Nuclear Physics | Physics JEE previous year questions with Solutions

Q 1 :

A radioactive nucleus $n_{2}$ has 3 times the decay constant as compared to the decay constant of another radioactive nucleus $n_{1}$ . If initial number of both nuclei are the same, what is the ratio of number of nuclei of $n_{2}$ to the number of nuclei of $n_{1}$ , after one half-life of $n_{1}$ ? [2025]

1/4
1/8
4
8

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2

3

4

(1)

$λ_{2} = 3 λ$

$λ_{1} = λ$

$N = N_{0} e^{- λ t}$

$N_{1} = N_{0} e^{- λ t}$

$N_{2} = N_{0} e^{- 3 λ t}$

$\frac{N_{2}}{N_{1}} = e^{- 2 λ t}$
$for t = \frac{\ln 2}{λ} \Rightarrow \frac{N_{2}}{N_{1}} = e^{- 2 λ \frac{\ln 2}{λ}} = \frac{1}{4}$

Q 2 :

A radioactive material P first decays into Q and then Q decays to non-radioactive material R. Which of the following figure represents time dependent mass of P, Q and R? [2025]

1

2

3

4

(2)

$P \to Q \to R$

Final mass of R will be equal to initial mass of P and mass of P is continuously decreasing with time.

Q 3 :

Consider the following radioactive decay process:

${}_{84}^{218}A \overset{α}{\to} A_{1} \overset{β^{-}}{\to} A_{2} \overset{γ}{\to} A_{3} \overset{α}{\to} A_{4} \overset{β^{+}}{\to} A_{5} \overset{γ}{\to} A_{6}$

The mass number and the atomic number of $A_{6}$ are given by: [2023]

211 and 80
210 and 80
210 and 82
210 and 84

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3

4

(2)

${}_{84}^{218}A \overset{α}{\to} {}_{82}^{214}A_{1} \overset{β^{-}}{\to} {}_{83}^{214}A_{2} \overset{γ}{\to} {}_{83}^{214}A_{3}$

${}_{83}^{214}A_{3} \overset{α}{\to} {}_{81}^{214}A_{4} \overset{β^{+}}{\to} {}_{80}^{210}A_{5} \overset{γ}{\to} {}_{80}^{210}A_{6}$

Q 4 :

If a radioactive element having half-life of 30 min is undergoing beta decay, the fraction of radioactive element remains undecayed after 90 min. will be: [2023]

$\frac{1}{8}$
$\frac{1}{16}$
$\frac{1}{4}$
$\frac{1}{2}$

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4

(1)

$\frac{N}{N_{0}} = {(\frac{1}{2})}^{t / t \frac{1}{2}} = {(\frac{1}{2})}^{\frac{90}{30}}$

$\frac{N}{N_{0}} = {(\frac{1}{2})}^{3} = \frac{1}{8}$

Q 5 :

Substance A has atomic mass number 16 and half-life of 1 day. Another substance B has atomic mass 1 number 32 and half-life of $\frac{1}{2}$ day. If both A and B simultaneously start undergo radioactivity at the same time with initial mass 320 g each, how many total atoms of A and B combined would be left after 2 days. [2023]

$3.38 \times 10^{24}$
$6.76 \times 10^{24}$
$6.76 \times 10^{23}$
$1.69 \times 10^{24}$

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4

(1)

${(N_{0})}_{A} = \frac{320}{16} = 20 moles$

${(N_{0})}_{B} = \frac{320}{32} = 10 moles$

$N_{A} = \frac{{(N_{0})}_{A}}{{(2)}^{2 / 1}} = \frac{20}{4} = 5$

$N_{B} = \frac{{(N_{0})}_{B}}{{(2)}^{2 / 5}} = \frac{10}{2^{4}} = 0.625$

$Total N = 5.625$

$Number of atoms = 5.625 \times 6.023 \times 10^{23} = 3.38 \times 10^{24}$

Q 6 :

A free neutron decays into a proton but a free proton does not decay into neutron. This is because [2023]

neutron is an uncharged particle
proton is a charged particle
neutron is a composite particle made of a proton and an electron
neutron has larger rest mass than proton

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(4)

As neutron has more rest mass than proton it will require energy to decay proton into neutron.

