Question

The activity of a radioactive sample falls from 800 decays per second to 200 decays per second in 15 minutes. Mean life of sample is

• A. 11 $min$
• B. 12 $min$
• C. 7.5 $min$
• D. 22 $min$

Answer 1

The correct option is A 11 $min$

$800\stackrel{\frac{t_1}{2}}{\to }400\stackrel{\frac{t_1}{2}}{\to }200$
$2t_{\frac{1}{2}}=15min$
$t_{\frac{1}{2}}=7.5min$
$\Rightarrow {\tau }_{avg}=1.44\times t_{\frac{1}{2}}$
${\tau }_{avg}=1.44\times 7.5\simeq 11min$