The activity of a sample of radioactive material `A_(1)` at time `t_(1)` and `A_(2)` at time `t_(2)(t_(2)gtt_(1))`. Its mean life is `T`.

Options

A. `A_(1)t_(1) = A_(2)t_(2)`
B. `(A_(1)-A_(2))/(t_(2)-t_(1)) =` constant
C. `A_(2) = A_(1)e^(((t_(1)-t_(2))/(T)))`
D. `A_(2) = A_(1)e^(((t_(1))/(t_(2)T)))`

Answer

C

Explanation

`A_(1) = A_(0)e^(-lambdat_(1)), A_(2) = A_(0)e^(-lambdat_(2)), lambda = (1)/(T)`
`(A_(2))/(A_(1)) = e^(-lambda(t_(2)-t_(1))) = e^(((t_(1)-t_(2))/(T))`
`A_(2) = A_(1) e^(((t_(1)-t_(2))/(T))`