Question

At any instant, the ratio of the number of radioactive substances is $2:1$. If their half-lives be respectively $12$ and $16$ hours, then after two days, what will be the ratio of the substances?

• A. $1:1$
• B. $2:1$
• C. $1:2$
• D. $1:4$

Answer 1

The correct option is A $1:1$

$2$ days correspond to $48$ hours.

For the first substance, $48$ hours corresponds to $\frac{48}{12}=4$ half life periods.

The amount left after $4$ half life periods is $(\frac{1}{2}{)}^4=\frac{1}{16}$

For the second substance, $48$ hours corresponds to $\frac{48}{16}=3$ half life periods.

The amount left after $3$ half life periods is $(\frac{1}{2}{)}^3=\frac{1}{8}$

The ratio of amount of two substances after 2 days will be
$\frac{2}{1}\times \frac{\frac{1}{16}}{\frac{1}{8}}=1:1$