The half life period of 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 and y have same decay rate initially and later on different decay rate.

(B) x and y decay at the same rate always.

(C) x will decay faster than y.

(D) y will decay faster than x.

*Solution*

Given, ${({t_{1/2}})_x} = {({t_{mean}})_y}$

$\therefore \frac{{0.693}}{{{\lambda _x}}} = \frac{1}{{{\lambda _y}}}$

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

$ \Rightarrow {\lambda _x} < {\lambda _y}$

If N is same, $A \propto \lambda $

$\therefore A_x < A_y $

Answer: (D)