The half life of a radioactive substance is 24 days. What is the time interval `(t_2-t_1)` between the time `t_2 " when " 2/3` of the original material had decayed and time `t_1 " when " 1/3` of its original material has decayed ?

Options

A. 24 days
B. 12 days
C. 36 days
D. 48 days

Answer

A

Explanation

`N/N_0 = (1/2)^(t//T)`
where t = total time and T = half life time
`t_2 = " time for " 2/3` decay
`therefore " when " 2/3` material decays , the material that is left behind
is `1/3 N_0 " or " N/N_0 = 1/3= (1/2)^(t_2//T) " "...(1)`
and when the decay is `1/3`, the material left behind is
`2/3 N_0 " or " N/N_0 = (2/3) = (1/2)^(t_1//T) " " ...(2)`
`therefore` Divide (1) by (2) , we get
`therefore 1/2 = (1/2)^((t_2-t_1)/(T)) therefore (1/2)^1 = (1/2)^((t_2-t_1)/(T))`
`therefore (t_2 - t_1)/(T) = 1 " or " t_2 - t_1 = T = 24` days