A sample of radioactive material A, that has an activity of `10 mCi(1 Ci=3.7xx10^(10)decays//s)`, has twice the number of nuclei as another sample of a different radioactive material B which has an activity of 20 mCi. The correct choices for half-lives of A and B would then be respectively :

Options

A. 5 days and 10 days
B. 20 days and 10 days
C. 10 days and 40 days
D. 20 days and 5 days

Answer

D

Explanation

`A_(B)=2A_(A), N_(A)=2N(B), A_(A)=lamda_(A)N_(A),A_(B)=lamda_(B)N_(B)`
`:.lamda_(B)N_(B)=2lamda_(A)N_(A)implieslamda_(B)=4 lamda_(A)`
`t_(1//2)=(In2)/(lamda)impliest_(B)=1/4 t_(A)`