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

Answer

d

Explanation

`R_(1) =N_(1) lambda , R_(2)=N_(2) lambda`
Also,
`T=log_(e).(2)/(lambda)` or `lambda=log_(e). (2)/(T)`
`:. R_(1) -R_(2) =(N_(1) -N_(2)) lambda`
`=(N_(1) -N_(2))log_(e).(2)/(T)`
`:. (N_(1) -N_(0))=((R_(1) -R_(2))T)/(log_(e) 2)`
i.e., `(N_(1) -N_(2)) prop (R_(1) -R_(2))T`.