The half lives of a radioactive sample are 30 years and 60 years from `alpha`- emission and `beta`- emission respectively If the sample decays both by alpha-emission and `beta`-emission simultaneously, the time after which, only one-fourth of the sample remain is

Options

A. 10 years
B. 20 years
C. 40 years
D. 45 years

Answer

C

Explanation

`lambda_(1)=1/30`
`lambda_(2)=1/60`
`lambda=lambda_(1)+lambda_(2)`
`lambda=1/20`
`N=(N_(0))/(2^(t)//t^(1//2))`
`N_(0)/4 = (N_(0))/((2)^(t//t^(1//2)))`
`:. t=2t_(1//2)=2xx(0.693)/lambda`
`t=2xx0.693xx20yrs`
`=27.72yrs`