In a radioactive material the activity at time `t_(1)` is `R_(1)` and at a later time `t_(2)`, it is `R_(2)`. If the decay constant of the material is `lambda`, then

Options

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

Answer

B

Explanation

A= Activity `=(-dN)/(dt) =lambdaN`
`A = A_(0)e^(-lambdat)`
In first case:
`R_(1) =A_(0)e^(-lambdat_(1))`
In second case, `R_(2) = A_(0)e^(-lambdat_(2))`
Divide the equation,
`R_(1)/R_(2) =e^(-lambdat_(1))/e^(-lambdat_(2))`
`R_(1) =R_(2)e^(-lambda(t_(1)-t_(2)))`