Question

Two half life radioactive substance is $20$ minutes. The approximate time interval $(t_2-t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it has decayed and time $t_1$ and $\frac{1}{3}$ of it had decayed is:

• A. $14min$
• B. $20min$
• C. $28min$
• D. $7min$

Answer 1

The correct option is B $20min$

$\frac{2}{3}{N}_0=N_0{e}^{-\lambda t_1}$

and $\frac{1}{3}{N}_0=N_0{e}^{-\lambda t_2}$

$2=e^{\lambda (t_2-t_1)}$

or, $\lambda (t_2-t_1)=ln2$

or, $t_2-t_1=\frac{ln2}{\lambda }=20min$.