Nuclear Physics | Physics JEE previous year questions with Solutions

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Topic Question Set

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

1

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.

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