The half-life period of a radioactive element X is same as the mean life of another radioactive element Y Initially, both of them have the same numbers of atoms then

Options

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 faster rate than y

Answer

C

Explanation

`(t_(1//2))_(x)=(t_("mean"))_(y)implies 0.693/lambda_(x)=1/lambda_(y) :. lambda_(x)=0.693 lambda_(y)`
`implies lambda_(x) lt lambda_(y) implies` 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.