfrac{1}{4}-\dfrac{1}{9})$$

$$\lambda=4.9\times 10^{-7}m$$

$$\lambda=4900 \overset{o}A$$

Calculate the frequency of the electron in the 1st Bohr orbit in a H-atom.

Velocity in Bohr's first orbit is given by $$mvr= \dfrac {nh} {2 \pi}$$

For Bohr's first orbit $$n=1$$

$$v = \dfrac{h}{2 \pi mr}$$

Radius $$r$$ is given by, $$r_n = 0.53\times10^{-10} \times n^2 \ meter$$

For Bohr's first orbit $$n=1$$

$$r = 0.53\times10^{-10}\ meter$$

Frequency $$\nu$$ is given by $$\nu = \dfrac{v}{2 \pi r} = \dfrac{h}{4 \pi^2 m r^2}$$

Mass of electron $$m = 9.1096 \times 10^{-31}kg$$

$$ \nu = \dfrac{6.62\times10^{-34}}{4 \pi^2 \times 9.1096 \times 10^{-31} \times (0.53 \times 10^{-10})^2} = 6530 \times 10^{12}Hz$$

State the postulates of Bohr's theory of hydrogen atom.

Hint: There are total of three postulates of Bohr's theory.

Step 1: First postulate.

Electrons move around the nucleus in the circular orbit.

Step 2: Second postulate.

The angular momentum of the electron is quantized which can be shown as,

$$L=n\hbar$$

Here, $$n=1,2,3,4...$$

Step 3: Third postulate,

The energy of the outer orbit is greater than the inner orbit. when electron jump from an orbit to another there is energy difference which is equal to,

$$E=nh\nu $$

Here, $$n=1,2,3,4...$$

a) Calculate the energy associated with the first orbit of $${ He }^{ + }$$. What is the radius of this orbit?
b) What is the lowest value of n that allows $$'g'$$ orbitals to exist?

(a) calculate the energy associated with the first orbit of $$He^{+}$$

$$E=-13.6 \dfrac{z^{2}}{n^{2}}$$

$$=-13.6\times \dfrac{2^{2}}{1^{2}}= 54.4\ ev$$

Radius of orbit $$r=529\times \dfrac{n^{2}}{z}\ nm$$

$$=529\times \dfrac{12}{2}$$

$$=264.5\ nm$$

(b) lower value of $$n=5$$

$$s\ p\ d\ f\ g$$

What is meant by imperfect sheilding of $$e^-$$ by the nucleus?

The shielding effect sometimes referred to as atomic shielding or electron shielding describes the attraction between an electron and the nucleus in any atom with more than are electron.

Order of shielding effect

$$S > P > d > f$$

Imperfect shielding is shielding by $$d$$ and $$f$$ orbital $$d$$ and $$f$$ orbital do not completely shield outermost electron

Write the electron configuration of third element of group $$15-(Z=33)$$

Third element of group 15 is $$As$$

$$As$$ configuration is $$1s^22s^22p^63s^23p^64s^23d^{10}4p^3$$

Name the Indian philosopher who proposed the theory matter.

This Indian sage and philosopher was known as Acharya Kanad, and some consider him as the “actual” father of Atomic theory.

He said the 'kana' is the smallest particle of any matter.

What will the weight of $${ C }_{ 6 }{ H }_{ 12 }{ O }_{ 6 }$$ which contain same total number of atom as present in $$176g$$ of $${ CO }_{ 2 }$$

1352081_1135328_ans_6095595e8d5b4be880ccbf78f79b4ff3.jpg

Give reason for the following:
Physical properties of isotopes of the same element are not identical.

Isotopes have similar chemical properties because isotopes of an element have same number of electrons. However, they have different number of neutrons, which affects the mass number.

Hence, they show different physical properties.

Give reason for the following:

The mass number of an atom is slightly less than the actual atomic mass.

Mass number = number of protons + number of neutrons in an atom.
Now, mass of protons and neutrons is measured in daltons or atomic mass unit,u but the mass of each neutron and proton is slightly greater than 1 dalton, so the mass number ofan atom is slightly less than the actual atomic mass.
Example: mass umber of calcium = 20 + 20 = 40 u
Actual atomic mass of calcium = 40.078 u

A $$12.5\ eV$$ electron beam is used to excite a gaseous hydrogen atom at room temperature. Determine the wavelengths and the corresponding series of the lines emitted.

The wavelength of emitted series is $$99.2 nm$$ and this belongs to he luman series of Bohr's Hydrogen spectrum$$.$$

The wavelength of series emitted during transition is given by the formula$$.$$

$$hc/E = 1$$

$$E = 12.5\,eV$$

$$hc = 1240\,eV$$

Therefore wavelength of emitted series is$$:$$

$$I=1240/12.5=99.2 nm$$

This belongs to the Lyman series of Bohr's Hydrogen spectrum$$.$$

What is the value of magnetic moment of zinc in$$+2$$ oxidation state?$$(z=30)$$

$$Zn = 3{d^{10}}{45^2}$$

$$Z{n^{2 + }} = 3{d^{10}}$$

unpaired electron $$ = 0 = n$$

magnetic moment $$ = \sqrt {n(n + 2)} $$

$$ = \sqrt {0(0 + 2)} $$

$$ = \sqrt {0 \times 2} = 0BM$$

The atomic number of an element X is 13.What will be the number of electrons in its ion $$X^{34}$$

If the atomic number of an element X is $$13$$.The number of electrons in its ion $$x^{3+}$$ will be 10. This is because $$x^{3+}$$ is a positively charged cation. An atom loses electrons from its valence shell and becomes positively charged ion called cation. Here, Atom $$X$$ loses $$3$$ electrons and acquires $$3+$$ charge. therefore the number of electrons lost will be $$3$$. and the number of electrons in its ion $$x^{3+}$$ will be $$10$$.

The potential energies of first, second and third Bohr's orbits of He $$^ + $$cation are $${E_1}$$, $${E_2}$$ and $${E_3}$$. Then What will be the correct sequence of these energies?

Potential energy $$\alpha \dfrac{1}{n^{2}}$$

so, $$E_{1} > E_{2} > E_{3}$$

State Bohr's Postulates and write its drawbacks.

Bohr proposed an atomic structure model, describing an atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the positively charged nucleus like planets around the sun in our solar system, with attraction provided by electrostatic forces, popularly known as Bohr’s atomic model.
drawback-
(1)-it does not explain the energy of an atom and it is stability
(2)-The Bohr atomic model theory made correct predictions for smaller-sized atoms like hydrogen, but poor spectral predictions are obtained when larger atoms are considered.
(3)-It failed to explain the Zeeman effect when the spectral line is split into several components in the presence of a magnetic field.
(4)-It failed to explain the Stark effect when the spectral line gets split up into fine lines in the presence of an electric field.

What point of Bohr's model of an atom can be used to arrive at this formula? Based on these points derive the above giving description of each step and each term.

1356151_1286343_ans_f9163d01dd3c4b6c8cd4c04d36a6a66e.jpg

The velocity of $$e^ {-}$$ in a certain Bohr orbit of the hydrogen atom bears the ratio $$1:275$$ to the velocity of light, What is the quantum no. $$"n"$$ of the orbit and the wave no. of the radiation emitted for the transition from the quantum $$\left(N+1\right)$$ to the ground state.

1309046_1290105_ans_fc05595423434f04a6f7b94607514678.jpg

State Bohr's Model.

Postulates of the Bohr Atomic Model$$.$$ Electrons revolve around the nucleus in a fixed circular path termed "orbits" or "shells" or "energy level'$$,$$ Every circular orbit have a certain amount of fixed energy and these circular orbits were termed orbits shells$$.$$

State bohr postulate of hydrogen atom that gives the relationship for the frequency of emitted photon in a transition.

When an electron makes a transition from one of its non-radiating orbits to another of lower energy, a photon is emitted having energy equal to the energy difference between the two states. The frequency of the emitted photon is then given by,

Calculate the total number of electrons present in $${\text{1}}{\text{.6}}\,{\text{g}}$$ of methane. Molecular wt. of methane= $${\text{16}}\,{\text{a}}{\text{.m}}{\text{.u}}$$

1306047_1380939_ans_0fa4cdf9dd554822bf19c82a222d537b.PNG

If the radius of $${{\text{3}}^{{\text{rd}}}}\;$$ Bohr;s orbit of H is x, then radius of $$\;\;\;{{\text{4}}^{{\text{th}}}}$$ orbit of $$\;{\text{L}}{{\text{i}}^{{\text{2 + }}}}$$ ion would be

1308783_1380200_ans_586fb94ce49a4f5d9b7823e99fddd5c4.PNG

If the number of electrons is an atom $$8$$ and the number of neutron is also $$8$$ then
(i) what is the atomic number of an atom?
(ii) what is the charge on the atom?

In any atom, the number of electrons is equaled to the number of protons which is an atomic number.

(i) So as the number of electrons is 8 in the atom its atomic number is $$8$$.

(ii) No chargee

What is matter?

Matter is any substance that has mass and takes up space by having volume.

For example, a car would be said to be made of matter, as it has mass and volume (occupies space).

Bohr's orbits are called stationary states. Why?

This is because the energies of the orbits in which the electrons revolve are fixed.

Radius of the first orbit of the electron in a hydrogen atom is $$0.53\mathring {A}$$. Find the centripetal acting on the electron.

1359681_1498765_ans_b2fb5e39629442258e95346574cff14c.jpeg

What are the limitations of J.J. Thomson's model of the atom?

Thomson's atomic model failed to explain how the positive charge holds on the electrons inside the atom. It also failed to explain an atom's stability. The theory did not mention anything about the nucleus of an atom.

Describe Bohrs model of the atom

Bohrs model of the atom

         (1) Atom has nucleus in the centre.

         (2) Electrons revolve around the nucleus.

         (3) Certain special orbits known as discrete orbits of electrons, are allowed inside the atom.

         (4) While revolving in discrete orbits the electrons do not radiate energy.

         (5) These orbits or shells are called energy levels.

         (6) These orbits or shells are represented by the letters K, L, M, N or the numbers n = 1, 2, 3, 4

State the postulates of Bohr atom model. Obtain the expression for the radius of the $$n^{th}$$ orbit of an electron based on Bohr's theory.

Bohr's postulates
two postulate
radius of electron in nth orbit
Explanation
Electrostatic force $$F = \dfrac{1}{4 \pi \varepsilon_0} \dfrac{ze^2}{r_n^2}$$
upto $$\omega_n^2 = \dfrac{ze^2}{4 \pi \varepsilon_0 mr_n^3}$$
$$L = mv_n r_n = mr_n \omega_n^2$$ (or) $$L = \dfrac{nh}{2 \pi}$$
upto $$\omega_n^2 = \dfrac{n^2 h^2}{4 \pi^2 m^2 r_n^4}$$
Up to $$r_n = \dfrac{n^2 h^2 \varepsilon_o}{\pi m ze^2}$$

What is meant by radioactivity?

Radioactivity is the spontaneous emission of radiation in the form of particles or high energy photons resulting from a nuclear reaction. It is also known as radioactive decay, nuclear decay, nuclear disintegration, or radioactive disintegration.

Alpha, beta, and gamma decay are three common Radioactivity processes.

Write two difference between isobars and isotops.

1691162_1572854_ans_90d828e4e6f6404a86e4dda006393db9.jpg

(a) How many atoms are there in exactly 12 g of carbon-12 element?(C=12 u).
(b) What name is given to this number?
(c) What name is given to the amount of substance containing this number of atoms?

$$\textbf{(a)}$$

$$\textbf{Given data:}$$

Given mass of carbon = 12 g

$$\textbf{Step 1: Calculate the number of moles in 12 g of carbon-12 element.}$$

$$Number\ of\ moles\ of\ carbon = \dfrac{given\ mass\ of\ carbon}{Atomic\ mass\ of\ carbon}$$

$$Number\ of\ moles\ of\ carbon = \dfrac{12}{12}$$

$$Number\ of\ moles\ of\ carbon = 1 mole$$

$$\textbf{Step 2: Calculate the number of atoms in 12 g of carbon-12 element.}$$

$$Number\ of\ moles\ of\ carbon = \dfrac{Number\ of\ atoms}{6.022 \times 10^{23}}$$

$$Number\ of\ atoms = 1 \times 6.022 \times 10^{23} = 6.022 \times 10^{23}$$

$$\textbf{Conclusion:}$$

Therefore, $$6.022 \times 10^{23}$$ atoms are there in exactly 12 g of carbon-12 element.

$$\textbf{(b)}$$

$$\bullet$$ The name given to this number is Avogadro's number.

$$\bullet$$ $$Avogadro's\ number = 6.022 \times 10^{23}$$

$$\textbf{(c)}$$

$$\bullet$$ 1 mole of substance contains this number of atoms.

$$\bullet$$ $$1\ mole = 6.022 \times 10^{23} number\ of\ atoms$$

Imagine removing one electron from $$He ^ { 4 }$$ and $$He ^ { 3 }.$$ Their energy levels, as worked out on the basis of Bohr model will be very close. Explain why.

