Question

$50$% of a radio active substance decays in $5$ hours. The time required for the $87.5$% decay is

• A. $10hours$
• B. $15hours$
• C. $12.5hours$
• D. $17.5hours$

Answer 1

The correct option is B $15hours$

Now, it is given that half life of the radio active substance is 5 hours.
Fraction of substance left after $87.5$% decays $=\frac{1}{8}$
Let no of half-lifes passed be $x$,
$\frac{1}{8}=(\frac{1}{2}{)}^x\Rightarrow x=3$

So, $3$ half lives i.e., $5\times 3years$ $=15years$