Question

The half-life period of a radio-active element X is same as the mean life time of another radio-active 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.
• D. X and Y decay at same rate always.

Answer 1

The correct option is B Y will decay faster than X.

The half life of X is $t_{1/2}=\frac{0.693}{{\lambda }_x}$ where ${\lambda }_x$ be the decay constant of X.

Mean life of Y is $\tau =\frac{1}{{\lambda }_y}$

Here, $t_{1/2}=\tau$ or $\frac{0.693}{{\lambda }_x}=\frac{1}{{\lambda }_y}$

or ${\lambda }_x=0.693{\lambda }_y\Rightarrow {\lambda }_y>{\lambda }_x$

Since, $N=N_0{e}^{-\lambda t}$ so Y will decay faster than X.