Question

The disintegration rate of a certain radioactive sample at any instant is 4750 dpm. Five minutes later, the rate becomes 2700 dpm. The half life of sample is :

• A. 6.13 min
• B. 5.13 min
• C. 4.13 min
• D. 8.13 min

Answer 1

Answer: (A)

6.13 min

The decay constant is
$\lambda =\frac{2.303}{t}log\frac{a}{a-x}$
$\lambda =\frac{2.303}{5}log\frac{4750}{2700}$
$\lambda =0.4606\times log1.7593=0.1129/min$

The half life period is
$t_{1/2}\frac{0.693}{\lambda }=\frac{0.693}{0.1129}=6.13min$