The number of nuclei of two radioactive substance is the same and their half-lives are 1 year and 2 years respectively. The ratio of their activities after 6 years will be

Options

A. `1:3`
B. `1:8`
C. `1:4`
D. `1:2`

Answer

B

Explanation

`(R_(1))/(R_(2))= (R_(0) e^(- lamda_(1)t))/(R_(0) e^(-lamda_(2)t))= e^(-6(lamda_(1)- lamda_(2)))`
`lamda_(1)= (ln 2)/(1), lamda_(2)= (ln 2)/(2)`
`rArr (R_(1))/(R_(2)) = e^(-6x ln 2x (1- (1)/(2))) = e^(-6x (1)/(2x) ln 2) rArr (R_(1))/(R_(2)) = e^(ln 2^(-3)) = (1)/(8)`