Atomic mass constant in the context of Standard atomic weight

The standard atomic weight of a chemical element (symbol A_r°(E) for element "E") is the weighted arithmetic mean of the relative isotopic masses of all isotopes of that element weighted by each isotope's abundance on Earth. For example, isotope Cu (A_r = 62.929) constitutes 69% of the copper on Earth, the rest being Cu (A_r = 64.927), so

Relative isotopic mass is dimensionless, and so is the weighted average. It can be converted into a measure of mass (with dimension M) by multiplying it with the atomic mass constant dalton.

The molecular mass (m) is the mass of a given molecule, often expressed in units of daltons (Da). Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The derived quantity relative molecular mass is the unitless ratio of the mass of a molecule to the atomic mass constant (which is equal to one dalton).

The molecular mass and relative molecular mass are distinct from but related to the molar mass. The molar mass is defined as the mass of a given substance divided by the amount of the substance, and is expressed in grams per mole (g/mol). That makes the molar mass an average of many particles or molecules (weighted by abundance of the isotopes), and the molecular mass the mass of one specific particle or molecule. The molar mass is usually the more appropriate quantity when dealing with macroscopic (weigh-able) quantities of a substance.

Atomic mass (m_a or m) is the mass of a single atom. The atomic mass mostly comes from the combined mass of the protons and neutrons in the nucleus, with minor contributions from the electrons and nuclear binding energy. 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 mass defect (explained by mass–energy equivalence: E = mc).

Atomic mass is often measured in dalton (Da) or unified atomic mass unit (u). One dalton is equal to ⁠+1/12⁠ the mass of a carbon-12 atom in its natural state, given by the atomic mass constant m_u = m(C)/12 = 1 Da, where m(C) is the atomic mass of carbon-12. Thus, the numerical value of the atomic mass of a nuclide when expressed in daltons is close to its mass number.

Relative atomic mass (symbol: A_r; sometimes abbreviated RAM or r.a.m.), also known by the deprecated synonym atomic weight, is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical element in a given sample to the atomic mass constant. The atomic mass constant (symbol: m_u) is defined as being ⁠1/12⁠ of the mass of a carbon-12 atom. Since both quantities in the ratio are masses, the resulting value is dimensionless. These definitions remain valid even after the 2019 revision of the SI.

For a single given sample, the relative atomic mass of a given element is the weighted arithmetic mean of the masses of the individual atoms (including all its isotopes) that are present in the sample. This quantity can vary significantly between samples because the sample's origin (and therefore its radioactive history or diffusion history) may have produced combinations of isotopic abundances in varying ratios. For example, due to a different mixture of stable carbon-12 and carbon-13 isotopes, a sample of elemental carbon from volcanic methane will have a different relative atomic mass than one collected from plant or animal tissues.