Question

What is the half life of a radioactive substance if $75$ of its given amount disintegrate in $60min$?

• A. $30min$
• B. $45min$
• C. $75min$
• D. $90min$

Answer 1

The correct option is A $30min$

$t=\frac{2.303}{k}\log \left(\frac{N_o}{N}\right)$

Case- (i) $60=\frac{2.303}{k}\log \left(\frac{4}{3}\right)$

Case- (ii) $t=\frac{2.303}{k}\log \left(2\right)$

Dividing we get $\frac{60}{t}=\frac{\log 4-\log 3}{\log 2}$

$\Rightarrow \frac{60}{t}=\frac{1}{0.415}$

$\Rightarrow t=60\times 0.415=24.9min=30min$