On removing one electron from $$He^{4}$$ and $$He^{3}$$, the energy levels, as worked out on the basis of Bohr model will be very close as both the nuclei are very heavy as compared to electron mass. Also after removing one electron from $$He^{4}$$ and $$He^{3}$$ atoms contain one electron and are hydrogen like atoms.

Define the following terms .
Atomic number

Atomic number: Number of electrons present in an atom which is equal to number of protons in a neutral atom.

Using an expression for energy of electron, obtain the Bohr's formula for hydrogen spectral lines.

$$mvr=\dfrac{nh}{2\pi}$$........................... equation 1
$$\dfrac{mv^2}{r}=\dfrac{kze^2}{r^2}$$.......................equation 2

$$v=\dfrac{kze^2}{\left(\dfrac{nh}{2\pi}\right)}$$

$$r = \dfrac{nh}{2\pi m} \left(\dfrac{kze^2}{nh} \times 2\pi\right)$$

$$=\dfrac{n^2h^2}{nkze^2}$$

$$KE=\dfrac{1}{2}mv^2=\dfrac{1}{2}m\left(\dfrac{kze^2\pi}{nh}\right)^2$$

$$\dfrac{1}{2}\dfrac{mk^2e^4 4\pi^2}{n^2}\left(\dfrac{z^2}{n^2}\right)$$

$$T.E=-KE$$

$$T.E=\left(\dfrac{2\pi^2mK^2e^4}{h^2}\right)\left(\dfrac{z^2}{h^2}\right)$$

When $$e^-$$ jumps from $$n_2$$ to $$n_1$$

$$E_{n_2}=c\left(\dfrac{z^2}{h^2}\right)$$

$$E_{n_1}=c\left(\dfrac{z^2}{n_1^2}\right)$$

Change in Energy :$$c(z)^2\left(\dfrac{1}{n_2^1}-\dfrac{1}{n_2^2}\right)$$

$$E_{n_2}=C\left(\dfrac{z^2}{n_2^2}\right)$$

$$E_{n_1}=C\left(\dfrac{z^2}{n_1^2}\right)$$

Change in Energy:$$C(z^2)\left(\dfrac{1}{n_1^2}-\dfrac{1}{n_2^2}\right)$$

$$\dfrac{hc}{\lambda}=Cz^2\left(\dfrac{1}{n_1^2}-\dfrac{1}{n_2^2}\right)$$

$$\dfrac{1}{\lambda}=\left(\dfrac{2\pi mk^2e^4}{h^2 C}\right)z^2\left(\dfrac{1}{h_1^2}-\dfrac{1}{h_2^2}\right)$$ also know as R (Regdbery 's constant)
$$\dfrac{1}{\lambda}=Rz^2\left(\dfrac{1}{n_1^2}-\dfrac{1}{n_2^2}\right)$$

Summarise the rules for writing of distribution of electrons in various shells for the first eighteen elements.

the following rules are followed for writing the number of electrons in different energy levels or shells.

(i) the maximum number of electrons presents in a shell is given by the formula $$ 2n^2 $$ where $$ 'n' $$ is the orbit number of energy level index $$ 1, 2, 3 ...$$ hence the maximum number of electrons in different shells are as follows :

First orbit or K-shell will be $$ = 2 \times 1^2 \times 2 $$ Second orbit or L shell will be $$ = 2 \times 2^2 = 8 $$ third orbit or M shell will be $$ = 2 \times 3^2 = 18 $$ fourth orbits or N-Shell will be $$ = 2 \times 4^2 = 32 $$ and so on.

(ii) The maximum number of electrons that can be accommodated in the outermost orbit is $$ 8 $$

(iii) Electrons are not accommodated in a given shell unless the inner shells are filled. That is the shells are filled in a stepwise manner.

Match the following

$$(A)= $$ Let isotopel be $$x \%$$, so isotope $$2$$ will be $$(100-x)\%$$
$$\therefore \ (z-1)(x)+(z-2)(100-x)=100z$$
$$\therefore \ x\ z-x+100z+200-x\ z-2x=100\ z$$
$$\therefore \ -3x=-200$$
$$\therefore \ 3x=200$$
$$\therefore \ x=66.66\%$$
$$\therefore \ $$ Isotope $$1 :\ 66.66\%$$ Isotope $$2:\ 100-66.66$$
$$: 33.33\%$$
$$\therefore \ 33.33\%$$ by mole
$$\%$$ mass $$=\dfrac {z-1}{z}\times \dfrac {z}{100}=\dfrac {z-1}{z}\times 0.666$$
$$\therefore \ $$ depend on $$z$$
$$\therefore \ A\to P_1R$$

$$(B)\ $$ Let isotope $$1$$ be $$x\%$$, so isotope, will be $$(100-x)\%$$
$$\therefore \ (z+1)(x)+(z+3)(100-x)=100(z+12)$$
$$\therefore \ x\ z+z+100\ z+300-x\ z-3\ x=100\ z+200$$
$$\therefore \ -2\ x=-100$$
$$\therefore \ =50\%$$
$$\therefore \ $$ Isotope $$I: 50\%$$, Isotop $$II:\ 50\%$$
$$\%$$ mass: $$\dfrac {z+1}{z+2}\times \dfrac {50}{100}=\dfrac {0.5 (t+1)}{z+2}$$
$$\therefore \ $$ depends on $$t$$
$$\therefore \ B\to Q, R$$

$$(C)\ $$ Let Isotope $$I$$ be $$x\%$$, so isotope $$II$$ will be $$(100-x)\%$$
$$z{x}+3\ z(100-x)=100\times 27$$
$$x\ z+300\ z-3\ x\ z=300\ z$$
$$-2\ x \ z=-100\ z$$
$$x=50\%$$
Isotope $$I: 50\%$$, Isotope $$II: 50\%$$
$$\%$$ man $$=\dfrac {z}{27}\times \dfrac {50}{100}=(0.5)(0.5)=0.25$$
Isotope $$I-25\%$$ by mass
Isotope $$II-75\%$$ by mass
$$\therefore \ C\to Q, S$$

$$(D)\ $$ Let Isotope $$I$$ be $$x\%$$, so isotope $$II$$ will be $$(100-x)\%$$
$$(z-1)(x)+(z+1)(100-x)=100\ z$$
$$x\ z-x+100\ z+100-\ x\ z-x=100\ z$$
$$-2\ x=100$$
$$x=50\%$$
Isotope $$I:50\%$$, Isotope $$I:50\%$$
$$\%$$ mass $$=\dfrac {z-1}{z}\times \dfrac {50}{100}=\dfrac {0.5(z-1)}{z}$$
$$\therefore \ $$ depends on $$z$$
$$\therefore \ D\to Q, R$$

State any two postulates of Bohr's theory of hydrogen atom.

The two postulates of Bohr's theory is given below:-

i) Electron in an atom revolves around the nucleus in circular orbits.

ii) While revolving in discrete orbits the electrons do not radiate energy.

An element has its electronic configuration as $$2, 8, 2$$. Now answer the following question:
What is the atomic number of this element?

Electronic configuration - $$2,8,2$$

Total number of electrons = $$2+8+2=12$$

Since atom is neutral

No. of electron = no. of protons

Atomic number of an element is equal to total number of protons in it.

$$\therefore$$ Atomic number = $$12$$

A bond order of 3 is computed for the diatomic molecule. It is possible that the bond may be made up of two $$ \sigma $$ and one $$\pi-bonds $$ -Explain.

Not possible. The order of filling orbitals and the differentiation of existing among bonding, antibonding, and non-bonding electrons never permit the establish more than one sigma bond.

Calculate the effective neutron capture radius of a nucleus having a cross-section of $$1.0$$ barn.

1911987_1740260_ans_6f3b126ff8c74c06a158a1e87d5c2466.jpg

Determine the effective atomic number of the metal atom in the following:
$$[Cr(CO)_6]$$

1898051_1729644_ans_91b670b5059f4e77aba80b0be83d8c3f.jpg

Give the atomic number of the inert gas in which the total number of d electrons is equal to the difference between the total number of p and s electrons.

Hint: The elements belong to group $$18$$ of the periodic table are called inert gas elements.

Step 1: Inert Gas Elements and their atomic numbers.

General electronic configuration is $$ns^2$$ $$np^6$$

Helium ($$He$$) is 2. Electronic configuration is $$1s^2$$

Neon ($$Ne$$) is 10. Electronic configuration is $$1s^2 2s^2 2p^6 $$.

Argon ($$Ar$$) is 18. Electronic configuration is $$1s^2 2s^2 2p^6 3s^2 3p^6$$

Krypton($$Kr$$) is36. Electronic configuration is $$1s^2 2s^2 2p^6 3s^2 3p^6 $$ $$3d^{10} 4s^2 4p^6$$

Xenon ($$Xe$$) is 54. Electronic configuration is $$1s^{2} 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 5s^2 5p^6 $$

Radon ($$Rn$$) is 86. Electronic Configuration is $$ 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 4f^{14} 5s^2 5p^6 5d^10 6s^2 6p^6 $$

Step 2: Number of d electrons.

$$He$$: We see that there are no $$d$$ electrons in it.

$$Ne$$: There are no $$d$$ electrons. The number of $$s$$ electrons is 4 and the number of $$p$$ electrons is 6.

The difference is $$6 - 4 = 2$$ which is not equal to the number of $$d$$ electrons present.

$$Ar$$: There are no $$d$$ electrons. The number of $$s$$ electrons is 6 and the number of $$p$$ electron is 12.

The difference is $$12-6=6$$ which is not equal to the number of $$d$$ electrons present.

$$Kr$$: The number of $$d$$ electrons = 10

The number of $$s$$ electrons = 8

The number of $$p$$ electrons = 18

The difference between the number of $$s$$ and the number of $$p$$ electrons is $$18-8=10$$ which is equal to the number of $$d$$ electrons present.

Therefore in krypton ($$Kr$$) ( atomic number 36 ), total number of $$d$$ electrons is equal to the difference between the total number of $$p$$ and $$s$$ electrons.

Determine the effective atomic number of the metal atom in the following:
$$[Fe(CN)_6]^{3-}$$

1898625_1729647_ans_6c74c03becd64077a0f0514667882b63.jpg

The electronic configuration of an element is $$1s^2,2s^2, 2p^6, 3s^2 3p^3$$. what is the atomic number of the element in the periodic table?

1980300_1727231_ans_b2c3635a84734c1086ced9ec4be4766b.jpg

An atom has the electron structure of 2,7.
(a) What is the atomic number of this atom?
(b) To which of the following would it be chemically similar?
$$_7 N,\ _{15} P,\ _{17} Cl, \ _{18}Ar$$
(c) Why would you expect it to be similar?

(a) The atomic number of the atom is 9

(b) It is similar to $$_{17} Cl$$ since both of them belong to same group.

Which ancient Indian philosopher suggested that all matter is composed of very small particles ?
What name was given by him to these particles ?

Maharishi Kanada suggested that all matter is composed of very small particles. He was given 'parmanu' for those particles.

What is the maximum number of electrons an M shell of the atom can accommodate?

Maximum of 18 e- can be accommodated in M shell of an atom.

What is the maximum number of electrons that can go into N shell of an atom?

Maximum of number of electrons in N shell is 32.
1600043_1766874_ans_b2d9ddabc295456794f02ba1cf9d2cec.png

What is the maximum number of electrons which can be accommodated in the $$K$$-shell of an atom?

Maximum of $$2 \ e^- $$can be accommodated in $$K$$-shell of an atom.

Name the scientists who described the arrangement of electrons in an atom.

J. J. Thomson described the arrangement of electrons in an atom.

What is the maximum number of electrons which can be accommodated in the L shell of an atom?

