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)`
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= A_(0) e^(-lamda t ) = A_(0) e^(-t//tau) [tau = (1)/(lamda)]`
`A_(1)= A_(0) e^(-t_(1)//T) rArr A_(0)= (A_(1))/(e^(-t_(1)//T)) = A_(1) e^(t_(1)//T)`
Hence, `A_(2)= A_(0) e^(-t_(2)//T)= (A_(1) e^(t_(1)//T)) e^(-t_(2)//T)`
`rArr A_(2)= A_(1) e^((t_(1)-t_(2))//T)`