JEE PYQ: Nuclear Physics Question 24
Question 24 - 2019 (09 Jan Shift 1)
A sample of radioactive material A, that has an activity of 10 mCi (1 Ci $= 3.7 \times 10^{10}$ 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:
(1) 5 days and 10 days
(2) 10 days and 40 days
(3) 20 days and 5 days
(4) 20 days and 10 days
Show Answer
Answer: (3)
Solution
For material A: $10 = (2N_0)\lambda_A$ For material B: $20 = N_0\lambda_B$ $\Rightarrow \lambda_B = 4\lambda_A \therefore T_{1/2,A} = 4T_{1/2,B}$ $\left[\because T_B = \frac{0.693}{\lambda}\right]$ i.e. 20 days half-lives for A and 5 days $(T_B)_B$ for material B.
BETA
