# In atomic mass units, what is the mass of an electron?

Oct 20, 2015

$5.4858 \cdot {10}^{- 4} \text{u}$

#### Explanation:

The mass of an electron is listed as being equal to

${m}_{\text{electron" = 9.10938356 * 10^(-31)"kg}}$

The unified atomic mass unit, or $u$, is defined as the mass of one nucleon, that is a proton or a neutron. More specifically, one unified atomic mass unit is equal to $\frac{1}{12} \text{th}$ of the mass of a carbon-12 atom.

A carbon-12 atom has six protons and six neutrons in its nucleus and a molar mass of $\text{12.0 g/mol}$. This means that you can find the value of $u$ in kilograms by using Avogadro's number

$12.0 \text{g"/color(red)(cancel(color(black)("mol"))) * (1color(red)(cancel(color(black)("mole"))))/(6.022 * 10^(23)"atoms") = 1.992693457 * 10^(-23)"g/atom}$

Since you need $\frac{1}{12} \text{th}$ of the mass of a single carbon-12 atom, it follows that you have

1/12 * 1.992693457 * 10^(-23)color(red)(cancel(color(black)("g"))) * "1 kg"/(10^3color(red)(cancel(color(black)("g")))) ~~ 1.660538922 * 10^(-27)"kg"

Therefore, you have

$\text{1 u" = 1.660538922 * 10^(-27)"kg}$

This means that the mass of an electron expressed in unified atomic mass units will be equal to

9.10938356 * 10^(-31)color(red)(cancel(color(black)("kg"))) * "1 u"/(1.660538922 * 10^(-27)color(red)(cancel(color(black)("kg")))) = 5.4858 * 10^(-4)"u"