The half-life period of a 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 and Y decay at same rate always (b) X will decay faster than Y (c) Y will decay faster than X (d) X and Y have same decay rate initially

Answer: (c). TX = τY ⇒ (0.693)/(λX) = (1)/(λY) ⇒ λX = 0.693λY. λY > λX, so Y has the larger decay constant and decays faster. So the answer is (c) Y will decay faster than X.

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Law of Radioactive Decay

The half-life period of a 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: (c)

$T_X = \tau_Y \Rightarrow \frac{0.693}{\lambda_X} = \frac{1}{\lambda_Y} \Rightarrow \lambda_X = 0.693\lambda_Y$ .
$\lambda_Y > \lambda_X$ , so Y has the larger decay constant and decays faster.
So the answer is (c) Y will decay faster than X.

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