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 $

$\large \frac{0.693}{\lambda_x} = \frac{1}{\lambda_y}$

λ_{x} = 0.693 λ_{y}

λ_{x} < λ_{y}

As , Rate of decay = λ N

Hence , y will decay at a faster rate than x