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

Answer

B

Explanation

Activity = `lambda .N `
`lambda_(A)N_(A) = 10 rArr lambda_(B) N_(B) = 20 `
`(lambda_(A))/(lambda_(B)). (N_(A))/(N_(B)) =1/2 rArr (lambda_(A))/(lambda_(B)) .2 = 1/2 rArr (lambda_(A))/(lambda_(B))=1/4 `
`rArr (t_(1//2_(B)))/(t_(1//2_(B))) = 1/4 rArr t_((1//2)._(A)) = 4 xx t _((1//2)` .