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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

20 years and 5 years ,respectively

B

20 years and 10 years , respectively

C

10 years each

D

5 years each

Text Solution

Verified by Experts

The correct Answer is:
A
`lambda_(1)N_(1) =5 xx 10^(-6) " Ci , " lambda_(2)N_(2)=10 xx 10^(-6) Ci`
`lambda_(2)N_(2) = 2lambda_(1)N_(1)`
and `N_(1)= 2N_(2)`
` :. lambda_(2)N_(2)=2lambda_(1)(2N)_(2) rArr =4lambda_(1)`
`rArr [(0.693)/((t_(1//2))_(2))] = 4 [ (0.693)/((t_(1//2))_(1))]rArr (t_(1//2))_(1)= 4 (t_(1//2))_(2)`
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