JEE Main 2021 · Physics · Atoms, Nuclei and Dual Nature of Radiation · medium

Radioactive samples A and B initially contain equal numbers of nuclei. The half-life of A is 2 h and that of B is 6 h. The ratio of the activity of A…

Single correct option

Radioactive samples

A

and

B

initially contain equal numbers of nuclei. The half-life of

A

2\ \mathrm{h}

and that of

B

6\ \mathrm{h}

. The ratio of the activity of

A

to that of

B

after

12\ \mathrm{h}

Show answer and solution

Answer: (C) $\dfrac{3}{16}$

Activity

=\lambda N

. Initially

\lambda_A/\lambda_B=T_B/T_A=3

with equal

N_0

. After

12\ \mathrm{h}

A

has gone through

6

half-lives,

N_A=N_0/64

;

B

through

2

half-lives,

N_B=N_0/4

. Hence

\dfrac{R_A}{R_B}=3\times\dfrac{1/64}{1/4}=\dfrac{3}{16}

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