Q 7 :

The half-life of a radioactive substance is T. The 7 time taken for disintegrating $\frac{7}{8} th$ part of its original mass will be [2023]

3T
8T
T
2T

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4

(1)

$t_{1 / 2} = T$

$1 \underset{T}{\to} \frac{1}{2} \underset{T}{\to} \frac{1}{4} \underset{T}{\to} \frac{1}{8}$

$t_{7 / 8} = 3 T$

Q 8 :

Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If $λ_{A}$ and $λ_{B}$ are decay constants of A and B respectively, then choose the correct relation from the given options. [2023]

$λ_{A} = λ_{B}$
$λ_{A} = 2 λ_{B}$
$λ_{A} = λ_{B} \ln 2$
$λ_{A} \ln 2 = λ_{B}$

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(3)

$T_{1 / 2} (A) = T_{a v} (B)$

$\frac{l n 2}{λ_{A}} = \frac{1}{λ_{B}} \Rightarrow λ_{A} = λ_{B} \ln 2$

Q 9 :

The half-life of a radioactive nucleus is 5 years. The fraction of the original sample that would decay in 15 years is [2023]

$\frac{1}{8}$
$\frac{1}{4}$
$\frac{7}{8}$
$\frac{3}{4}$

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3

4

(3)

$15 year = 3 half lives$

$Number of active nuclei = \frac{N_{0}}{8}$

$Number of decay = \frac{7 N_{0}}{8}$

Q 10 :

A radioactive material is reduced to 1/8 of its original amount in 3 days. If $8 \times 10^{- 3} kg$ of the material is left after 5 days the initial amount of the material is [2023]

32 g
256 g
40 g
64 g

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2

3

4

(2)

$N = N_{0} {(\frac{1}{2})}^{n}$

$\frac{N_{0}}{8} = N_{0} {(\frac{1}{2})}^{n} \Rightarrow n = 3$

$3 half lives = 3 days$

$1 half life = 1 day$

$5 days = 5 half life$

$N = N_{0} {(\frac{1}{2})}^{n}$

$8 \times 10^{- 3} = N_{0} {(\frac{1}{2})}^{5}$

$N_{0} = 256 \times 10^{- 3} kg$

$\Rightarrow N_{0} = 256 g$

Topic Question Set

Q 2 :

A radioactive material P first decays into Q and then Q decays to non-radioactive material R. Which of the following figure represents time dependent mass of P, Q and R? [2025]

Q 3 :

Consider the following radioactive decay process:

${}_{84}^{218}A \overset{α}{\to} A_{1} \overset{β^{-}}{\to} A_{2} \overset{γ}{\to} A_{3} \overset{α}{\to} A_{4} \overset{β^{+}}{\to} A_{5} \overset{γ}{\to} A_{6}$

The mass number and the atomic number of $A_{6}$ are given by: [2023]

Q 4 :

If a radioactive element having half-life of 30 min is undergoing beta decay, the fraction of radioactive element remains undecayed after 90 min. will be: [2023]

Q 6 :

A free neutron decays into a proton but a free proton does not decay into neutron. This is because [2023]

Q 7 :

The half-life of a radioactive substance is T. The 7 time taken for disintegrating $\frac{7}{8} th$ part of its original mass will be [2023]

Q 8 :

Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If $λ_{A}$ and $λ_{B}$ are decay constants of A and B respectively, then choose the correct relation from the given options. [2023]

Q 9 :

The half-life of a radioactive nucleus is 5 years. The fraction of the original sample that would decay in 15 years is [2023]

Q 10 :

A radioactive material is reduced to 1/8 of its original amount in 3 days. If $8 \times 10^{- 3} kg$ of the material is left after 5 days the initial amount of the material is [2023]

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