Radioactivity of a sample at `T_(1)` time is `R_(1)` and at time `T_(2)` is `R_(2).` If half-life of sample is T, then in time `(T_(2)-T_(1)),` the number of decayed atoms is proportional to

Options

A. `R_(1)T_(2)-R_(2)T_(2)`
B. `(R_(1)-R_(2))T`
C. `((R_(1)-R_(2)))/(T)`
D. `R_(1)-R_(2)`

Answer

B

Explanation

Let `R_(1)=N_(1)lamdaandR_(2)=N_(2)lamda`
Mean life, `T=(1)/(lamda)`
`R_(1)-R_(2)=(N_(1)-N_(2))lamda=(N_(1)-N_(2))(1)/(T)`
So, number of atoms disintegrated in `(T_(2)-T_(1))` is
`=N_(1)-N_(2)=(R_(1)-R_(2))T`