A radioactive material of half-life `T` was kept in a nuclear reactor at two different instants. The quantity kept second time was twice of the kept first time. If now their present activities are `A_1` and `A_2` respectively, then their age difference equals

Options

A. `T_(ln2)|ln'(A_(1))/(A_(2))|`
B. `T|ln'(A_(1))/(A_(2))|`
C. `T_(A)/(ln2)|ln'(A_(2))/(2A_(1))|`
D. `T|ln'(A_(2))/(2A_(1))|`

Answer

C

Explanation

`A_(1)=lambda^(-lambda(t_(1)-t_(2))) implies "ln" (2A_(1))/A_(2)=-lambda Deltatimplies Deltat= (T"ln" A_(2)/(2A_(1)))/(ln2)`