Question

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

Answer 1

Answer: (B)

Let $\lambda _{X}$ and $\lambda _{Y}$ be the decay constants of the radioactive elements $X$ and $Y$ respectively.
Here, half - life period of element $X$ = mean life time of element Y
$\therefore $ $\frac{0.693}{\lambda _{X}}=\frac{1}{\lambda _{Y}}$ or $\lambda _{X}=0.693 \, \lambda _{Y}$
or $\lambda _{Y}>\lambda _{X}$
Therefore, the element Y will decay faster.