A sample of radioactive material A, that has an activity of 10 mCi, has twice the number of nuclei as another sample

Question

A sample of radioactive material A, that has an activity of 10 mCi(1 Ci = 3.7 × 1010 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 :

(1) 20 days and 5 days

(2) 20 days and 10 days

(3) 5 days and 10 days

(4) 10 days and 40 days

Answer 1

Ans: (1) 20 days and 5 days

Sol: Activity A = $\lambda$N 

For A     10 = (2N₀)$\lambda$_A 

For B     20 = N₀$\lambda$_B 

$\therefore \lambda_B=4\lambda_A\implies(T_{1/2})_A =4(T_{1/2})_B$