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

Answer 1

Correct Answer - C
`(t_(1//2))_x = (t_(mean))_y`
or `0.693/(lambda_x) = (1)/(lambda_y)`
:. `lambda_x = 0.693 lambda_y`
`lambda_x lt lambda_y`
or Rate of decay`=lambdaN`
Initially, number of atoms(N) of both are equal but since `lambda_y gt lambda_x`, therefore, y will decay at a faster rate than x .
:. The correct option is (c) .