The half life period of radioactive element x is same as the mean life time of another radioactive element y. Initially they have the same number of atoms. Then: (a) x-will decay faster than y. (b) y-will decay faster than x. (c) x and y have same decay rate initially and later on different decay rate. (d) x and y decay at the same rate always.

Answer: (b). Tx = (0.693)/(λx) and τy = (1)/(λy). Tx = τy ⇒ λx = 0.693 λy, so λy > λx. With equal N₀, larger λ means faster decay, so y decays faster than x: answer (b).

The half life period of radioactive element x is same as the mean… | JEE Main 2021 (1 Sep, Shift 2)

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Law of Radioactive Decay

The half life period of radioactive element x is same as the mean life time of another radioactive element y. Initially they have the same number of atoms. Then:

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Answer: (b)

$T_x = \frac{0.693}{\lambda_x}$ and $\tau_y = \frac{1}{\lambda_y}$ .
$T_x = \tau_y \Rightarrow \lambda_x = 0.693\,\lambda_y$ , so $\lambda_y > \lambda_x$ .
With equal $N_0$ , larger $\lambda$ means faster decay, so y decays faster than x: answer (b).

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