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 :

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

Given that `lambda_(1)N_(1)= 5muCi`
`lambda_(2)N_(2)=10 mu Ci`
`lambda_(2)N_(2)=2lambda_(1)N_(1)`
Also `N_(1)=2N_(2)`
Then `lambda_(2)N_(2)=2lambda_(1)(2N_(2))`
`lambda_(2)=4lambda_(1)`