Question

$1$ unified atomic mass unit is equal to?

Answer 1

Step 1: Given data

$1$ unified atomic mass unit.

• $1$ unified atomic mass unit is a unit of atomic and molecular mass.
• It is one-twelfth of the mass of an unbound carbon-$12$ atom, at rest and in the ground state.

Step 2: Formula used

The relationship between the unified atomic mass unit and kilogram(kg) is given by the following formula:

$$\begin{gathered} \mathrm{unified}\mathrm{atomic}\mathrm{mass}=\frac{1}{\mathrm{Avagadro}\text{'}\mathrm{s}\mathrm{Number}\left({\mathrm{N}}_{\mathrm{A}}\right)} \\ \Rightarrow 1\mathrm{u}=\frac{1}{{\mathrm{N}}_{\mathrm{A}}}\mathrm{kg} \end{gathered}$$

where the value of Avagadro's number is $6.02214179\times {10}^{23}$.

Step 3: Calculation of 1 unified atomic mass unit

Calculate the value of 1 unified mass unit by putting the value of the Avagadro's Number into the formula:

$$\begin{gathered} 1\mathrm{u}=\frac{1}{6.02214179\times {10}^{23}} \\ =1.66\times {10}^{-24}\mathrm{g} \\ =1.66\times {10}^{-27}\mathrm{kg} \end{gathered}$$

Hence $1$unified mass unit is equal to $1.66\times {10}^{-27}\mathrm{kg}$.