Explanation:
D Given that,
Initial number of nuclei $\left(\mathrm{N}_{0}\right)=1 \mathrm{mg}$
Half-life $\left(\mathrm{T}_{1 / 2}\right)=1620$ year
Total time $(\mathrm{t})=3240$ year.
We know that,
$\mathrm{n}=\frac{\mathrm{t}}{\mathrm{T}_{1 / 2}}=\frac{3240}{1620}=2$
$\mathrm{n}=2$
Mass of Radium left after 2 half-lives,
$\mathrm{N}=\mathrm{N}_{0}\left(\frac{1}{2}\right)^{\mathrm{n}}$
$\mathrm{N}=1 \times\left(\frac{1}{2}\right)^{2}$
$\mathrm{~N}=\frac{1}{4}=0.25 \mathrm{mg}$
Mass of Radium disintegrate,
$=1-0.25$
$=0.75 \mathrm{mg}$
Number of radium atom disintegrate,
$=0.75 \times 2.68 \times 10^{18}$
$=2.01 \times 10^{18}$