The radioactivity of a sample is `A_1` at time `t_1` and `A_2` at time `t_2` If the mean life of the specimen is `T`, the number of atoms that have disintegrated in the time interval of `(t_2 - t_1)` is :

Options

A. `(A_1 - A_2)`
B. `((A_1 - A_2))/(T)`
C. `(A_1 - A_2) T`
D. `A_1 t_1 - A_2 t_2`

Answer

C

Explanation

( c) `A_1 = N_1 lambda, A_2 = N_2 lamda`
Mean life, `T = (1)/(lamda)`
`A_1 - A_2 = (N_1 - N_2) lamda = (N_1 - N_2) (1)/(T)`
So, number of atoms disintegrated in
`(t_2 - t_1) sec = (N_1 - N_2) = (A_1 - A_2) T`.