Question

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

Answer 1

`5.4858 * 10^(-4)"u"`

Explanation:

The mass of an electron is listed as being equal to

`m_"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 `1/12"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 `"12.0 g/mol"`. This means that you can find the value of `u` in kilograms by using Avogadro's number

`12.0"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 `1/12"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

`"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"`