Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If λA and λB are decay constants of A and B respectively, then choose the correct relation from the given options. (a) λA = λB ln 2 (b) λA ln 2 = λB (c) λA = 2λB (d) λA = λB

Answer: (a). Half-life of A: TA = (ln 2)/(λA); mean life of B: τB = (1)/(λB). (ln 2)/(λA) = (1)/(λB) ⇒ λA = λB ln 2. So the answer is (a).

Two radioactive elements A and B initially have same number of atoms… | JEE Main 2023 (11 Apr, Shift 1)

Q35JEE Main 2023 · 11 APR · SHIFT 1Medium

Law of Radioactive Decay

Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If $\lambda_A$ and $\lambda_B$ are decay constants of A and B respectively, then choose the correct relation from the given options.

Show answer and solution

Answer: (a)

Half-life of A: $T_A = \frac{\ln 2}{\lambda_A}$ ; mean life of B: $\tau_B = \frac{1}{\lambda_B}$ .
$\frac{\ln 2}{\lambda_A} = \frac{1}{\lambda_B} \Rightarrow \lambda_A = \lambda_B \ln 2$ .
So the answer is (a).

Report a mistake

Law of Radioactive Decay question from JEE Main 2023 (11 Apr, Shift 1)

More questions on Law of Radioactive Decay