The maximum number of electrons present in a shell is given by the formula $$2n^2$$, where ‘n’ is the orbit number or energy level index, 1,2,3,….

Value for L shell is given be $$n=2$$.

A maximum of $$2(2)^2 = 8 e^-$$ can be accommodated in the L shell of an atom.

Why is the atomic number of the elements more important to a chemist than its atomic mass?

Atomic numbers represents the number of electrons in the element and also in electronic configuration and physical and chemical properties.

What is the maximum number of electrons which can be accommodated in:
(a) the innermost shell of an atom?
(b) the outermost shell of an atom?

(a) Maximum of 2 e- can be accommodated in innermost shell of an atom.

(b) Maximum of 8 e- can be accommodated in outermost shell of an atom.

Describe Thomson's model of an atom.

Thomson's model of an atom:-

Thomson proposed the model of an atom be similar to that of a Christmas pudding.

Thomson proposed that:-

i. An atom consists of a sphere of positive charge with negatively charged electrons embedded in it.

ii. The positive and the negative charges in an atom are equal in magnitude due to which an atom as a whole is electrically neutral.

1625157_1772655_ans_e808b13a66454859aa471d641e1ce868.png

Name the particles which actually determine the mass of an atom.

Protons and neutrons actually determine the mass of atom.

(a) Describe Thomson's model of the atom. Which subatomic particle was not present in Thomson's model of the atom?
(b) The mass number of an element isIt contains 7 electrons. What is the number of protons and neutrons in it? What is the atomic number of the element?

(a) J.J Thomson proposed a model of atom that is similar to a water melon.

The electron in the sphere is considered as seeds in watermelon.

He proposed that:

1. Atom consists of a positively charged sphere and the electrons are embedded in it.

2. The negative and positive charges are equal in magnitude so atom is electrically neutral.

This model did not tell us about the presence of neutrons in the atom.

(b) When mass no. is 18 and no. of electrons is 7 then

(i) No. of protons = 7

(ii) No. of neutrons = 18 - 7 = 11

(iii) Atomic no. = 7

What are the various letters used by Bohr to represent electron shell in an atom?

K, L, M, N were the letters used by Bohr to represent electron shells in an atom.

(a) What is meant by (i) atomic number, and (ii) mass number, of an element? Explain with the help of an example.
(b) What is the relation between the atomic number and mass number of an element?
(c) If an element M has mass number 24 and atomic number 12, how many neutrons does its atom contain?

(a) Atomic number is the number of protons in one atom of an element.

Mass number is the total number of protons and neutrons present in one atom of the element.

Example- The total no. of protons in a carbon atom is 6, so its atomic no. is 6.

Also, one atom of Na contains 11 protons and 12 neutrons, so its mass no. is 23.

(b) Mass No. = Atomic no. + No. of neutrons

= 24 - 12 = 12

Draw the sketch of Bohr's model of an atom.

Sketch of Bohr's model of an atom
1624954_1772672_ans_455b2d39a46d45e994f1a24f5535d034.png

Explain Bohr-Bury scheme.

Bohr-Bury scheme-

i. The maximum number of electrons that could be present in a shell is given by the rule $$2n^2$$, where n is the orbit number or energy level.

Example, in first shell, $$n = 1,$$ then number of electrons = $$(2\times (1)^2) = 2 \ electrons$$

Similarly, for other shells, the diagram is shown below:

ii. The maximum number of electrons that can be accommodated in the outermost orbit is 8.

iii. Electrons are not accommodated in a given shell unless all the inner shells are completely filled.

1624906_1772664_ans_8f1a2a1ea851433588a0e190630480dd.png

What is the usual symbol for (a) an electron (b) a proton, and (c) a neutron?

(a) e-

(b) p+

Identify the pair of isotopes from the following:

$$ _{8}^{16}\textrm{X} $$ , $$ _{7}^{16}\textrm{X} $$ , $$ _{8}^{17}\textrm{X} $$

$$ _{8}^{16}\textrm{X} $$ , $$ _{8}^{17}\textrm{X} $$ are a pair of isotopes as they have a same atomic number but a different mass number.

Here $$8$$ is the atomic number and $$ 16, 17 $$ are a mass number which is different so these are isotopes.

What is meant by man-made elements ?

Man-made elements are elements that do not occur naturally but are produced in the laboratory. There are 24 man-made elements that were synthesized in the laboratory and find place in the periodic table. They are unstable and radioactive in nature. Examples include Darmstadtium, Technetium etc.

Match the names of the Scientists given in List I with their contributions towards the understanding of the atomic structure as given in List II

Ernest Rutherford found that the atom is mostly empty space, with nearly all of its mass concentrated in a tiny central nucleus. The nucleus is positively charged and surrounded at a great distance by negatively charged electrons
J.J. Thomson is known for the discovery of electrons.
Dalton gave the atomic theory which stated matter consist of atoms, indivisible and indestructible building blocks.
Neil Bohr proposed a model of the atom in which electrons were able to occupy certain orbits around the nucleus.
James Chadwick proved the existence of neutrons.
E.Goldstein is known for discovering canal rays.
Moseley is famous for his contribution to atomic number.

So correct answer is given as

$$A \rightarrow 3, B \rightarrow 4, C \rightarrow 1, D \rightarrow 2, E \rightarrow 6, F \rightarrow 7, G \rightarrow 5$$

There are $$ 15 $$ protons and $$16 $$ neutrons in the nucleus of an element . Calculate its atomic number and mass number .

Atomic number of the element is $$15$$ as the number of protons in one atom of the element represents the atomic number of that element.

Mass number of element = number of protons + number of neutron

$$ = 15 + 16 $$

$$ = 31 $$

Draw the sketch of Thomson's model of an atom.

1666699_1772675_ans_a4ae36b8754d44e4bd63080fa4839b6d.PNG

Why is Thomson's model of an atom compared with watermelon ?

According to Thomson’s model of the atom, the atom is a sphere of positive charge with negatively charged electrons embedded in it. It is compared with a watermelon because the sphere of positive charge represents the red, edible part of watermelon whereas electrons embedded in a positively charged sphere represent the black seeds.
1624774_1775070_ans_02c1a3f0e3b442d8b0db9f322529d481.JPG

1624774_1775070_ans_02c1a3f0e3b442d8b0db9f322529d481.JPG

Draw a sketch of Bohr's model of an atom with four shells .

Bohr's model
1624940_1775090_ans_91c439f8c92f43b7970c0dace2e18873.JPG

Complete the following crossword puzzle (Figure 5.1) Across:
(1) An element with atomic number 12.
(2) Highly reactive and soft metal which imparts yellow colour when subjected to flame and is kept in kerosene
(3) Metal used in making cans and member of Group 14.
(4) A lustrous non-metal which has 7 electrons in its outermost shell.
(5) The first element of second Period
(6) An element which is used in making fluorescent bulbs and is second member of Group 18 in the Modern Periodic Table
(7) A radioactive element which is the last member of halogen family.
(8) Metal which is an important constituent of steel and forms rust when exposed to moist air.
(9) The first metalloid in Modern Periodic Table whose fibres are used in making bullet-proof vests

(1) Magnesium
(2) Sodium
(3) Tin
(4) Iodine.
(5) Lithium
(6) Neon
(7) Astatine
(8) Iron
(9) Boron

Isotopes have same _ but different __.

Atomic number, Mass number

Does the particle have an excess of electrons or a deficiency of electrons

excess of electrons

An atom having atomic mass number $$13$$ has $$7$$ neutrons, What is the atomic number of the atom?

Mass number $$(A)$$ is the sum of the number of protons and neutrons present in the nucleus.
$$A=n+p$$
$$P=A-n=13-7=6$$
No. of protons =no.of electrons = atomic number
The atomic number of the atom is $$6$$.

Give the following a suitable word/phrase.
Atoms of same element with same atomic number but a different mass number.

Isotopes.

Define Atomic number.

$$Atomic$$ $$number$$ refers to the number of protons present in an atom. It is denoted by Z.

How did Neils Bohr visualise the atom?

Neils Bohr explained that atom is like a solar system with an empty space with a minute central nucleus, like Sun and electrons life planets revolve around it.

An excess of electrons produces a _____ charge.

negative

State the number of atoms of each kind, present in
(a) $$C_6H_{12}O_6$$
(b) $$H_2SO_4$$
(c) $$HNO_3$$
(d) $$CaCO_3$$
Also name these compounds.

(a)

$$\textbf{Element}$$	$$\textbf{Symbol}$$	$$\textbf{Number of atoms}$$
Carbon	C	6
Hydrogen	H	12
Oxygen	O	6

The name of the compound is Glucose.

(b)

$$\textbf{Element}$$	$$\textbf{Symbol}$$	$$\textbf{Number of atoms}$$
Hydrogen	H	2
Sulphur	S	1
Oxygen	O	4

The name of the compound is Sulphuric acid.

(c)

$$\textbf{Element}$$	$$\textbf{Symbol}$$	$$\textbf{Number of atoms}$$
Hydrogen	H	1
Nitrogen	N	1
Oxygen	O	3

The name of the compound is Nitric acid.

(d)

$$\textbf{Element}$$	$$\textbf{Symbol}$$	$$\textbf{Number of atoms}$$
Calcium	Ca	1
Carbon	C	1
Oxygen	O	3

The name of the compound is Calcium Carbonate.

Name three fundamental particles of the atom. Give the symbol with charge, on each particle.

The fundamental particles of the atom are: electrons, protons and neutrons.

Particles	Symbol	Charge
electron	$$e^{-}$$	$$-1$$ or $$1.602 \times 10^{-19}C.$$ Where $$-1$$ represent its one unit negative electrical charge
proton	$$p^{+}$$	$$+1$$ or $$1.602 \times 10^{-19} C.$$ Where $$+1$$ represents one unit +ve electrical charge.
neutron	$$n^\circ$$	$$0$$

On the basis of Thomson's model of an atom, explain how an atom as whole is neutral.

According to Thomson's atomic model, an atom consists of a positively charged sphere, and electrons are embedded in it.

As electrons are embedded into this sphere, and the total positive charge of the sphere is equal to the total negative charge of electrons, and hence, the atom remained electrically neutral.

An element has $$ 2 $$ electrons in its N shell.
What is its atomic number ?

$$ K\;\;L\;\;M\;\;N$$

$$2\; \;\;8\;\;\;8\;\;\;\;2$$

hence atomic number = 20, element is Calcium.

State one observation which shows that atom is not indivisible.

Chadwick discovered neutral particle present in an atom by bombarding light nuclei like beryllium with alpha particles. This observation shows that the atom is divisible.

Name the three fundamental particles of an atom:

Electrons, protons neutrons are the three fundamental particles of an atoms.

$$_{24}^{12}Mg$$ and $$_{26}^{12}Mg$$ are symbols of two isotopes of magnesium
Compare the atoms of these isotopes with respect to:
composition of their nuclei

	$$_{24}^{12}Mg$$	$$_{26}^{12}Mg$$
No. of electrons	$$12$$	$$12$$
No. of protons	$$12$$	$$12$$
No. of neutrons	$$24-12=12$$	$$26-12=14$$

Hence, composition of nuclei
$$ 12 Mg^{24} \rightarrow \begin{bmatrix} p & n \\ 12+ & 12 \end{bmatrix} \ \ 12 Mg^{26} \rightarrow \begin{bmatrix} p & n \\ 12+ & 14 \end{bmatrix}$$

What is the atomic number of carbon?

The atomic number of carbon is $$6$$.

Elements $$X,\ Y$$ and $$Z$$ have atomic number $$6,\ 9$$ and $$12$$ respectively. Which one :
has four electron in its outermost shell ?

$$X(2,4)$$ has four electron in its valence shell

Match the atomic numbers among, $$4,8,10,15$$ and $$19$$ with An element with $$4$$ shells.

Atomic number $$19$$

Electronic configuration $$(19):2,8,8,1$$

Write the names of the particles represented by the following symbols and explain the meaning of superscript and sub; script number attached.

$$P=$$ proton
$$n=$$ neutron
$$e=$$ electron
Top Superscript number. These superscript number show their mass number
Bottom Subscript number. These numbers show their atomic number.

Match the atomic numbers, $$4,8,10,15$$ and $$19$$ with: Element which does not form ion.

Atomic number $$10$$

Electronic configuration $$(10):2,8$$

Complete the statement by filling the gaps using the appropriate terms.
Electron ...... is complete in each hydrogen in a hydrogen molecule.

