The total number of neutrons in 7 mg of ${ }^{14}\mathrm{C}$, is:$24.088\times {10}^z\text{ neutrons }$. The value of z is nearly

$$\begin{gathered} {\text{ One atom of }}_6^{14}\mathrm{C}\text{ has }14-6\text{ i.e. }8\text{ neutrons. } \\ \therefore 7\mathrm{mg}{\text{ of }}_6^{14}\mathrm{C}=\frac{7\times {10}^{-3}\mathrm{g}}{14\mathrm{g}{\mathrm{mol}}^{-1}}=0.5\times {10}^{-3}\mathrm{mol} \\ =0.5\times {10}^{-3}\mathrm{mol}\times 6.022\times {10}^{23}\text{ atom }{\mathrm{mol}}^{-1} \\ =3.011\times {10}^{20}\text{ atoms } \\ \text{ Thus, total neutrons in }7{\mathrm{mg}}_0^{14}\mathrm{C}=8\times 3.011\times {10}^{20}\text{ neutron } \\ =24.088\times {10}^{20}\text{ neutrons } \end{gathered}$$