Question

The rate of disintegration of a radioactive substance falls from 800 decay/min to 100 decay/min in 6 hours. The half-life of the radioactive substance is:

• A. 6/7 hr
• B. 2 hr
• C. 3 hr
• D. 1 hr

Answer 1

Answer: (B)

2 hr

$A=A_0{e}^{-\lambda t}$
$\Rightarrow 100=800e^{-\lambda (6\times 60)}$
$\Rightarrow e^{-360\lambda }=\frac{1}{8}$
$\Rightarrow -360\lambda =ln\frac{1}{8}$$=-ln8$

$\Rightarrow \lambda =\frac{ln{2}^3}{360}=\frac{ln2}{120}$

$\therefore T_{1/2}=\frac{ln2}{\lambda }=\frac{ln2}{\left(ln2/120\right)}=120min$
or $T_{1/2}=2hrs$