Electron duplet is complete in each hydrogen in a hydrogen molecule.

What is the name of Thomson's model?

The name of Thomson's model is plum pudding model.

Thomson proposed the plum pudding model of the atom, which had negatively charged electrons embedded in a positively charged soup.

Give reasons
Physical properties of isotopes are different

Physical properties are depends atomic mass of an element. Isotope has different atomic mass hence they differ in their physical properties

From the symbol $$_{17}Cl^{35}$$ state atomic number of chlorine.

The atomic number of chlorine $$(z)=17$$

The number of electron = number of protons $$= 17$$

Name the species which has no electron.

A specie with no electron is $$H^+$$.

Compare the properties of electrons, protons and neutrons.

NCERT Solutions for Class 9 Science Structure of the Atom part 2

List the three fundamental particles and their properties.

The fundamental particles present in an atom are:

Positively charged particles called protons (p)
The negatively charged particles called electrons (e) and.
Neutral particles called neutrons (n)

Name the scientist who discovered Neutrons.

$$\text{James Chadwick}$$

The essential nature of the atomic nucleus was established with the discovery of the neutron by James Chadwick in 1932

Name the scientist who proposed about electrons.

$$\text{J. J. Thomson}$$

The British physicist J. J. Thomson performed experiments studying cathode rays and discovered that they were unique particles, later named electrons.

State the postulates of the Bohr atomic model.

1962540_1823917_ans_b9275dd5f3874e38be7e500db431494b.jpg

What is atomic number ?

Atomic number of an atom is the number of protons present in the nucleus of an atom of an element or the number of electrons present in an atom of an element.

How many maximum number of electrons can be present in first, second, third and fourth shell ?

Periodic number	Shell	Formula	Max electrons in shell
$$1$$	$$K$$	$$2n^2$$	$$2$$
$$2$$	$$L$$	$$2n^2$$	$$8$$
$$3$$	$$M$$	$$2n^2$$	$$18$$
$$4$$	$$N$$	$$2n^2$$	$$32$$

Draw sketch of Bohr's model of an atom with three shells.

Draw a sketch of Bohr's model of an atom with three shells ...

Complete the table of details about shells and subshells.
Shell $$K_{1}$$ $$L_{2}$$ $$M_{3}$$ $$N_{4}$$
Subshell
No. of Electrons
No of electrons in $$KLMN$$ shell.

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Arrange the following sub-shells in the in-creasing order of energy $$5p,2s,4f,3s,4s,3d,6s$$

Orbitals are arranged with increasing energy on the basis of $$(n + l)$$ rule.
The higher the value of $$(n + l)$$ for an orbital the higher is its energy. Similarly, the lower the value of $$(n + l)$$ for an orbital the lower is its energy.
If two orbitals possess the same $$(n + l)$$ value, the orbital with a lower $$n$$ value will have the lower energy.

the correct order is $$2s<3s<4s<3d<5p<6s<4f$$

What are the fundamental particles of matter?

The fundamental particles of matter are protons, electrons, and neutrons.

Write the atomic number of the element with outer configuration $$4s^1.$$

Electronic configuration for outer configuration $$4s^1 = 1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^1.$$
So, Atomic number $$= 19$$

No of electrons in each shell.
Shell $$s$$ $$p$$ $$d$$ $$f$$
No. of Electrons

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Out of $$4f$$ and $$4d$$ which orbital will experience a higher effective nuclear charge?

Nuclear charge is defined as the net positive charge experienced by an electron in the orbital of a multi electron atom. The closer the orbital the greater is the nuclear charge experienced by the electron in it $$4d$$ will experience greater nuclear charge than $$4f$$ as $$4d$$ closer to the nucleus.

An atom having mass number $$40$$ and $$20$$ neutrons in its nucleus. What is the atomic number of the element ?

As Mass number = Atomic No. + Number of neutrons
$$\implies $$ 40 = Atomic No. + 20
$$\therefore$$ Atomic number = 20.

How many electrons can be accomodated in an orbital ?

An orbital can accommodate a maximum of two electrons.

Write the atomic number at an element with outer configuration $$3d^3.$$

Exact configuration for outer configuration $$3d^3.$$
$$1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2, 3d^3 = 23$$

So, Atomic number $$= 23$$

Complete the table

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Write the sub-shell electronic configuration of this atom.

The sub-shell electronic configuration of this atom. is $$1s^2,2s^2,2p^6,3s^2,3p^6,3d^5,4s^2$$

A compound of vanadium pentoxide $$(V20;)$$ is used as catalyst.
How vanadium ion is represented?

$$as\ V^{+5}$$

vanadium pentaoxide = $$V_2O_5$$

for the oxidation state of V.

$$2\times x+5\times (-2)=0$$

$$x=+5\Rightarrow V^{+5}$$

How many shells are present in this atom?

$$3$$ shells are present in this atom. $$(\because n=3)$$

Complete the subshell electronic configuration of He?

$$1s^2$$

Helium atoms have 2 electrons and the shell structure is 2. The ground state electron configuration of ground state gaseous neutral helium is $$1s^2$$

Certain subshell of an atom are given below $$2s, 2d, 3f, 3d, 5s, 3p$$
Which are the subshell that are not possible?

according to quantum numbers, the $$l$$ value should be less than $$n $$ (principal quantum number) so in

$$2d : n=2 \ and \ l= 2$$

$$ 3f : n=3 \ and \ l=3$$

that's why $$2d$$ and $$3f$$ are not possible.

Complete the table

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What is the maximum number of the electron that can be accommodated in the $$'s'$$?

the maximum number of electron that can be accommodated in the ′s′ is 2

Write names of subshells in accordance with increasing energy level,

$$1s<2s<2p<3s<3p<4s<3d<4p<5s<4d<5p<6s<4f<5s$$.....
1757036_1833545_ans_011fe5e4f0074e3ab87e94ec13653092.png

What may be the maximum number of electrons to be filled in the $$'p'$$ subshell?

$$6$$ electrons

The p sub level has 3 orbitals, so can contain 6 electrons max.

Certain subshell of an atom is not possible from given below $$2s, 2d, 3f, 3d, 5s, 3p$$
Give the reason.

$$d-$$subshell is not possible in $$2^{nd}$$ shell
$$f-$$subshell is not possible in $$3^{rd}$$ shell

according to quantum numbers, the $$l$$ value should be less than $$n $$ (principal quantum number) so in

$$2d : n=2 \ and \ l= 2$$

$$ 3f : n=3 \ and \ l=3$$

that's why $$2d$$ and $$3f$$ are not possible.

Write a short note about Niels Bohr's atomic model.

Niels Bohr proposed the atomic model in $$1912$$. He suggested that electrons move around the nucleus in specific orbits at a fixed distance from the nucleus in circular paths known as Orbits.

Electrons do not lose energy while moving in these orbits and thus, these orbits are called stationary or stable orbits.

The energy of the orbit nearest to the nucleus is the least and goes on increasing as the distance from the nucleus increases.

The arrangement of electrons around the nucleus in an atom can be explained as follows:

1. The first orbit closest to the nucleus is called the $$K$$ orbit and can accommodate a maximum of $$2$$ electrons.

2. The second orbits is called the $$L$$ orbit and can accommodate a maximum of $$8$$ electrons.

3. The third orbits is called $$M$$ orbit and can accommodate a maximum of $$18$$ electrons.

4. The fourth is the outermost orbit called $$N$$ orbit and can accommodate a maximum of $$32$$ electrons.

The electrons are arranged in the order in these orbits. The electrons fill the next orbit only after filling the previous one.

Which are the subshells of each shell?

$$K- 1s,$$
$$L-2s,\ 2p,$$
$$M-3s$$

Which are the fundamental particles whose masses are mainly responsible for the mass of an atom?

Protons and neutrons are the fundamental particles whose masses are mainly responsible for the mass of an atom.

How many $$'s'$$ subshell electrons are in $$1s^{2},2s^{2},2p^{6},3s^{2},3p^{2}$$

$$6$$ Electrons

$$1s\rightarrow2,2s\rightarrow2,3s\rightarrow2$$ $$\therefore (2+2+2=6)$$

Give information about properties of isotopes.

Properties of isotopes are:

1. Atomic masses of isotopes are different.

2. Chemical properties of isotopes are similar.

3. Isotopes occupy the same position in the periodic table.

Bohr models of atoms $$A,\ B,\ C$$ are given (Symbols are not real).
Write the atomic number, mass number, and electronic configuration of the atoms.

Element	Atomic number	Mass number	Electron configuration
$$A$$	$$6$$	$$12$$	$$2,4$$
$$B$$	$$7$$	$$15$$	$$2,5$$
$$C$$	$$6$$	$$14$$	$$2,4$$

What is indicated by hydrogen and sodium spectrum?

From the study of hydrogen spectrum, it has been proved that hydrogen atom has one electron.

On the other hand, the study of sodium spectrum has proved that sodium has more than one electron in its atom.

Explain Bohr model of atom?

$$\bullet$$ Electrons revolve around the nucleus in fixed paths called orbits or shells.

$$\bullet$$ Electrons in each shell have definite energy hence shells are also called energy levels.

$$\bullet$$ As long as an electron revolves in a particular orbit its energy remains constant.

$$\bullet$$ The energy of the shell increases as the distance from the nucleus increases.

$$\bullet$$ The shells around the nucleus can be numbered from near the nucleus $$1,2,3,4 ....$$ or represented by the letters $$K, L, M, N$$

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Which scientist and by which discovery invented neutrons?

James Chadwick discovered neutrons in $$1932$$ while doing a research on radioactivity.

Which of the subshell to which the last electron was added?

$$3s$$

as $$3s $$ has highest energy among given subshell hence, the last electron was added in $$3s$$.

If number of electrons in an atom is 8 and number of protons is also $$8$$, then
(i) what is the atomic number of the atom? and
(ii) what is the charge on the atom?

(i) Atomic number = Number of Protons = 8
(ii) In the given atom, total number of positive charge is equal to the total number of negative charge.
Number of Protons (8) = Number of electrons (8)
So, the charge on the atom will be zero.

What is the difference between ground state and excited state ?

Ground state means the lowest energy state. When the electrons absorb energy and jump to outer orbits, this state is called excited state.

What is the difference between atomic mass and mass number ?

Mass number is a whole number because it is the sum of number of proton and number of neutrons whereas atomic mass is fractional because it is the average relative mass of its atoms as compared with mass an atom of C-12 isotope taken as $$12$$.

State Bohr's postulates for explaining the spectrum of hydrogen atoms. Derive a formula for total energy of electron in n orbit.

Bohr Model for Hydrogen Atom and Hydrogen Like ions:

The drawbacks of Rutherford model were removed by Niels Bohr in 1913. Bohr proposed a new atom model. He applied the quantum theory of radiation, as developed by Max Planck and Einstein, to the Rutherford model. Following are the postulates of the Bohr’s theory.

1. An atom consists of a small and massive central core, called nucleus around which planetary electrons are revolving. The centripetal force required for their rotation is provided by the electrostatic attraction between the electrons and the nucleus. While revolving in the permissible orbits, an electron does not radiate energy. These non-radiating orbits are called ‘stationary orbits'.

$$F_{coulomb} = F_{centripetal}$$

If an electron moves around the nucleus of the charge, Ze in the nth stable orbit, then

$$\dfrac{K(Ze)e}{r_n^2} = \dfrac{mv_n^2}{r_n}$$

where $$r_n$$ is the radius of nth orbit and $$v_n$$ is the velocity of electron in nth orbit. So, Then the frequency v of the emitted or absorbed Where m is the radius of nth orbit and $$v_n$$ is the velocity of electron in nth orbit. So,

$$\dfrac{k(Ze)e}{r_n^2} = \dfrac{mv_n^2}{r_n}$$ ............(i)

2. According to the second postulate the electrons are permitted to revolve only in those orbits in which the angular momentum of an electron is an integral multiple of $$\dfrac{n}{2\pi},$$ h being Planck's constant.

These orbits are called stable orbits. If mass of electron is m, orbital velocity is v and radius of orbit is r, then

Angular momentum $$= n \times \dfrac{h}{2\pi}$$

$$mvr = \dfrac{nh}{2\pi}$$ ...........(2)

3. An atom can emit or absorb radiation in the form of discrete energy photons only when an electron jumps from a higher to a lower orbit or from a lower to a higher orbit, respectively. If $$En_1$$ and $$En_2$$ are the energies associated with these permitted orbits.

