At time t = 0, N 1 nuclei of decay constant λ 1 and N 2 nuclei of decay constant λ 2 are mixed. The decay rate of the mixture is:

- N 1 λ 1 e - λ 1 t + N 2 λ 2 e - λ 2 t

- N 1 λ 1 N 2 λ 2 e - λ 1 + λ 2 t

Physics - Nuclei - Quiz-1

Atoms having different atomic number as well as different mass number but having same number of neutrons

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isotopes
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isobars
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isotones
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isodiaphers

In a radioactive substance at t = 0, the number of atoms is 8 $\times 10^{4}$ , its half-life period is 3 yr. The number of atoms equal to $1 \times 10^{4}$ will remain after an interval of:
[UP CPMT 2010]

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9 yr
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8 yr
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6 yr
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24 yr

What is the respective number of $α$ and $β$ -particles emitted in the following radioactive decay?

$X_{90}^{{}_{200}} \to Y_{80}^{168}$

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6 and 8
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6 and 6
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8 and 8
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8 and 6

The half-life of radium is 1622 years. How long will it take for seven-eighth of a given amount of radium to decay

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3244 years
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6488 years
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4866 years
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811 years

The mass of a proton is 1.0073 u and that of the neutron is 1.0087 u (u = atomic mass unit) The binding energy of ${}_{2}H e^{4}$ is (mass of helium nucleus = 4.0015 u)

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28.4 MeV
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0.061 u
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0.0305 J
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0.0305 erg

The binding energies of the nuclei A and B are $E_{a} a n d E_{b}$ respectively. Three atoms of the element B fuse to give one atom of element A and an energy Q is released. Then $E_{a}, E_{b}$ and Q are related as:

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$E_{a} - 3 E_{b} = Q$
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$3 E_{b} - E_{a} = Q$
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$E_{a} + 3 E_{b} = Q$
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$E_{b} + 3 E_{a} = Q$

A free neutron decays into a proton, an electron and:

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a beta particle.
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an alpha particle.
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an antineutrino.
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a neutrino.

In a radioactive sample the fraction of initial number of radioactive nuclei, which remains undecayed after n mean lives is

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$\frac{1}{e^{n}}$
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$e^{n}$
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$1 - \frac{1}{e^{n}}$
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${(\frac{1}{e - 1})}^{n}$

The activity of a radioactive sample is measured as 9750 counts/min at t = 0 and as 975 counts/min at t = 5 min. The decay constant is approximately:

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0.922/min
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0.691/min
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0.461/min
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0.230/min

The energy equivalent of one atomic mass unit is:

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$1.6 \times 10^{- 19} J$
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$6.02 \times 10^{23} J$
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931 MeV
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9.31 MeV

Solar energy is due to:

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fusion reaction.
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fission reaction.
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combustion reaction.
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chemical reaction.

At time t = 0, N₁ nuclei of decay constant λ₁ and N₂ nuclei of decay constant λ₂ are mixed. The decay rate of the mixture is:

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$- N_{1} N_{2} e^{- (λ_{1} + λ_{2}) t}$
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$- (\frac{N_{1}}{N_{2}}) e^{^{- (λ_{1} + λ_{2}) t}}$
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$- (N_{1} λ_{1} e^{- λ_{1} t} + N_{2} λ_{2} e^{- λ_{2} t})$
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$- N_{1} λ_{1} N_{2} λ_{2} e^{^{- (λ_{1} + λ_{2}) t}}$

A nucleus ${}_{n}^{m}X$ emits one $α$ and two $β -$ particles. The resulting nucleus is

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${}_{n}^{m - 4}X$
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${}_{n - 2}^{m - 4}X$
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${}_{n - 4}^{m - 4}X$
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None of these

The half-life period of a radioactive substance is 6 h. After 24 h activity is 0.01 $μ$ Ci, what was the initial activity?

