A radioactive sample `S_(1)` having an acitivity of `5 mu Ci` has twice the number of nuclei as another sample `S_(2)` which has a activity of `10 mu Ci`. The half lives of `S_(1)` and `S_(2)` can be

Options

A. 20 years and 5 years, respectively
B. 20 years and 10 years, respectively
C. 10 years each
D. 5 years each

Answer

A

Explanation

Let `lambda_(1) and lambda_(2)` be the decay constants and `N_(1) and N_(2)` be the number of active nuclei present for the two samples `S_(1)` and `S_(2)` respectively. Then
`lambda_(1)N_(1)=5muCi, lambda_(2)N_(2)=10muCi," (given) "lambda_(2)N_(2)=2lambda_(1)N_(1)`
`"Also, "N_(1)=2N_(2)" (given)"`
Then `lambda_(2)N_(2)=2lambda_(1)(2N_(2))`
or `lambda_(2)=4lambda_(1)rArr (T_(1//2))_(1)=4(T_(1//2))_(2)`.