Then the frequency v of the emitted of absorbed were radiation is given by,

$$En_2 - En_1 = hv = \dfrac{hc}{\lambda}$$

This is known as Bohr's frequency condition

Total energy of Electron in $$n^{th}$$ Orbit

Total energy (EI) in any stable orbit is equal to the sum of the kinetic energy and potential energy. Kinetic energy of electron.

$$K_{n} = \dfrac{1}{2} mv^2$$

From equation (2) in Article number 14.3.1

$$v^2 = \dfrac{1}{4\pi \epsilon_0} \dfrac{Ze^2}{mr_n}$$

$$\therefore K_{n} = \dfrac{1}{2}m \times \dfrac{1}{4\pi \epsilon_0} \dfrac{Ze^2}{mr_n}$$

or $$K_{n} = \dfrac{1}{8} \times \dfrac{Ze^2}{\pi \epsilon_0r_n}$$ .............(1)

$$K_{n} = \dfrac{Ze^2}{8\pi \epsilon_0 r_n}$$

Potential energy of electron

$$U = \dfrac{1}{4\pi \epsilon_0} \dfrac{Ze(-e)}{r_n}$$

or $$U = -\dfrac{1}{4\pi\epsilon_0} \dfrac{Ze^2}{r_n}$$ ............(2)

$$\therefore$$ Total energy of electron

$$E_{n} = E_{k} + U$$

$$= \dfrac{1}{8\pi \epsilon_0} \dfrac{Ze^2}{r_n} - \dfrac{1}{4\pi \epsilon_0} \dfrac{Ze^2}{r_n}$$

or $$E_{n} = \dfrac{1}{4\pi \epsilon_0} \dfrac{Ze^2}{r_n} \left [ \dfrac{1}{2} - 1 \right ]$$

or $$E_{n} = -\dfrac{1}{4\pi \epsilon_0} \dfrac{Ze^2}{2r_n}$$ ..............(3)

$$E_{n} = \dfrac{-Ze^2}{8\pi \epsilon_0 r_n}$$

Again put the value of $$r_n$$ from equation $$(4)$$ in article number 14.3.1.

$$E_{n} = - \dfrac{Ze^2}{8 \pi \epsilon_0 \times \left [ \dfrac{\epsilon_0 n^2 h^2}{\pi me^2 Z} \right ] }$$

or $$E_{n} = \dfrac{Z^2}{n^2} \left [ \dfrac{e^4m}{8\epsilon_0^2 h^2} \right ]$$ ............(4)

or $$E_{n} = \dfrac{Z^2}{n^2} \left [ \dfrac{(1.6 \times 10^{-19})^4 \times 9.1 \times 10^{-31}}{8 \times (8.86 \times 10^{-12})^2 \times (6.6 \times 10^{-34})^2 } \right ]$$

$$= -\dfrac{Z^2}{n^2} \times 13.6 \times 1.6 \times 10^{-19} J$$

or $$E_{n} = -\dfrac{Z^2}{n^2} \times 13.6 \,eV$$ ............(5)

For hydrogen atom $$Z = 1$$

$$\therefore E_{n} = \dfrac{13.6}{n^2} eV$$ ........(6)

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What do you think would be the observation if the $$α$$-particle scattering experiment is carried out using a foil of metal other than gold?

The foil to be used in the alpha scattering experiment should be very thin. Gold is a very malleable metal so due to this property, it can easily be turned into a thin foil. If any other metal foil is used instead of gold then also there will be no change in the observations if the metal foil to be used is as thin as gold foil.

If we use a thick foil, then more $$\alpha$$-particles will bounce back thereby affecting the predictions of the experiment.

Complete the following Table :

    First row:

Since atomic no. is 9 so, the element is Fluorine.
Atomic no. = No. of protons = no. of electrons =9
Mass number = no. of protons + no. of neutrons =9+10=19

    Second row:

Since atomic no. is 16161616161616 so, no. of protons = no. of electrons =16
No. of neutrons = Mass no. – no. of protons =32–16=16

    Third row:

No. of protons = Atomic no. =12
So, the element is Magnesium.
No. of electrons = no. of protons =12
No. of neutrons = Mass no. – no. of protons =24–12=12

    Fourth row:

No. of protons = Atomic no. =1
So, the element is Deuterium.
No. of electrons = no. of protons =1
No. of neutrons = Mass no. – no. of protons =2–1=1

    Fifth row:

No. of protons = Atomic no. =1
The element is Protium since the mass number is 1

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Isotopes of an element have:
(a) the same physical properties
(b) different chemical properties
(c) different number of neutrons
(d) different atomic numbers

(a) x
(b) x
(c) correct

(d) x

Isotopes of an element have same atomic number but different mass number. Thus Isotopes of an element have different numbers of neutrons.

What was Thomson's model of atom ?

Thomson assumed that an electron is two thousand times lighter than a proton and believed that an atom is made up of thousands of electrons. In this atomic structure model, he considered atoms surrounded by a cloud having positive as well as negative charges. Thomson’s model of an atom is similar to a plum pudding.

Postulates of Thomson's Atomic model :

Postulate 1: An atom consists of a positively charged sphere with electrons embedded in it

Postulate 2: An atom as a whole is electrically neutral because the negative and positive charges are equal in magnitude

Thomson atomic model is compared to watermelon where,

Watermelon seeds as negatively charged particles.
The red part of the watermelon as positively charged.

How many electrons in sulphur $$ (Z = 16)$$ can have $$ n + l = 3 $$ ?

$$_{16}S = 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{4} $$

For $$1s^{2} , n + l = 1 + 0 = 1 $$

For $$2s^{2} , n + l = 2 + 0 = 2 $$

For $$2p^{6} , n + l = 2 + 1 = 3 $$

For $$3s^{2} , n + l = 3 + 0 = 3 $$

For $$3p^{4} , n + l = 3 + 1 = 4 $$

Thus $$n + l = 3 $$ for $$2p^{6}$$ and $$3s^{2}$$ electrons i.e., for $$8$$ electrons.

What do you understand by stationary states?

Bohr proposed that electrons do not radiate energy as they orbit or circle the nucleus, but exist in states of constant energy, which he called stationary states. This means that the electrons orbit at fixed distances from the nucleus.

Each stationary state corresponds to a particular set of electron orbits around the nucleus. These states are distinct and can be numbered as $$n = 1,2,3,4...$$ and so on. Here, $$n$$ is the principal quantum number, also called the shell number.

Fill in the blanks:
The arrangement of different electromagnetic waves in order of their wavelengths is called ________.

The arrangement of different electromagnetic waves in order of their wavelengths is called Electromagnetic spectrum

Fill in the blanks:
The splitting of lines in the magnetic field is called ________.

The splitting of lines in the magnetic field is called Zeeman effect.

The energy of separation of an electron is $$30.6\ eV$$ moving in an orbit of $$Li^{2+}$$. The number of waves made by the electron in one complete revolution in the orbit is:

As the energy of separation of an electron is $$30.6 eV$$ means it has this much energy in the ground state.

By calculation, as $$E = -\displaystyle \dfrac {13.6Z^{2}}{n^{2}}$$;

Here $$Z$$ is $$3$$, $$n=2$$

So, the number of waves made by the electron in one complete revolution in the orbit is $$2$$.

The atomic mass of an element is 133 and number of neutrons is 41.8% more than number of protons. Find the number of unpaired electrons.

Atomic mass = no. of protons + no. of neutrons = n + p
Given that; $$n = p + (\frac{41.8}{100})p$$
Therefore 133 = $$n = p +p + (\frac{41.8}{100})p$$
133 = $$\frac{100p + 100p + 41.8p}{100}$$
Therefore p = $$\frac{133 \times 100}{241.8}$$ = 55
Therefore electronic configuration = $$[Xe]6s^{1}$$
No. of unpaired electrons = 1.

The average atomic mass of a sample of an element $$X$$ is $$16.2\ u$$. What are the percentages of isotopes $$_{ 8 }^{ 16 }{ X }$$ and $$_{ 8 }^{ 18 }{ X }$$ in the sample?

Let the percentage of $$_8^{16}X$$ be $$A$$ %. Then the percentage of $$_8^{18}X$$ be $$(100-A)$$ %.

$$\therefore$$ $$16\times\dfrac{A}{100}+18\times\dfrac{100-A}{100}=16.2$$

$$\implies 1800-2A=1620$$

$$\implies A=90$$

So the answer is 90% $$_8^{16}X$$ and 10% $$_8^{18}X$$

Electrons of energy 12.09 eV can excite hydrogen atoms. To which orbit is the electron in the hydrogen atom raised and what are the wavelengths of the radiations emitted as it drops back to the ground state?

Initial state is $$1$$ and let final state be $${ n }_{ 2 }$$

$$E=13.6\times { z }^{ 2 }\left( \frac { 1 }{ { n }_{ 1 }^{ 2 } } -\frac { 1 }{ { n }_{ 2 }^{ 2 } } \right) \\ 12.09=13.6\left( 1-\frac { 1 }{ { n }_{ 2 }^{ 2 } } \right) \\ \Rightarrow { n }_{ 2 }=3$$

$${ R }_{ H }$$=Rydberg constant

$$\frac { 1 }{ { R }_{ H } } =912{ A }^{ \bullet }\\ \frac { 1 }{ \lambda } ={ R }_{ H }\left( \frac { 1 }{ { n }_{ 1 }^{ 2 } } -\frac { 1 }{ { n }_{ 2 }^{ 2 } } \right) \\ { \lambda }_{ 3\rightarrow 1 }=\frac { 9 }{ 8{ R }_{ H } } =1026{ A }^{ \bullet }\\ { \lambda }_{ 3\rightarrow 2 }=\frac { 36 }{ 5{ R }_{ H } } =6,566.4{ A }^{ \bullet }$$

State the postulates of Bohr atoms model. Obtain an expression for the radius of $$n^{th}$$ orbit of an electron of hydrogen atom based on Bohr's theory.

The postulates of Bohr's atom model are:
(i) An electron cannot revolve round the nucleus in all possible orbits. The electrons can revolve round the nucleus only in those allowed or permissible orbits for which the angular momentum of the electron is an integral multiple of $$\dfrac {h}{2\pi}$$. (where $$h$$ is Planck's constant $$(6.626\times 10^{-34} Js)$$. These orbit are called stationary orbits or non-radiating orbits and an electron revolving in these orbits does not radiate any energy. If $$m$$ and $$v$$ are the mass and velocity of the electron in a permitted orbit of radius $$r$$, then angular momentum of electron $$=mvr$$ =$$\dfrac{nh}{2\pi}$$, where $$n$$ is called principal quantum number and has the integral values 1, 2, 3..... This is called Bohr's quantization condition.
(ii) An atom radiates energy, only when an electron jumps from a stationary orbit of higher energy to an orbit of lower energy. If the electron jumps from an orbit of energy $$E_{2}$$ to an orbit of energy, $$E_{1}$$, a photon of energy $$hv = E_{2} - E_{1}$$ is emitted. This condition is called Bohr's frequency condition.
Radius of the nth orbit $$(r_{n})$$ : Consider an atom whose nucleus has a positive charge $$Ze$$, where $$Z$$ is the atomic number that gives the number of protons in the nucleus and $$e$$, the charge of the electron which is numerically equal to that of proton. Let an electron revolve around the nucleus in the $$nth$$ orbit of radius $$r_{n}$$.
By Coulomb's law, the electrostatic force of attraction between the nucleus and the electron $$= \dfrac {1}{4\pi \epsilon_{0}} \dfrac {(Ze)(e)}{r_{a}{2}} .....(1)$$
where $$\epsilon o$$ is the permittivity of the free space.
Since, the electron revolves in a circular orbit, it experiences a centripetal force,
$$\dfrac {mv^{2}}{r_{n}} = mr_{n}\omega_{n}^{2} .... (2)$$
where $$m$$ is the mass of the electron, $$v_{n}$$ and $$\omega_{n}$$ are the linear velocity and angular velocity of the electron in the $$n^{th}$$ orbit respectively.
The necessary centripetal force is provided by the electrostatic force of attraction.
For equilibrium, from equation $$(1)$$ and $$(2)$$,
$$\dfrac {1}{4\pi \epsilon_{o}} \dfrac {Ze^{2}}{r_{n}^{2}} = \dfrac {mv_{n}^{2}}{r_{n}} .... (3)$$
$$\dfrac {1}{4\pi \epsilon_{o}} \dfrac {Ze^{2}}{r_{n}^{2}} = mr_{n}\omega_{n}^{2} ..... (4)$$
From equation $$(4)$$,
$$\omega_{n}^{2} = \dfrac {Ze^{2}}{4\pi \epsilon_{o}mr_{n}^{3}} ..... (5)$$
The angular momentum of an electron in $$n^{th}$$ orbit is,
$$L = mv_{n}r_{n} = mr_{n}^{2}\omega_{n} .... (6)$$
By Bohr's first postulate, the angular momentum of the electron
$$L = \dfrac {nh}{2\pi} .... (7)$$
where $$n$$ is an integer and is called the principal quantum number.
From equations $$(6)$$ and $$(7)$$,
$$mr_{n}^{2}\omega_{n} =\dfrac {nh}{2\pi}$$
(or) $$\omega_{n} = \dfrac {nh}{2\pi mr_{n}{2}}$$
Squaring both sides,
$$\omega_{n}^{2} = \dfrac {n^{2}h^{2}}{4\pi^{2} m^{2}r_{n}^{2}} .... (8)$$
From equations $$(5)$$ and $$(8)$$,
$$\dfrac {Ze^{2}}{4\pi \epsilon_{o}mr_{n^{3}}} = \dfrac {n^{2}h^{2}}{4\pi^{2} m^{2}r^{2}}$$
(or) $$r_{n} = \dfrac {n^{2}h^{2}\epsilon_{o}}{\pi m^{2} Ze^{2}} .... (9)$$
From equation $$(9)$$, it is seen that the radius of the $$n^{th}$$ orbit is proportional to the square of the principal quantum number. Therefore, the radii of the orbits are in the ratio $$1 : 4 : 9$$.
For hydrogen atom, $$Z = 1$$
$$\therefore$$ from equation $$(9)$$,
$$r_{n} =\dfrac{ n^{2}h^{2}\epsilon_{o}}{\pi me^{2}} .... (10)$$
Substituting the known values in the above equation we get,
$$r_{n} = n^{2} \times 0.53\overset {\circ}{A}$$
If $$n = 1, r_{1} = 0.53\overset {\circ}{A}$$
This is called Bohr radius.

