The total mass of neutrons in 7 mg of ¹⁴C is  $4.0354\times {10}^{-\mathrm{x}} \mathrm{kg}$.

Determine the value of x.

$7 \mathrm{mg}=7\times {10}^{-3} \mathrm{g}$

Molar mass of 14C is 14 g/mol and moles present in $7\times {10}^{-3 }\mathrm{g}$ is:

$\mathrm{Moles}=\frac{7\times {10}^{-3} \mathrm{g}}{14 \mathrm{g}/\mathrm{mol}}=5\times {10}^{-4} \mathrm{mol}$

There are 8 neutrons in ¹⁴C:

$\mathrm{Number} \mathrm{of} \mathrm{neutrons}=8\times 5\times {10}^{-4} \mathrm{mol}\times 6.023\times {10}^{23} {\mathrm{mol}}^{-1}=2.4092\times {10}^{21}$

Mass present in $2.4092\times {10}^{21}$neutrons

$$\begin{gathered} \text{ Mass of one neutron }=1.675\times {10}^{-27}\mathrm{kg} \\ =1.675\times {10}^{-27}\times 2.4088\times {10}^{21} \\ =4.0354\times {10}^{-6} \mathrm{kg} \end{gathered}$$