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. `A_(1)t_(2)-A_(2)t_(1)`
B. `(A_(1)-A_(2))T`
C. `(A_(1)-A_(2))^(-1)`
D. `A_(1)T-A_(2)T^(2)`

Answer

B

Explanation

`A_(1) = lambdaN_(1), A_(2) = lambdaN_(2)`
`N_(1) = A_(1)/lambda, N_(2) = A_(2)/lambda`
`N_(1)-N_(2)` = Number of atoms disintegrated `=A_(1)/lambda -A_(2)/lambda`
`=1/2(A_(1)-A_(2)) =((A_(1)-A_(2))T)/0.693`