The mean lives of a radioactive substance are 1620 years and 405 years for `alpha`-emission and `beta`-emission, respectively. Find out the time during which three fourths of a sample will decay if it is decaying both by `alpha`-emission and `beta`-emission simultaneously.

Options

A. 4.675 yr
B. 7.20 yr
C. 5.45 yr
D. 324 yr

Answer

C

Explanation

`lamda=(lamda_(1)+lamda_(2))=(1)/(1620)+(1)/(520)=2.54xx10^(-3)yr^(-1)`
`therefore" " t_(1//2)=(1n(2))/(lamda)=272.8 yr`
(1/4) th of the material remainsintact after 2 half-lives.