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# The half -life period of a radioactive element A is same as mean life of another radioactive element B . Initially both of them have same number of atoms

$(a)\;x\;and\;y\;have\;same\;decay\;rate\;initially\qquad(b)\;x\;and\;y\;decay\;at\;same\;rate\qquad(c)\;y\;will\;decay\;at\;a\;faster\;rate\;than\;n\qquad(d)\;x\;will\;decay\;at\;faster\;rate\;than\;y$

Answer : (c) y will decay at a faster rate than n
Explanation :
$(t_{\large\frac{1}{2}})_{A}=(t_{mean})_{B}$
$\large\frac{0.693}{\lambda_{A}}=\large\frac{1}{\lambda_{B}}$
$\lambda_{A}=0.693 \lambda_{B}$
$\lambda_{A} < \lambda_{B}$
or rate decay = $\lambda N$
Initially no . of atoms (N) of both are equal but since $\;\lambda_{B} > \lambda_{A}\; , B$ will decay at a faster rate than x .