Q40 / 125 · BITSAT 2020 · Chemistry
A radioactive isotope having a half - life period of 3 days was received after 12 days. If $3 \mathrm{~g}$ of the isotope is left in the container, what would be the initial mass of the isotope?
- A$12 \mathrm{~g}$
- B$36 \mathrm{~g}$
- Correct answerC$48 \mathrm{~g}$
- D$24 \mathrm{~g}$
Solution
Given $t_{1 / 2}=3$ Total time $\mathrm{T}=12$
No. of half lives $(n)=\frac{12}{3}=4$ $\left(\frac{1}{2}\right)^{n}=\frac{\mathrm{N}}{\mathrm{N}_{\mathrm{o}}}
\therefore\left(\frac{1}{2}\right)^{4}=\frac{3}{\mathrm{~N}}$
$\frac{3}{\mathrm{~N}}=\frac{1}{16}$
$N=48$
Hence, the correct answer is option: 'C'.