The radioactivity of a sample is `R_(1)` at a time `T_(1)` and `R_(2)` at time `T_(2)`. If the half-life of the specimen is T, the number of atoms that have disintegrated in the time `(T_(2) -T_(1))` is proporational to

Options

A. `R_1 T_1 = R_2 T_2`
B. `R_1 - R_2`
C. `((R_1 - R_2))/(T)`
D. `(R_1 - R_2)`

Answer

D

Explanation

(d) `R_1 = N_1 lamda, R_2 N_2 lamda`
Also `T = (log_e 2)/(lamda)`or `lamda = (log_e 2)/(T)`
`:. R_1 - R_2 = (N_1 - N_2) lamda`
` =(N_1 - N_2) (log_e 2)/(T)`
`:. (N_1 - N_2) = ((R_1 - R_2)T)/(log_e 2)`
i.e., `(N_1 - N2) prop (R_1 - R_2) T`.