# Atomic mass constant

In physics and chemistry, the atomic mass constant, mu, is one twelfth of the mass of an unbound atom of carbon-12 at rest and in its ground state.[1] It serves to define the atomic mass unit and is, by definition, equal to 1 u. The 2010 CODATA recommended value is 1.660538921(73)×10−27 kg [2][3].

In practice, the atomic mass constant is determined as the ratio of the electron rest mass me to the electron relative atomic mass Ar(e) (that is, the mass of the electron on a scale where 12C = 12).[4] The relative atomic mass of the electron can be measured in cyclotron experiments, while the rest mass of the electron can be derived from other physical constants.

$m_{\rm u} = \frac{m_{\rm e}}{A_{\rm r}({\rm e})} = \frac{2R_\infty h}{A_{\rm r}({\rm e})c\alpha^2}$

The current uncertainty in the value of the atomic mass constant – one part in 20 million – is almost entirely due to the uncertainty in the value of the Planck constant.

## Energy equivalents

The atomic mass constant can also be expressed as its energy equivalent, that is muc2. The 2010 CODATA recommended values are:

1.492417954(66)×10−10 J [5][3]
931.494061(21) MeV [6][3]

The megaelectronvolt (MeV) is commonly used as a unit of mass in particle physics, and these values are also important for the practical determination of relative atomic masses. Although relative atomic masses are defined for neutral atoms, they are measured (by mass spectrometry) for ions: hence, the measured values must be correct for the mass of the electrons that were removed to form the ions, and also for the mass equivalent of the electron binding energy, Eb/muc2. The total binding energy of the six electrons in a carbon-12 atom is 1030.1089 eV = 1.650 4163×10−16 J: Eb/muc2 = 1.105 8674×10−6, or about one part in 10 million of the mass of the atom.[7]