Not considering the electronic spin, the degeneracy of the second excited state $$\left(n=3\right)$$ of $$H$$-atom is $$9$$, while the degeneracy of the second excited state of $${H}^{-}$$ is _______.

$${H}^{-}$$ is a multielectron species. Hence, it will follow $$\left(n+l\right)$$ rule.
$${H}^{-} \left(2e\right) \longrightarrow 1{s}^{2} 2{s}^{0} 2{p}^{0}$$ (ground state)
$$\longrightarrow 1{s}^{1} 2s 2{p}^{1}$$ (second excited state)

What is the distance of closest approach to the nucleus of an $$\alpha$$-particle which undergoes scattering by $${180}^{o}$$ in Geiger-Marsden experiment?

$${r}_{0}=4.13 fm$$.
For closest approach.
$$\dfrac{1}{2}m{v}^{2}=K\dfrac{Ze \times e}{{r}_{0}}$$
For Rutherford experiment,
$$\dfrac{1}{2}m{v}^{2}=5.5 MeV = 5.5 \times {10}^{6} \times 1.6 \times {10}^{-19} J = 8.8 \times {10}^{-13} J$$
$$8.8 \times {10}^{-13} = \dfrac{9 \times {10}^{9} \times 2 \times 79 \times {\left(1.6 \times {10}^{-19}\right)}^{2}}{{r}_{0}}$$
$${r}_{0}=4.136 \times {10}^{-15} m$$
$${r}_{0}=4.13 fm$$.

Match the electronic transitions of List-I with spectral properties of List-II.

The transition $$\displaystyle n=6 \longrightarrow n=3 $$ corresponds to 6 lines in the spectrum. Spectral lines are in infrared region.

$$\displaystyle n=7 \longrightarrow n=3$$ corresponds to 10 lines in the spectrum .
Spectral lines are in infrared region.

$$\displaystyle n=5 \longrightarrow n=2$$ corresponds to 6 lines in the spectrum.
Spectral lines are in visible region.

$$\displaystyle n=6 \longrightarrow n=2$$ corresponds to 10 lines in the spectrum.
Spectral lines are in visible region.

Note: The number of lines in transition $$\displaystyle n_2 \rightarrow n_1$$ will be $$\displaystyle \dfrac {(n_2-n_1)(n_2-n_1+1)}{2}$$

In an atom first four shells $$(K, L, M$$ and $$N$$) are completely filled. Then what is the total number of electrons in that atoms?

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Radius of nucleus may be given as $${R}_{N}={R}_{0}{A}^{1/3}$$, where $$A=$$ mass number and $${R}_{0}=$$ constant. Show that the nuclear matter density is nearly constant. $${R}_{0}=1.2\times {10}^{-15}$$.

Radius of a nucleus of mass number is given by

R=$${ R }_{ 0 }{ A }^{ 1/3 }$$

Where,$${ R }_{ 0 }$$ = 1.2 x $$1{ 0 }^{ -15 }$$m

This implies that the volume of the nucleus is proportional to $${ R }^{ 3 }$$ is proportional to A.

Volume of nucleus=$$\dfrac { 4 }{ 3 } \pi { r }^{ 3 }$$

=+$$d\frac { 4 }{ 3 } \pi ({ R }_{ 0 }{ A }^{ 1/3\ \ }){ }^{ 3 }$$

=$$\dfrac { 4 }{ 3 } \pi { { R }_{ 0 }^{ 3 }A }$$

Density of nucleus=$$\frac { mass\quad of\quad nucleus }{ volume\quad of\quad nucleus } $$

=$$\dfrac { ma }{ \dfrac { 4 }{ 3 } \pi { R }_{ 0 }^{ 3 }A } \\ $$

=$$\dfrac { 3m }{ 4\pi { R }_{ 0 }^{ 3 } } \\ \\ $$

This equation shows that the density of nucleus is constant, independent of A for all nuclei.

Calculate the energy required to excite $$1$$ L of hydrogen gas at $$1$$ atm and $$298$$K to the first excited state of atomic hydrogen. The energy for the dissociation of $$H-H$$ bond is $$436\ kJ\ mol^{-1}$$.

Mole of $$ H_2$$ present in one litre $$=PV/RT$$

$$=1\times1/0.0821\times298$$

$$=0.0409$$

Thus energy needed to break $$H-H$$ bonds in 0.0409 mole of $$H_2=0.0409\times436=17.83KJ$$

Also energy needed to excite on $$H-$$atom from 1st to 2nd energy level$$=13.6(1−1/4)eV$$

$$=10.2eV$$

$$=10.2\times1.6\times10^{−19}J$$

Energy needed to excite $$0.0409\times2\times 6.02\times10^{23}$$ atoms of H$$=10.2\times1.6\times10^{−19}\times0.0409\times2\times 6.02\times10^{23}J$$

$$=80.36KJ$$

Total energy needed$$=17.83+80.36$$ $$=98.19KJ$$

If each hydrogen atom in the ground state of $$1.0$$ mol of $$H-$$atoms is excited by absorbing photons of energy $$8.4$$ eV, $$12.09$$ eV and $$15.0$$ eV of energy, then the number of spectral lines emitted is equal to:

Is dated hydrogen atom can absorbing of the

touching photons of energy, given by the

eqn

$$ E = 13.6(1-\dfrac{1}{n^{2}})eV $$

taking $$ n = 3 $$

$$ E\approx 12.8 (or) 12.1 eV $$

These, it can absorb $$ 12.1 eV $$

1194693_1034414_ans_118d10fcd4c9406c8651764cdc6d0048.jpeg

Suppose the potential energy between electron and proton at a distance r is given by -$$\frac{ke^2}{3r^3}$$. Use Bohr's theory to obtain energy of such a hypothetical atom.

Since H atom is a bounded system U cannot be positive

U = - $$ke^2/3r^3$$

Electrostatic force of attraction at a distance r will be

F = -dU/dr

$$ = -ke^2/r^4$$

Assuming a circular radius of the orbit

$$mv2/r = ke^2/r^4$$

$$= mv^2 = ke^2/r^3$$

$$= 1/2mv^2 = ke^2/2r^3$$

$$= K.E = ke^2/2r^3$$

E = K.E + U

$$= ke^2/2r^3 + (- ke^2/3r^3)$$

$$= ke^2/6r^3$$

Gives the energy level of the atom

In a hypothetical H-atom the mass of electron & its charge is double of what we consider calculate the total energy (in eV) of electron in the $$1^{st}$$ orbit of such a hypothetical H-atom?

$$E_n = -\dfrac{2 \pi^2 me^4}{n^2h^2}$$

if mass and charge doubled

$$E_n = -\dfrac{2 \pi^2 (2m)(2e)^4}{n^2h^2}$$

$$E_n =- \dfrac{(32)2 \pi^2 me^4}{n^2h^2}$$

$$E_1 = -32\times13.6eV = 435.2 eV$$

What should be the kinetic energy of electron in the first orbit of hydrogen atom?

According to Bohr's postulate-

$$mvr = \cfrac{nh}{2 \pi}$$

Squaring both sides, we get

$${m}^{2} {v}^{2} {r}^{2} = \cfrac{{n}^{2} {h}^{2}}{4 {\pi}^{2}}$$

$$m{v}^{2} = \cfrac{{n}^{2} {h}^{2}}{4 {\pi}^{2} m {r}^{2}}$$

Dividing the above equation by $$2$$, we get

$$\cfrac{1}{2} m{v}^{2} = \cfrac{{n}^{2} {h}^{2}}{8 {\pi}^{2} m{r}^{2}} ..... \left( 1 \right)$$

As we know that,

$$K.E. = \cfrac{1}{2} m{v}^{2} ..... \left( 2 \right)$$

From $${eq}^{n} \left( 1 \right) \& \left( 2 \right)$$, we have

$$K.E. = \cfrac{{n}^{2} {h}^{2}}{8 {\pi}^{2} m{r}^{2}}$$

As we know that,

$$r = 0.529 \cfrac{{n}^{2}}{Z} \mathring{A} = 0.529 \times {10}^{-10} m \cfrac{{n}^{2}}{Z}$$

$$n = 1 \; \left( \text{Given} \right)$$

$$Z = 1$$

$$\therefore r = 0.529 \times {10}^{-10} \cfrac{{1}^{2}}{1} = 0.529 \times {10}^{-10} \; m$$

Molar mass of hydrogen atom, $$\left( m \right) = 1$$

$$\therefore K.E. = \cfrac{{1}^{2} \times 6.62 \times 6.62 \times {10}^{-68}}{8 \times 3.14 \times 3.14 \times 0.529 \times 0.529 \times {10}^{-20} \times 1}$$

$$\Rightarrow K.E. = 1.98 \times {10}^{-48} \; J = 1.23 \times {10}^{-29} \; eV$$

A sample of hydrogen atoms gas contains 100 atoms All the atoms are excited to the seventh state. The total energy released by all the atoms is $$ \frac { 4800 }{ 49 } $$ Ry( Where Ry = 13 eV) then discuss the following things

a)Maximum energy of the emitted photon will be less then $$ \frac { 4800 }{ 49 } Ry $$
b)Maximum energy of the emitted photon may be grater than $$ \frac { 48 }{ 49 } Ry $$
c)The value of n = 6
d)total number of photon that can be emitted this sample may be less than 600

Given that,

Number of atoms, $$n=100$$

Energy released by all the atoms is $$E=\dfrac{4800}{49}Ry$$

Maximum energy of one photon is

$$ \dfrac{\dfrac{4800}{49}}{100}=\dfrac{48}{49} $$

$$ \dfrac{48}{49}Ry=Ry\left( \dfrac{1}{{{1}^{2}}}-\dfrac{1}{n{{'}^{2}}} \right) $$

$$ n'=7 $$

$$ \therefore n=6 $$

Maximum number of photons that can be emitted is 600.

Using postulates of Bohr's theory of hydrogen atom, show that
(i) Radii of orbits increases as $$n^2$$ and
(ii) The total energy of electron increases as $$\dfrac{1}{n^2}$$, where $$n$$ is the principal quantum number of the atom.

$$\textbf{Step 1- Relation between radius of orbit and principal quantum number}$$

According to the Bohr's theory.

