JEE Main 2017 · Physics · Atoms, Nuclei and Dual Nature of Radiation · medium

Two radioactive samples A and B have half-lives of 10 minutes and 20 minutes and contain the same number of nuclei at t = 0. At t = 40 minutes the…

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Two radioactive samples

A

and

B

have half-lives of

10

minutes and

20

minutes and contain the same number of nuclei at

t = 0

. At

t = 40

minutes the ratio of the activity of

A

to that of

B

Show answer and solution

Answer: (A) $1:2$

After

40

minutes sample

A

has gone through

4

half-lives, so

N_A = N_0/16

; sample

B

has gone through

2

, so

N_B = N_0/4

. Activity is

\lambda N

, and

\lambda_A/\lambda_B = T_B/T_A = 2

. Hence

\dfrac{A_A}{A_B} = 2\times\dfrac{1/16}{1/4} = 2\times\dfrac14 = \dfrac12

. The ratio

1:4

is the ratio of the numbers of surviving nuclei, not of the activities, because the shorter-lived sample has the larger decay constant.

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