Question

Express unified atomic mass$\left(\mathrm{a}.\mathrm{m}.\mathrm{u}\right)$ unit in $\mathrm{kg}$.

Answer 1

Step 1: Number of Carbon atoms in one mole Carbon

The molecular mass of the carbon is $12\mathrm{g}$

Avogadro's number ' $6.02\times {10}^{23}$ ' is the number of atoms in one mole of any substance.

The number of atoms present in $12\mathrm{g}$ of Carbon $\left({}_6{}^{12}\mathrm{C}\right)$ is $6.02\times {10}^{23}$.

Step 2: Mass of one Carbon atom

To find the mass of one carbon atom$\left(\mathrm{m}\right)$, divide the Molecular mass of carbon by the total number of atoms present.

$$\begin{gathered} \mathrm{m}=\frac{12}{6.02\times {10}^{23}} \\ =1.99\times {10}^{-23}g \end{gathered}$$

Step 3: Unified atomic mass$\left(\mathrm{a}.\mathrm{m}.\mathrm{u}\right)$

The ${\frac{1}{12}}^{\mathrm{th}}$mass of a Carbon$\left({\mathrm{C}}^{12}\right)$ atom is equal to one unified atomic mass unit$\left(\mathrm{a}.\mathrm{m}.\mathrm{u}\right)$.

$$\begin{gathered} 1\mathrm{a}.\mathrm{m}.\mathrm{u}=\frac{1}{12}\times 1.99\times {10}^{-23} \\ =1.66\times {10}^{-24}\mathrm{g} \end{gathered}$$

To convert 'gram$\left(\mathrm{g}\right)$' into 'kilogram$\left(\mathrm{kg}\right)$' multiply it with${10}^{-3}$.

That is,

$1.66\times {10}^{-24}\times {10}^{-3}=1.66\times {10}^{-27}\mathrm{kg}$

Therefore, the Unified atomic mass$\left(\mathrm{a}.\mathrm{m}.\mathrm{u}\right)$ unit in $\mathrm{kg}$ is $1.66\times {10}^{-27}\mathrm{kg}$.