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 ^(-lamda ( t _(1) - t _(2)))`
C. `R _(1) = R _(2) e ^(lamda( t _(1) - t _(2)))`
D. `R _(1) = R _(2) (t _(2) //t _(1))`

Answer

B

Explanation

According to activity law, `R = R (0) e ^(-lamdar)`
`R _(1) = R _(0) e ^(-lamda t_(1)) and R _(2) = R _(0) e ^(- lamda t _(2))`
`(R _(1))/(R _(2)) = (R _(0) e ^(- lamda t _(1)))/( R _(0) e ^(- lamda t _(2))) = e ^(- lamda ( t _(1) - t_(2)))`
`or R _(1) = R _(2) e ^(- lamda (t _(1) - t _(2))`