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The half-life of a radioactive element $A$ is the same as the mean-life of another radioactive element $B.$ Initially both substances have the same number of atoms, then
$A$ and $B$ decay at the same rate always .
$A$ and $B$ decay at the same rate initially.
$A$ will decay at a faster rate than $B.$
$B$ will decay at a faster rate than $A$
Solution
${\left( {{{\text{T}}_{1/2}}} \right)_{\text{A}}} = {\left( {{{\text{t}}_{{\text{mean}}}}} \right)_{\text{B}}}$
$ \Rightarrow \frac{{0.693}}{{{\lambda _A}}} = \frac{1}{{{\lambda _B}}}$ $ \Rightarrow {\lambda _A} = 0.693{\lambda _B}$
or $\quad \lambda_{A} < \lambda_{B}$
Also rate of decay $=\lambda \mathrm{N}$
Initially number of atoms $(N)$ of both are
equal but since $\lambda_{\mathrm{B}}>\lambda_{\mathrm{A}},$ therefore Bwill decay at a faster rate than $\mathrm{A}$