Angular mometum, $$L = \dfrac {nh}{2\pi}$$

$$\dfrac {nh}{2\pi} = mvr$$ $$....(1)$$

Electrostatic force due to proton on revolving electron,

$$F_{e} = \dfrac {kq^{2}}{r^{2}} = \dfrac {ke^{2}}{r^{2}}$$

and centripetal force,

$$F_{e} = \dfrac {mv^{2}}{r}$$

$$\dfrac {ke^{2}}{r^{2}} = \dfrac {mv^{2}}{r} \Rightarrow \dfrac {ke^{2}}{r} = mv^{2}$$

From equation $$(1)$$,

$$v = \dfrac {nh}{2\pi mr}$$

$$\dfrac {ke^{2}}{r} = m\left (\dfrac {nh}{2\pi mr}\right )^{2}$$

$$\dfrac {ke^{2}}{r} = \dfrac {mn^{2}h^{2}}{(2\pi)^{2} m^{2}r^{2}}$$

$$r = \dfrac {mn^{2}h^{2}}{4\pi^{2} ke^{2}m^{2}} \Rightarrow r = \dfrac {n^{2}h^{2}}{4\pi^{2}mke^2}$$ $$....(2)$$

$$r\propto n^{2}$$

$$\textbf{Step 2 - Show total energy of electron increases as}$$ $$\dfrac {1}{n^{2}}$$

Total energy,

$$E = P.E + K.E$$

$$P.E = -\dfrac {1}{4\pi \varepsilon_{0}} \dfrac {e^{2}}{r}$$

$$K.E = \dfrac {1}{4\pi \varepsilon_{0}} \dfrac {e^{2}}{2r}$$

$$\therefore E = \dfrac {-ke^{2}}{2r}$$

From equation $$(2)$$,

$$E = \dfrac {-ke^{2}}{\dfrac {2\times n^{2}h^{2}}{4\pi^{2} ke^{2} m}} = \dfrac {-ke^{2} m 4\pi^{2} ke^{2}}{2n^{2}h^{2}} \Rightarrow E \propto \dfrac {1}{n^{2}}$$

What transition of $${ Li }^{ +2 }$$ spectrum will have same wavelength as that of second line of Balmer series in $${ He }^{ + }$$ spectrum?

As we know that,

$$\cfrac{1}{\lambda} = {R}_{H} {Z}^{2} \left( \cfrac{1}{{{n}_{1}}^{2}} - \cfrac{1}{{{n}_{2}}^{2}} \right)$$

For $${He}^{+}$$-

$$\cfrac{1}{\lambda} = {R}_{H} {\left( 2 \right)}^{2} \left( \cfrac{1}{{2}^{2}} - \cfrac{1}{{4}^{2}} \right)$$

For $${Li}^{+2}$$-

$$\cfrac{1}{\lambda} = {R}_{H} {\left( 3 \right)}^{2} \left( \cfrac{1}{{{n}_{1}}^{2}} - \cfrac{1}{{{n}_{2}}^{2}} \right)$$

Given that $$\lambda$$ is same.

Therefore,

$${R}_{H} {\left( 3 \right)}^{2} \left( \cfrac{1}{{{n}_{1}}^{2}} - \cfrac{1}{{{n}_{2}}^{2}} \right) = {R}_{H} {\left( 2 \right)}^{2} \left( \cfrac{1}{{2}^{2}} - \cfrac{1}{{4}^{2}} \right)$$

$$\Rightarrow \left( \cfrac{1}{{{n}_{1}}^{2}} - \cfrac{1}{{{n}_{2}}^{2}} \right) = \left( \cfrac{1}{{3}^{2}} - \cfrac{1}{{6}^{2}} \right)$$

Therefore,

$${n}_{1} = 3$$

$${n}_{2} = 6$$

Hence the transition is from $$n = 6$$ to $$n = 3$$.

The potential energies of first, second and third Bohr's orbit of He$$^+$$ cation are $${E_1}$$, $${E_2}$$ and $${E_3}$$ respectively. Write the correct sequence of these energies in increasing order.

$$He^+$$ cation is $$H-$$like species.

For $$H-$$ like species, potential energy $$E$$ is given as $$-\dfrac {13.6\ z^2}{n^2}eV$$

whose $$z=$$ atomic number of $$H-$$like species

$$n=$$ energy level or shell number

Since, there is negative in potential energy expression so, higher the $$n$$ value smaller is the negative value or higher is the potential energy.

$$E=\dfrac {13.6\ z^2}{n^2}eV$$

$$E=-k\dfrac {1}{n^2}eV$$

$$E\propto -\dfrac {1}{n^2}$$

where, $$k=13.6\ z^2$$

Here, $$z=2$$ for $$He^+$$

The correct sequence of the potential energies in measuring order is $$E_1 < E_2 < E_3$$.

The ratio of energy of ground state energy of hydrogen and first excited state energy of $$B{e^{3 + }}$$ will be-

2041926_1366657_ans_f382b5e4f5e64aa9b25e37875790e7b3.jpg

Find the ratio of maximum wavelength of minimum wavelength for the lines of Balmer series in hydrogen spectrum.

For Balmer
$$\dfrac{1}{\lambda} = R \left(\dfrac{1}{2^2} - \dfrac{1}{n^2}\right)$$
$$\dfrac{1}{\lambda_{max}} = R \left(\dfrac{1}{2^2} - \dfrac{1}{3^2}\right)$$
$$\dfrac{1}{\lambda_{min}} = R \left(\dfrac{1}{2^2} - \dfrac{1}{\infty^2}\right)$$

$$\dfrac{\dfrac{1}{\lambda_{max}}}{\dfrac{1}{\lambda{min}}} = \dfrac{\left(\dfrac{1}{4} - \dfrac{1}{9}\right)}{\left(\dfrac{1}{4}\right)}$$

$$\dfrac{\dfrac{1}{\lambda_{max}}}{\dfrac{1}{\lambda_{min}}} = \dfrac{\dfrac{5}{36}}{\dfrac{1}{4}}$$

$$\dfrac{\lambda_{min}}{\lambda_{max}} = \dfrac{5}{36} \times \dfrac{4}{1} = \dfrac{5}{9}$$

$$\dfrac{\lambda_{max}}{\lambda_{min}} = \dfrac{9}{5}$$

A hydrogen like atom (described by the Bohr's model) is observed to emit six wavelength, originating from all possible transition between a group of levels. These levels have energies between -0.85 eV and -0.544 eV(including both these value)
(a) Find the atomic number of the atom.
(b) Calculate the smallest wavelength emitted in these transition.
(use $$hc=1240 eV nm, E_1 H=-13.6 eV$$)

1785880_1741516_ans_1a4ef4a7427c40cd88f68bd7386ab1df.jpg

What is radial distribution function ? Draw this function for the 1s, 2s ,3s, 2p, 3p and 4 p orbitals in a hydrogen atom.

Determine the effective atomic number of the metal atom in the following:
$$[Ni(NH_3)_6]^{2+}$$

1962233_1729651_ans_163d3fed27604c03b1ac7603e42505f2.jpg

Determine the effective atomic number of the metal atom in the following:
$$[Co(CN)_6]^{4-}$$

1962232_1729649_ans_2c12945936cb42759b2bd5c5b4d50d1d.jpg

Would the Bohr formula for the H - atom remain unchanged if proton had a charge $$\left[\dfrac{+4}{3}\right]e$$ and electron a charge $$\left[\dfrac{-3}{4}\right]e $$, where $$e = 1.6 \times 10^{-19}C$$. Given reasons for your answer.

As there is no interchange in the position of proton and electron only the magnitude of charge changes as Coulombian force will be same as product of both charges
$$\dfrac{+4}{3} e \times \dfrac{-3}{4} e =e^2$$ is same as earlier.
$$P = +1 e$$ and $$ e = - 1e$$ , $$+1e \times -1e = -e^2$$. So electrostatic force does not change.
So Bohr's formula for the new H- atom remain same.

A deficiency of electrons produces a _____ charge.

2034015_1801096_ans_049e79b69b4b4a1bb0309ae3fe1a741f.jpeg

Using Bohr model, calculate the electric current created by the electron when the H - atom is in the ground state.

Let for an electron of H atom velocity in orbit $$= v\ m/s$$
Radius of orbit $$= a_0 = $$ Bohr's radius
So the number of revolutions per second $$\nu = \dfrac{2 \pi a_o}{\nu}$$
$$\because I = ^-ev \left[\because \nu = \dfrac{2\pi a_o}{\nu}\right]$$
$$= \dfrac{-e2 \pi a_0}{nu}$$
$$(-)$$ sign shows that the direction of current is opposite to the direction of motion of electron.

Would the Bohr formula for the H-atom remain unchanged If proton had a charge $$(+4/3)e$$ and electron had a charge $$(-3/4)e$$, where $$e = 1.6 \times 10^{-19} C$$? Give reasons for your answer.

According to Bohr, for an electron around a stationary nucleus the electrostatics force of attraction provides the necessary centripetal force.

$$\dfrac{1}{4\pi\epsilon_0}\dfrac{q_1q_2}{r^2} = \dfrac{mv^2}{r}$$

Hence the magnitude of electrostatic force F ∞ q₁ x q₂If proton had a charge (+4/3)e and electron a charge (-3/4)e, then the Bohr formula for the H-atom remains same, since the Bohr formula involves only the product of the charges which remain constant for given values of charges

State the postulates of the Bohr's model of an atom.

The postulates of Bohr's model of an atom are
1. Electrons revolve around the nucleus of an atom in a certain definite path called the Orbit or stationary state of the shell.
2. The shells are having different energy levels denoted as K, L, M, N.
3. As long as the electron remains in an orbit, it neither absorbs nor emits energy.
4. The electron can move only in that orbit in which angular momentum is quantized, i.e., the angular momentum of the electron is an integral multiple of $$\dfrac{h}{2 \pi}$$.

What is meant by radioactivity ?

The property of disintegration of an unstable atomic nucleus into a stable atomic nucleus, by the emission of radiations, is known as radioactivity.

Bohr models of atoms $$A,\ B,\ C$$ are given (Symbols are not real).
Among these, which are isotopes? Why?

1962622_1836710_ans_fbcaaa1483084f0392d11efd6cf1023a.jpg

Explain the use of radioactive isotopes in the study of mechanism of photosynthesis in plants and hydrolysis of esters.

Photosynthesis in plants -

When water enriched in $$O^{18}$$ isotope is used in photosynthesis, it is found that the oxygen evolved in the process comes entirely from water while oxygen of $$CO_2$$ is retained in organic compound.

$$CO_2^{16} + H_2O^{18} \rightarrow \underset{Glucose}{\dfrac{1}{6} (C_6H_{12} O_6^{16})} + O_2^{18}$$

Hydrolysis of Esters -

The mechanism of ester hydrolysis can be studied by using water labelled with $$O^{18}$$. It is found that the acid produced in the process comes from water while the oxygen of ester is retained in alcohol.

$$R - COOR + H_2O^{18} \rightleftharpoons RCOO^{18}H + R-OH$$

Describe the Bohr quantum conditions in terms of the wave theory: demonstrate that an electron in a hydrogen atom can move only along those round orbits which accommodate a whole number of de Broglie waves.

1882931_1854535_ans_d94b400b8e7045499edecb14694be853.jpg

Making use of the Hund rules, find the number of electrons in the only partially filled subshell of the atom whose basic term is
(a) $$^{3}F_{2} $$; (b) $$^{2}P_{3/2} $$; (c) $$^{6}S_{5/2} $$

1879401_1855540_ans_ba7c9eae060f47be84d61ee35d42076f.jpeg

What do you observe in the spectrum of $$NaCl $$ ?

Two yellow lines with wavelengths $$5890 \mathring A $$ and $$5896 \mathring A $$.

Using the Hund rules, write the spectral symbol of the basic term of the atom whose only partially filled subshell
(a) is filled by $$1/3$$, and $$ S = 1$$;
(b) is filled by $$70\%$$, and $$S = 3/2$$.

1879391_1855543_ans_da18a78f3ddb4e8db275177acd0698ee.jpeg

Shell	$$K_{1}$$	$$L_{2}$$	$$M_{3}$$	$$N_{4}$$
Subshell
No. of Electrons

Structure Of Atom - Class 11 Medical Chemistry - Extra Questions

Atoms of two elements $$P$$ and $$Q$$ have $$5$$ electrons in $${2}^{nd}$$ shell and $${3}^{rd}$$ shell respectively. What could be the geometric representations of $$P$$ and $$Q$$? What will be the atomic numbers of these elements?

