Question

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
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 then `Y`.

Answer 1

Correct Answer - C
( c) `(T_(1//2))_x = (t_(mean))_y`
`rArr (0.693)/(lamda_x) = (1)/(lamda_y) rArr lamda_x = 0.693 lamda_y` or `lamda_x lt lamda_y`
Also rate of decay `= lamda N`
Initially number of atoms (N) of both are equal but since `lamda_y gt lamda_x`, therefore, `y` will decay at a faster rate then `x`.