Question

Half life of a radioactive substance is $1$ hour. The time taken for disintegration of $87.5$% substance is

• A. $2hrs$
• B. $3hrs$
• C. $3.5hrs$
• D. $4hrs$

Answer 1

The correct option is B $3hrs$

$t_{1/2}=1hr$

$87.5$% disintegrated
i.e. $12.5$% left which is $\frac{1}{8}$ of initial amount.

$\therefore \frac{1}{8}=(\frac{1}{2}{)}^3$

$n=3$

$⟶t_{87.5}=3t_{1/2}$

$\therefore t_{87.5}=3hrs$