Question

A radioactive isotope has a half-life of 3 days was received after 12 days. It was found that there were 3 $g$ of the isotope in the container. The initial weight of the isotope when packed was:

• A. $12g$
• B. $24g$
• C. $36g$
• D. $48g$

Answer 1

The correct option is D $48g$

Half life of isotope$=3$ days.

Number of days after it was received$=12$ days.

Amount left after 12 days=3 gm.

$100\%\stackrel{3days}{\to }50\%\stackrel{6days}{\to }25\%\stackrel{9days}{\to }12.5\%\stackrel{12days}{\to }6.25\%$

Let $x$ be the initial mass of compound.

$\therefore \frac{6.25}{100}\times x=3$ gm.

$x=\frac{3\times 100}{6.25}=48$ gm.

$\therefore$ Initial weight of the isotope$=48$ gm.