Question

What is the half life of a radioactive substance if it has a count rate of $500$ counts/sec and $62.5$ counts/sec two hours later?

• A. $10min$
• B. $20min$
• C. $30min$
• D. $40min$
• E. $50min$

Answer 1

The correct option is D $40min$

Given : $R_o=500$ counts/sec $R=62.5$ counts/sec $t=2$ hr

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

$\frac{0.693}{T_{1/2}}\times 2=\ln \frac{500}{62.5}$

$\frac{0.693}{T_{1/2}}\times 2=2.079$ $(\ln 8=2.079)$

$⟹$ $T_{1/2}=0.67hr=40min$