when electron in hydrogen atom jumps from energy state $$n_i=4 \;to\; n_f=3,2,1$$. Identify the special series to which the emission lines holding belong.

(b) How many electrons will be present in the sub-shells having $$m_s$$ value of -1/2 for n = 4 ?

(ii) State the energy conversion taking place in a cathode ray tube.

(iii) Write one use of cathode ray tube.

From the relation $$R = R_{0}A^{1/3}$$, where $$R_{0}$$ is constant and A is the mass number of the nucleus, show that nuclear matter density is independently of A

The photoelectric work function for a metal surface is 2.3 eV. If the light of wavelength $$ 6800\ A^\circ$$ is incident on the surface of metal find threshold frequency and incident frequency. Will there be an emission of photoelectrons or not ?

[Velocity of light c = $$3 \times 10^8 m/s$$, Planck's constant, $$h=6\cdot 63 \times 10^{-34 }Js$$]

(i) What names are given to the symbols b and $$\theta$$ shown here?

(ii) What can we say about the values of b for (i) $$\theta = 0^\circ$$ (ii) $$\theta = 0^\circ$$ = p radians?

$$824\, \overset{\circ}{A}, 970\, \overset{\circ}{A}, 1120\, \overset{\circ}{A}, 2504\, \overset{\circ}{A}, 5173\, \overset{\circ}{A}, 6100\, \overset{\circ}{A}$$

Which of these lines cannot belong to the hydrogen atom spectrum? (Given Rydbergconstant $$R = 1.03 \times 10^7\,m^{-1}$$ and $$\dfrac{1}{R}= 970 \,\overset{\circ}{A}$$. Support your answer with suitable calculations.

In which model is it completely wrong to ignore multiple scattering for the calculation of a average angle of scattering of a particles by a thin foil?

Keeping other factors fixed, it is found experimentally that for small thickness $$t$$, the number of $$\alpha$$-particles scattered at moderate angles is proportional to $$t$$. What clue does this linear dependence on $$t$$ provide?

(a) $$2$$ and $$3$$; (b) $$3$$ and $$3$$; (c) $$5/2$$ and $$2$$?

(ii) Find the relation between the three wavelengths $${ \lambda }_{ 1 }$$,$${ \lambda }_{ 2 }$$ and $${ \lambda }_{ 3 }$$ from the energy level diagram shown below.

(b) The electron in hydrogen atom in initially in the third excited state.What is the maximum number of spectral lines which can be emitted.When it finally moves to the ground state?

Mass of electron= $$9.1\times { 10 }^{ -31 }Kg$$

Charge on the electron$$=1.6\times { 10 }^{ -19 }C$$

Planck's constant=$$6.63\times { 10 }^{ -34 }J-s$$

Permitivitty of free space = $$\quad 8.85\times { 10 }^{ -12 }{ C }^{ 2 }/N{ m }^{ 2 }\quad $$

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

Planck's constant $$\left(h\right)=6.63 \times {10}^{-34}J-s$$,

Velocity of light in air $$\left(c\right)=3 \times {10}^{8}{m}/{s}$$).

a) Draw a spectral series of emission lines in hydrogen.

b) Name the different series of hydrogen atom.

c) In which region Lyman series is located.

(b) Why is it experimentally found difficult to detect neutrinos in this process?

(i) Wavelength of $$H_ \gamma$$ (gamma) line of Balmer series.

(ii) Shortest wavelength of Bracket series.

Identify the quantum numbers $$n$$ of the upper and the lower energy states involved in the transition.

$$ =\dfrac { \pi { me }^{ 4 } }{ { 2 }\epsilon _{ 0 }^{ 2 }{ h }^{ 3 }{ n }^{ 3 } }$$ or frequency of revolution, $$f=\dfrac { \pi { me }^{ 4 } }{ { 2 }\epsilon _{ 0 }^{ 2 }{ h }^{ 3 }{ n }^{ 3 } }$$

well $$250\ pm$$ wide, is in its ground state. How much energy must it

absorb if it is so jump up to the state with $$n=4?$$

what are the highest

$$25\ pm$$

What is the probability of detection by the probe?