A dipositive ion has an electronic arrangement $$2, 8, 8$$. Find out the number of electrons, protons and neutrons in that element if its mass number is $$40$$.

Write the two postulates Bohr's atomic model.

Name two processes which provide the best evidence for the motion of particles in matter.

Find the radius of nucleus of an atom having atomic mass number equal to$$\left( Take\ { R }_{ 0 }\ =\ 1.3\times { 10 }^{ -15 }m \right)$$

Represent each of the following in terms of its symbols:i) a proton ii) an electron iii) a neutron

Out of 6s and 4f orbitals, which is filled first and why?

If number of electrons in an atom is 8 and number of protons is also 8, then (i) what is the atomic number of the atom ? and (II) what is the charge on the atom?

Calculate energy of electron which is moving in the orbit that has its radius. sixteen times the radius of first Bohr orbit for $$H-atom$$

The atomic numbers of two elements A and B are 11 and 12 respectively. Which element exhibits highest metallic property ? Write the molecular formula of the compounds formed when theses elements combine with the element 'Z' having atomic number 8.

An element belonging to 3d series of modern periodic table has spin magnetic moment =5.92 B.M.in +3 oxidation state. Determine the atomic number of element.

"The atomic number and mass number of sodium are $$11$$ and $$23$$ respectively".What information does this statement convey?

What is meant by the statement that "the atomic number of sodium is eleven"?

A hydrogen atom in ground state is heated by a photon exciting the electron to the $$3rd$$ excite state. The electron then drop to the $$2nd$$ orbit what is the frequency of radiation emitted and absorbed in the process.

The energy required to excite an electron of H-atom from first orbit to second orbit is

Name the three constituent of an atom and state their mass and charge of each. How are they distributed in an atom?

Define 'atomic number' and 'mass number'.

What are the postulates of Bohr's model of an atom?

Postulates of the Bohr Atomic Model:

Electrons revolve around the nucleus in a fixed circular path termed “orbits” or “shells” or “energy level.”

The orbits are termed as “stationary orbit.”

Every circular orbit will have a certain amount of fixed energy and these circular orbits were termed orbital shells. The electrons will not radiate energy as long as they continue to revolve around the nucleus in the fixed orbital shells.

The different energy levels are denoted by integers such as n=1 or n=2 or n=3 and so on. These are called as quantum numbers. The range of quantum number may vary and begin from the lowest energy level (nucleus side n=1) to highest energy level.

The different energy levels or orbits are represented in two ways such as 1, 2, 3, 4… or K, L, M, N….. shells. The lowest energy level of the electron is called the ground state.

The change in energy occurs when the electrons jump from one energy level to other. In an atom, the electrons move from lower to higher energy level by acquiring the required energy. However, when an electron loses energy it moves from higher to lower energy level.

If number of electrons in an atom is $$8$$ and number of protons is also $$8$$, then:(i) What is the atomic number of an atom?(ii) What is the charge on the atom?(iii) Why does moon have very cold and very hot temperature even though it is present at the same distance from the sun as the earth is?

Mass of single atom of silver is $$1.794\times{10}^{-22}$$. What is atomic mass of silver.

The electronic spectrum is characteristic of an element.If true then enter 1, if false enter 0.

What do you mean by the dual nature of an electron?

An atom of an element has one electron in the valence shell and the two inner shells have 8 electrons each. Find the atomic number of that element.

The highest number of unpaired electrons are in $$ Fe^{3+},Fe^{2+},Fe^{+}$$ :

Define Isotopes.

An neutral atom has the same number of ......... as electrons.

An atom is made up of protons, neutrons and ..........

An atom of the element is $$^{35}_{17}Cl$$. Complete the following table.ElementMass numberAtomic numberNo. of protonsNo. of electronsNo. of neutrons

Match column I with column II and select the correct option from the codes given below:

Which of the following is (are) matter?Chair, air, love, smell, hate, almonds, thought, cold, cold-drink, the smell of perfume.

Compare the properties of protons, electrons and neutrons.

What are the characteristics of the particles of matter?

What are the limitations of J. J. Thomson's model of the atom?

Describe Bohr's model of the atom.

State Bohr's postulate of hydrogen atom which successfully explains the emission lines in the spectrum of hydrogen atom.Use Rydberg formula to determine the wavelength of $$H_{\alpha}$$ line.[Given: Rydberg constant $$R = 1.03 10^7 m^{-1}$$]

Column-I Column-II

According to Bohr's atomic model, electrons revolve in _______ orbits.

Three elements 'X', 'Y' and 'Z' have atomic numbers $$7, 8,$$ and $$9$$ respectively. Write the formula of the compound formed when 'X' combines with 'Z'.

On what basis did Bohr assume the concept of stationary orbits for an electron?

An atom of an element has one electron in the valence shell and the two inner shells have $$8$$ electrons each. Find the atomic number of that element.

True or False The radius of energy of Bohr's orbit is equal to integral multiples of 0.529.

___________ elements have same number of protons.

Filling the blanks................. can be classified chemically into pure substances and mixtures.

Fill in the blanks According to Bohr's atomic model , electrons revolve around the nucleus in _________ orbits.

Shadow is not a matter because it has no mass and does not occupy _______.

Fill in the blanks with suitable words:The particle of an atom that has no charge is ________.

Correct the following statements.a) Water boils at $$100^0\ C$$ under atmospheric pressure.b) The liquid evaporates above its boiling point.c) Solids have the largest interparticle space.d) Gases have the strongest interparticle forces.

Which rule is violated in the electronic configuration $$1s^0 2s^2 2p^4$$?

State Aufbau principle.

Fill in the blanks with suitable words:The fundamental particle not present in a normal hydrogen atom is ________.

Give the main postulates of Bohr's model of an atom.

State the postulate of Bohr's theory regarding angular momentum of an electron.

State the postulate of Bohr's theory regarding emission off a photon.

Write Bohr's any two postulates for hydrogen atom.

The energy levels of an atom of a certain element are shown in the given figureWhich one of the transitions A, B, C, D or E will result in the emission of photons of electromagnetic radiation of wavelength 618.75 nm?Support your answer with mathematical calculations.

Write the statement of Bohr's Second postulate of quantisation. Determine the wavelength of first spectral line in the Lyman series of the hydrogen spectrum.[Rydberg constant R$$=1.097\times 10^7m^{-1}$$].

Total energy of an electron orbiting around the nucleus of an atom is always negative. What is the significance of this?

a. What are Isotopes?b. Write any three applications of Avogadros law?

What is meant by 'Quantization of charge'?

Write three postulates of Bohr. Mention two limitations of Bohr model.

Derive an expression for potential and kinetic energy of an electron in any orbit of a hydrogen atom according to Bohr's atomic model.

State the basic postulates of Bohr's theory of atomic spectra.

Determine the number of revolutions made by an electron in one second in the $$2$$nd Bohr orbit of $$H$$-atom.

According to Bohr, 'Angular momentum of an orbiting electron is quantised'. What is meant by this statement?

Match the List 1 and List 2.

Write two limitations of Bohr's model.

The approximate radius of a $$H-atom$$ is $$0.05\ nm$$, and that of a proton is $$1.5\times 10^{-15}m$$. Assuming both the hydrogen atom and the proton to be spherical, calculate a fraction of the space in an atom of hydrogen that is occupied by the nucleus.

(a) State Bohr's postulate to define stable orbits in hydrogen atom. How does de Broglie's hypothesis explain the stability of these orbits?(b) A hydrogen atom initially in the ground state absorbs a photon which excites it to the $$n = 4$$ level. Estimate the frequency of the photon.

Find out the wavelength of the electron orbiting in the ground state of hydrogen atom.

Write the postulates of Bohr's atomic model. What is the relationship between the radii of the $$n$$th and first bohr orbit of hydrogen atom?

State whether True or False.(a) J.J. Thomson proposed that the nucleus of an atom contains only nucleons.(b) A neutron is formed by an electron and a proton combining. Therefore, it is neutral.(c) The mass of an electron is about $$\displaystyle \frac{1}{2000}$$ times that of a proton.

Calculate the shortest and longest wavelength of Balmer series of $$H_2$$ spectrum. Given $$R=1.097\times 10^7$$ $$m^{-1}$$.

Represent each of the following in terms of its symbols:
i) a proton ii) an electron
iii) a neutron

The electronic spectrum is characteristic of an element.
If true then enter 1, if false enter 0.

An atom of the element is $$^{35}_{17}Cl$$. Complete the following table.
Element Mass number Atomic number No. of protons No. of electrons
No. of neutrons

Which of the following is (are) matter?
Chair, air, love, smell, hate, almonds, thought, cold, cold-drink, the smell of perfume.

State Bohr's postulate of hydrogen atom which successfully explains the emission lines in the spectrum of hydrogen atom.
Use Rydberg formula to determine the wavelength of $$H_{\alpha}$$ line.
[Given: Rydberg constant $$R = 1.03 10^7 m^{-1}$$]

True or False
The radius of energy of Bohr's orbit is equal to integral multiples of 0.529.

Filling the blanks.
................ can be classified chemically into pure substances and mixtures.

Fill in the blanks
According to Bohr's atomic model , electrons revolve around the nucleus in _________ orbits.

Fill in the blanks with suitable words:
The particle of an atom that has no charge is ________.

Correct the following statements.
a) Water boils at $$100^0\ C$$ under atmospheric pressure.
b) The liquid evaporates above its boiling point.
c) Solids have the largest interparticle space.
d) Gases have the strongest interparticle forces.

Fill in the blanks with suitable words:
The fundamental particle not present in a normal hydrogen atom is ________.

The energy levels of an atom of a certain element are shown in the given figureWhich one of the transitions A, B, C, D or E will result in the emission of photons of electromagnetic radiation of wavelength 618.75 nm?
Support your answer with mathematical calculations.

a. What are Isotopes?
b. Write any three applications of Avogadros law?

(a) State Bohr's postulate to define stable orbits in hydrogen atom. How does de Broglie's hypothesis explain the stability of these orbits?
(b) A hydrogen atom initially in the ground state absorbs a photon which excites it to the $$n = 4$$ level. Estimate the frequency of the photon.

State whether True or False.
(a) J.J. Thomson proposed that the nucleus of an atom contains only nucleons.
(b) A neutron is formed by an electron and a proton combining. Therefore, it is neutral.
(c) The mass of an electron is about $$\displaystyle \frac{1}{2000}$$ times that of a proton.

Write electronic configurations of the elements (number in the brackets indicate atomic numbers)
oxygen $$(8)$$

In the Bohr's model, for unielectronic species following symbols are used.
$$K_{n, z} \rightarrow $$ Kinetic energy electron in $$n^{th}$$ orbit with atomic number "z".
Calculate z in all cases.

Identify the following elements.
a) $$_{25}X^{55}$$
b) $$_{17}X^{35}$$
c) $$_{20}X^{40}$$

In the Bohr's model, for unielectronic species following symbols are used.
$$r_{n, z} \rightarrow $$ Radius of $$n^{th}$$ orbit with atomic number "z".
Calculate z in all cases.

Isotopes are the atoms of element having the atomic number but mass number.

The kinetic energy of the $$e^{-}$$ in the $$2^{nd}$$ Bohr orbit of a hydrogen atom is:
(as in Bohr's radius)

a) Calculate the energy associated with the first orbit of $${ He }^{ + }$$. What is the radius of this orbit?
b) What is the lowest value of n that allows $$'g'$$ orbitals to exist?

Give reason for the following:
Physical properties of isotopes of the same element are not identical.

Give reason for the following:

The mass number of an atom is slightly less than the actual atomic mass.

If the number of electrons is an atom $$8$$ and the number of neutron is also $$8$$ then
(i) what is the atomic number of an atom?
(ii) what is the charge on the atom?

(a) How many atoms are there in exactly 12 g of carbon-12 element?(C=12 u).
(b) What name is given to this number?
(c) What name is given to the amount of substance containing this number of atoms?

Define the following terms .
Atomic number

An element has its electronic configuration as $$2, 8, 2$$. Now answer the following question:
What is the atomic number of this element?

Determine the effective atomic number of the metal atom in the following:
$$[Cr(CO)_6]$$

Determine the effective atomic number of the metal atom in the following:
$$[Fe(CN)_6]^{3-}$$