Question

The half-life of a radioactive substance is 20 min. The approximate time interval $(t_2-t_1)$ between the time $t_2$ when 2/3 of it has decayed and time $t_1$ when 1/3 of it had decayed is ;

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

Answer 1

The correct option is B 20 min

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

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

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

$\lambda (t_2-t_1)=ln2$

$(t_2-t_1)=\frac{ln2}{2}=20min$

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

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

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

$\lambda (t_2-t_1)=ln2$

$(t_2-t_1)=\frac{ln2}{\lambda }=20min$