Strength of source $=8$ mci $=8.0 \times 3.7 \times 10^7 \mathrm{disint} / \mathrm{sec}$
Halflife $\mathrm{T}=5.3$ years $=5.3 \times 3.154 \times 10^7 \mathrm{sec}$
New, $\frac{\mathrm{dN}}{\mathrm{dt}}=\lambda \mathrm{N}$
where $\lambda=\frac{0.693}{\mathrm{~T}}=\frac{0.693}{5.3 \times 3.154 \times 10^7}$
$$
\begin{aligned}
& \frac{\mathrm{dN}}{\mathrm{dt}}=\text { rate of disintegration, } \\
\Rightarrow & 8.0 \times 3.7 \times 10^7=\frac{0.693}{5.3 \times 3.154 \times 10^7} \mathrm{~N} \\
\Rightarrow & \mathrm{N}=\frac{8 \times 3.7 \times 10^7 \times 5.3 \times 3.15 \times 10^7}{0.693}=7.15 \times 10^{16}
\end{aligned}
$$
By Avogadro's number
$$
\begin{aligned}
& 6.023 \times 10^{23}=60 \mathrm{~g} \text { for }{ }_{27}^{60} \mathrm{C}_0 \\
\Rightarrow & 7.15 \times 10^{16} \text { atoms } \\
=& \frac{60}{6.023 \times 10^{23}} \times 7.15 \times 10^{16} \mathrm{gm} \\
=& 7.12 \times 10^{-7} \mathrm{gm} \mathrm{of}_{27}^{60} \mathrm{C}_0
\end{aligned}
$$