The half life of a radioactive substance is `20` minutes . The approximate time interval `(t_(2) - t_(1))` between the time `t_(2)` when `(2)/(3)` of it had decayed and time `t_(1)` when `(1)/(3)` of it had decay is

Options

A. `7 min`
B. `14 min`
C. `20 min`
D. `28 min`

Answer

C

Explanation

`(2)/(3)N_(0)=N_(0)e^(-lambdat_(1))`
`(1)/(3)N_(0)=N_(0)e^(-lambdat_(2))`
`2=e^(lambda(t_(2)-t_(1)))`
`lambda(t_(2)-t_(1))= l n 2`
`(t_(2)-t_(1))= ( l n 2)/(lambda)=20 "min"`