The half-life of a radioactive nucleus is `50` days. The time interval `(t_2 -t_1)` between the time `t_2` when `(2)/(3)` of it has decayed and the time `t_1` when `(1)/(3)` of it had decayed is

Options

A. `30 days`
B. `50 days`
C. `60 days`
D. `15 days`

Answer

B

Explanation

Here, T=50days
form `N/(N_(0))=(1/2)^(t//T)`
`1/3=(1/2)^(t_(2)//T)`
and `2/3=(1/2)^(t_(1)//T)`
Divide `1/2(1/2)^((t_(2)-t_(1))//T)`
`:. (t_(2)-t_(1))/T=1 or t_(2)-t_(1) T=50 days`