Question

A sample of a radioactive substance has a half-life of $20$ minutes. If the sample's activity is $200$ counts/second. Find out the number of counts/second after one hour passes?

• A. $6.25$ counts/sec
• B. $12.5$ counts/sec
• C. $25$ counts/sec
• D. $50$ counts/sec
• E. $100$ counts/sec

Answer 1

Answer: (C)

$25$ counts/sec

Given : $T_{1/2}=20$ min $t=1$ hr $=60$ min $R_o=200$ counts/sec

Using : $\frac{0.693}{T_{1/2}}t=\ln \frac{R_o}{R}$

$\therefore$ $\frac{0.693}{20}\times 60=\ln \frac{R_o}{R}$

$⟹\ln \frac{R_o}{R}=2.079$

$\therefore$ $R=R_o{e}^{-2.079}=200\times 0.125=25$ counts/sec