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 : 6`
C. `1 : 4`
D. `1 : 2`

Answer

C

Explanation

Let us assume that the initial total number of radioactive substance sre the same .
Sample - 1 Half life `T_(1//2)=1` year.
Sample - 2 Half life `T_(1//2)=2` year.

`(dN_(1))/(dt)=-lambda_(1)*(N_(0))/(64)rArr(dN_(1))/(dt)=-(0.694)/(1yr)*(N_(0))/(64)`.
`(dN_(2))/(dt)=-lambda_(2)*(N_(0))/(8)rArr(dN_(2))/(dt)=-(0.694)/(2yr)*(N_(0))/(8)`.
`therefore` Ratio of activities `=(2xx8)/(1xx64)=(1)/(4)`.