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. (a)`20` min
B. (b)`28` min
C. (c)`7` min
D. (d)`14` min

Answer

A

Explanation

`:' N/N_(0)=[1/2]^(1//T) :. 1/3 =[1/2]^(1_(1)/T)` & `2/3=[1/2]^(1/T)`
`=1/2=[1/2]^((1_(2)-1_(1))1/T)implies 1=((1_(2)-t_(1)))/Timplies T=t_(2)-t_(1)`
`implies t_(2)-t_(1)=20` min