Q: The half-life period of a radioactive element x is same as the mean life time of another radioactive element y. Initially both of them have the same number 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
Ans: (C)
Sol: $\large (t_{1/2})_x = ( t_{mean})_y $
$\large \frac{0.693}{\lambda_x} = \frac{1}{\lambda_y}$
λx = 0.693 λy
λx < λy
As , Rate of decay = λ N
Hence , y will decay at a faster rate than x