The half-lives of radioactive sample are 30 years and 60 years for two decay processes. If the sample decays by both the processes simultaneously. The time after which, only one-fourth of the sample will remain is

Options

A. 10 years
B. 20 years
C. 40 years
D. 60 years

Answer

C

Explanation

`lambda=lambda_1+lambda_2`
`:.` `(1n2)/(T)=(1n2)/(T_1)=(1n2)/(T_1)` (T=Half-life)
or `T=(T_1T_2)/(T_1+T_2)=20y`
`1/4th` sample remains after 2 half-lives or 40 y.