Question

The half-life period of a radioactive element X is same as the mean life of another radioactive element Y. Initially, both of them have the same numbers of atoms then.

• A. X and Y have the same decay rate initially
• B. X and Y decay at the same rate always
• C. Y will decay at a faster rate than X
• D. X will decay at a faster rate than Y

Answer 1

Answer: (C)

Y will decay at a faster rate than X

Half life of x$=$ mean life of y
Let ${\lambda }_x$ and ${\lambda }_y$ be decay constants of x and y, then condition $\left(1\right)$ implies
$\frac{0.693}{{\lambda }_x}=\frac{1}{{\lambda }_y}$
${\lambda }_y=\frac{{\lambda }_x}{0.693}\Rightarrow {\lambda }_y>{\lambda }_x$.
As rate of decay $\alpha \lambda$; hence decay of y will be faster than that of x.