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A radioactive sample S1 having an activi...

A radioactive sample `S_1` having an activity of `5muCi` has twice the number of nuclei as another sample `S_2` which has an activity of `10muCi`. The half-lives of `S_1` and `S_2` can be

A

(a) 20 yr and 5 yr, respectively

B

(b) 20 yr and 10 yr, respectively

C

(c) 10 yr each

D

(d) 5 yr each

Text Solution

Verified by Experts

The correct Answer is:
A
Activity of `S_1=1/2`
or `lambda_1N_1=1/2(lambda_2N_2)`
or `lambda_1/lambda_2=(N_2)/(2N_1)`
or `T_1/T_2=(2N_1)/(N_2)` (T=half-life`=(1n2)/(lambda)`)
Given, `N_1=2N_2`
`:.` `T_1/T_2=4`
`:.` Correct option is (a).
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