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At some instant, a radioactive sample S(...

At some instant, a radioactive sample `S_(1)` having an activity 5 `muCi` has twice the number of nuclei as another sample `S_(2)` which has an activity of 10 `muCi`. The half lives of `S_(1) and S_(2)` are :

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
Acticity of `S_(1)=(1)/(2) ("activity of" S_(2))`
or `(lambda_(1))/(lambda_(2))=(N_(2))/(2 N_(1))`
`(T_(1))/(T_(2))=2(N_(1))/(N_(2))" "(T=half-life =(ln2)/(lambda))`
Given `N_(1)=2N_(2)`
`(T_(1))/(T_(2)) =4`.
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