How many different energies are possible

(a) (i) State the function of component P.

(ii) Tick one box to complete the sentence correctly.

A cathode-ray oscilloscope contains

$$\square$$ air at about five times normal atmospheric pressure.

$$\square$$ air at about normal atmospheric pressure.

$$\square$$ air at about one fifth of normal atmospheric pressure.

$$\square$$ a vacuum.

$$\square$$ neon gas.

(b) Fig. $$11.2$$ shows the front view of the screen of the cathode-ray oscilloscope.

With no voltage applied between the X-plates or between the Y-plates, the spot is at A.

(i) Places two ticks in each of the each of the table to describe the voltage across the plates when the spot is at points B and C. the column for the spot at A has been completed as an example.

(iii) Explain your answers for the spot at point B.

In 1911, Ernest Rutherford and his assistants Geigerand Marsden conducted an experiment in which they scattered alpha particles (nuclei of helium atoms) from thin sheets of gold. An alpha particle, having charge $$+2_e$$ and mass $$6.64 \times 10^{-27} \,kg$$, is a product of certain radio active decays. The results of the experiment led Rutherford to the idea that most of an atoms mass is in a very small nucleus, with electrons in orbit around it. (This is the planetary model of the atom, which well study in Chapter 42.) Assume an alpha particle, initially very far from a stationary gold nucleus, is fired with a velocity of $$2.00 \times 10^7 \,m/s$$ directly toward the nucleus $$(charge +79_e)$$. What is the smallest distance between the alpha particle and the nucleus before the alpha particle reverses direction? Assume the gold nucleus remains stationary.

The positively charged part of the atom possess most of the mass in ..................

(Rutherford's model / both the models)

An atom has a nearly continuous mass distribution in a ............. but has a highly non-uniform mass distribution in.

(Thomson's model / Rutherford's model)

(a) $$CO_2 (O - C - O) $$; (b) $$C_2H_2 (H - C - C - H) $$

(a) the radius of the first Bohr orbit and the velocity of an electron moving along it;

(b) the kinetic energy and the binding energy of an electron in the ground state;

(c) the ionization potential, the first excitation potential and the wavelength of the resonance line $$(n' = 2 \rightarrow n = 1) $$.

(b) What is the significance of negative sign in the expression for the energy?

(c) Draw the energy level diagram showing how the line spectra corresponding to Paschen series occur due to transition between energy levels.

Rutherford's atomic model was successful in explaining stability of the atom.

(1) Some rays were completely deflected back.

(2) Most of the rays passed straight.

Give reasons for the above observations.

(i) the purpose of covering cathode by thorium and carbon.

(ii) the purpose of the fluorescent screen.

(iii) how is it possible to increase the rate of emission of electrons.

$$(ii)$$ What happens if the negative potential is changed on a grid?

Find the wavelength of the emitted radiation.

and is in its first excited state. Fig. indicates the five longest

wavelengths of light that the electron could absorb in transitions

from this initial state via a single photon absorption: $$\lambda_a=80.78\ nm,\lambda_b=33.66\ nm, \lambda_c=19.23\ nm, \lambda_d=12.62\ nm, $$ and $$\lambda_e=8.98\ nm$$.

What is the width of the potential well?

Is the probability of backward scattering (i.e, scattering of $$\alpha$$-particles at angles greater than $$90^{0}$$) predicted by Thomson's model much less, about the same, or much greater than that predicted by Rutherford's model?

(a) $$59-61^{\circ} $$ ; (b) over $$ \theta_{0} = 60^{\circ} $$.

(a) the energy of alpha particles;

(b) the differential cross section of scattering $$ d \sigma / d \Omega $$ (kb/sr) corresponding to the angle $$ \theta = 60^{\circ} $$.

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