The half-life of a radioactive element A is the same as the mean-life of another radioactive element B. Initially both substances have the same number of atoms, then: (a) A and B decay at the same rate always. (b) A and B decay at the same rate initially. (c) A will decay at a faster rate than B. (d) B will decay at a faster rate than A.

Answer: (d). TA = τB ⇒ (0.693)/(λA) = (1)/(λB) ⇒ λA = 0.693λB. λB > λA, and with equal N at the start, λ N is larger for B; B stays the faster decayer. So the answer is (d) B will decay at a faster rate than A.

The half-life of a radioactive element A is the same as the mean-life… | JEE Main 2013 (22 Apr, Shift 1)

Q98JEE Main 2013 · 22 APR · SHIFT 1Medium

Law of Radioactive Decay

The half-life of a radioactive element A is the same as the mean-life of another radioactive element B. Initially both substances have the same number of atoms, then:

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Answer: (d)

$T_A = \tau_B \Rightarrow \frac{0.693}{\lambda_A} = \frac{1}{\lambda_B} \Rightarrow \lambda_A = 0.693\lambda_B$ .
$\lambda_B > \lambda_A$ , and with equal $N$ at the start, $\lambda N$ is larger for B; B stays the faster decayer.
So the answer is (d) B will decay at a faster rate than A.

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