The activity of a radioactive substance is `R_(1)` at time `t_(1)` jand `R_(2)` at time `t_(2)(gt t_(1))` its decay constant is `lambda` Then

Options

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

Answer

b

Explanation

Let `R_0` be the initial activity. Then,
`R_1 =R_0 e^(-lambda t_(1))`
and `R_2 =R_0 e^(-lambda t_(2))`
`:.R_2/R_1= e^(lambda (t_(1)-t_(2)))`
or `R_2 =R_1 e^(lambda (t_(1)-t_(2)))`