Atomic mass

Stylized lithium-7 atom: 3 protons, 4 neutrons, and 3 electrons (total electrons are ~​14300th of the mass of the nucleus). It has a mass of 7.016 Da. Rare lithium-6 (mass of 6.015 Da) has only 3 neutrons, reducing the atomic weight (average) of lithium to 6.941.

The atomic mass (ma or m) is the mass of an atom. Although the SI unit of mass is kilogram (symbol: kg), the atomic mass is often expressed in the non-SI unit dalton (symbol: Da, or u) where 1 dalton is defined as ​112 of the mass of a single carbon-12 atom, at rest.[1] The protons and neutrons of the nucleus account for nearly all of the total mass of atoms, with the electrons and nuclear binding energy making minor contributions. Thus, the atomic mass measured in Da has nearly the same value as the mass number. Conversion between mass in kg and mass in Da can be done using the atomic mass constant ${\displaystyle m_{\rm {u}}={{m({\rm {^{12}C}})} \over {12}}=1\ {\rm {Da}}}$.

The formula used for conversion is:[2][3]

${\displaystyle 1\ {\rm {Da}}=m_{\rm {u}}={M_{\rm {u}} \over {N_{\rm {A}}}}={M(^{12}C) \over {12\ N_{\rm {A}}}}=1.66053906660(50)\cdot 10^{-27}\ {\rm {kg}}}$

where ${\displaystyle M_{\rm {u}}}$ is the molar mass constant, ${\displaystyle N_{\rm {A}}}$ is the Avogadro constant and ${\displaystyle M(^{12}C)}$ is the experimentally determined molar mass of carbon-12.

The relative isotopic mass (see section below) can be obtained by dividing the atomic mass ma of an isotope by the atomic mass constant mu yielding a dimensionless value. Thus, the atomic mass of a carbon-12 atom is 12 Da (or 12 u), but the relative isotopic mass of a carbon-12 atom is simply 12. The sum of relative isotopic masses of all atoms in a molecule is the relative molecular mass.

The atomic mass of an isotope and the relative isotopic mass refers to a certain specific isotope of an element. Because usually substances are not isotopially pure, it is convenient to use the elemental atomic mass which is the average (mean) atomic mass of an element, weighted by the abundance of the isotopes. The dimensionless (standard) atomic weight is the weighted mean relative isotopic mass of a (typical naturally-occurring) mixture of isotopes.

The atomic mass of atoms, ions, or atomic nuclei is slightly less than the sum of the masses of their constituent protons, neutrons, and electrons, due to binding energy mass loss (as per E = mc2).[4]

Relative isotopic mass

Relative isotopic mass (a property of a single atom) is not to be confused with the averaged quantity atomic weight (see above), that is an average of values for many atoms in a given sample of a chemical element.

While atomic mass is an absolute mass, relative isotopic mass is a dimensionless number with no units. This loss of units results from the use of a scaling ratio with respect to a carbon-12 standard, and the word "relative" in the term "relative isotopic mass" refers to this scaling relative to carbon-12.

The relative isotopic mass, then, is the mass of a given isotope (specifically, any single nuclide), when this value is scaled by the mass of carbon-12, where the latter has to be determined experimentally. Equivalently, the relative isotopic mass of an isotope or nuclide is the mass of the isotope relative to 1/12 of the mass of a carbon-12 atom.

For example, the relative isotopic mass of a carbon-12 atom is exactly 12. For comparison, the atomic mass of a carbon-12 atom is exactly 12 daltons. Alternately, the atomic mass of a carbon-12 atom may be expressed in any other mass units: for example, the atomic mass of a carbon-12 atom is about 1.998467052×10−26 kg.

As is the case for the related atomic mass when expressed in daltons, the relative isotopic mass numbers of nuclides other than carbon-12 are not whole numbers, but are always close to whole numbers. This is discussed more fully below.