In a radioactive material the activity at time `t_1` is `R_1` and at a later time `t_2`, it is `R_1`. If the decay constant of the material is `lamda`, then

Options

A. `R_(1)=R_(2)(t_(2)//t_(1))`
B. `R_(1)=R_(2)`
C. `R_(1)=R_(2)e^(-lambda(t_(1)//t_(2)))`
D. `R_(1)=R_(2)e^(lambda(t_(1)//t_(2)))`

Answer

C

Explanation

`(dN)/(dt_(1))(=R_(1))=-lambdaN`
`(dN)/(dt_(2))(=R_(2))=-lambdaN'`
But `(N')/N=e^(-lambda(t_(2)-t_(1))) :. (R_(2))/(R_(1))=e^(-lambda(t_(2)-t_(1)))`
or `R_(1)=R_(2)e^(lambda(t_(2)-t_(1)))=R_(2)e^(-lambda(t_(2)-t_(1)))`