A radioactive sample S1 having an activity of 5 μCi has twice the number of nuclei as another sample S2…

Q: A radioactive sample S1 having an activity of 5 μCi has twice the number of nuclei as another sample S2 which has an activity of 10 μCi. The half lives of S1 and S2 can be

(A) 20 yr and 5 yr, respectively

(B) 20 yr and 10 yr, respectively

(C) 10 yr each

(D) 5 yr each

Ans: (A)

Sol: Activity = λ N

According to question ;

$\large \lambda_1 N_1 = \frac{1}{2}( \lambda_2 N_2 )$

$\large \frac{\lambda_1}{\lambda_2} = \frac{N_2}{2 N_1}$

Since $\lambda \propto \frac{1}{T}$ ; (Where T = half life)

$\large \frac{T_1}{T_2} = \frac{2 N_1}{N_2}$

$\large \frac{T_1}{T_2} = 4 $ ; (Given , N1 = 2 N2)