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0.04 $μ$ Ci
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0.08 $μ$ Ci
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0.24 $μ$ Ci
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0.16 $μ$ Ci

The radius of a nucleus of a mass number A is directly proportional to [MH CET 1999; AMU (En.) 2001; UPSEAT 2004; DUMET 2010]

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$A^{3}$
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A
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$A^{2 / 3}$
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$A^{1 / 3}$

$m_{P}$ and $m_{n}$ are masses of proton and neutron respectively. An element of mass m has Z protons and N neutrons, then

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$m > Z m_{p} + N m_{n}$
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$m = Z m_{p} + N m_{n}$
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$m < Z m_{p} + N m_{n}$
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m may be greater than, less than or equal to $Z m_{p} + N m_{n}$ , depending on the nature of the element.

The nuclei ${}_{6}C_{13} a n d {}_{7}N_{14}$ can be described as [1990]

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isotones
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isobars
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isotopes of carbon
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isotopes of nitrogen

The radioactivity of a sample is $A_{1}$ at a time $t_{1}$ and $A_{2}$ at time $t_{2}$ . If the mean life of the specimen is T, the number of atoms that have disintegrated in the time interval of $t_{2} - t_{1}$ is:

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$A_{1} - A_{2}$
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$\frac{A_{1} - A_{2}}{T}$
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$(A_{1} - A_{2}) T$
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$A_{1} t_{1} - A_{2} t_{2}$

What is the radius of iodine atom? (atomic no. 53, mass no. 126) [1988]

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$2.5 \times 10^{- 11} m$
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$2.5 \times 10^{- 9} m$
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$7 \times 10^{- 9} m$
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$7 \times 10^{- 6} m$

Which of the following statements is true for nuclear forces? [1990]

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They obey the inverse square law of distance.
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They obey the inverse third power law of distance.
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They are short range forces.
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They are equal in strength to electromagnetic forces.

The relationship between disintegration constant $[λ]$ and half-life [T] will be:

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$λ = \frac{\log_{10} 2}{T}$
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$λ = \frac{\log_{e} 2}{T}$
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$λ = \frac{T}{\log_{e} 2}$
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$λ = \frac{\log_{2} e}{T}$

Alpha particles are

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2 free protons
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helium atoms
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singly ionized helium atoms
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doubly ionised helium atoms

A radioactive sample with a half-life of 1 month has the label: 'Activity = 2 microcurie on 1-8-1991'. What would be its activity two months earlier?

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1.0 microcurie
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0.5 microcurie
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4 microcurie
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8 microcurie

If the nuclear force between two protons, two neutrons and between proton and neutron is denoted by $F_{p p}, F_{n n} a n d F_{p n}$ respectively, then:

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$F_{p p} \approx F_{n n} \approx F_{p n}$
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$F_{p p} \neq F_{n n} a n d F_{p n} = F_{n n}$
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$F_{p p} = F_{n n} = F_{p n}$
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$F_{p p} \neq F_{n n} \neq F_{p n}$

A radioactive element has half-life period 800 yr. After 6400 yr, what fraction will remain? [1989]

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$\frac{1}{2}$
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$\frac{1}{16}$
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$\frac{1}{8}$
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$\frac{1}{256}$

If a proton and anti-proton come close to each other and annihilate, how much energy will be released:

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$1.5 \times 10^{- 10} J$
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$3 \times 10^{- 10} J$
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$4.5 \times 10^{- 10} J$
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None of these

The stable nucleus that has a radius half of the radius of $F e^{56}$ is:

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$L i^{7}$
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$N a^{21}$
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$S^{16}$
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$C a^{40}$

The mass density of a nucleus varies with mass number A as [1992]

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$A^{2}$
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A
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Constant
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$\frac{1}{A}$

Energy released in the fission of a single ${}_{92}U_{235}$ nucleus is 200 MeV. The fission rate of a ${}_{92}U_{235}$ filled reactor operating at a power level of 5 W is

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$1.56 \times 10^{- 10} s^{- 1}$
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$1.56 \times 10^{11} s^{- 1}$
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$1.56 \times 10^{- 16} s^{- 1}$
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$1.56 \times 10^{- 17} s^{- 1}$

In one $α$ and 2 $β - e m i s s i o n s$ [1999]

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mass number reduced by 2
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mass number reduces by 6
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atomic number reduces by 2
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atomic number remains unchanged

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Practice Physics Quiz Questions and Answers

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Practice Physics Quiz Questions and Answers

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