Relative Atomic Mass

Summary: The weighted average mass of an element’s naturally occurring isotopes on a scale where one atom of carbon-12 is exactly 12, calculated as Ar = Σ(isotope mass × fractional abundance). Tags: igcse chemistry Created: 2026-07-18

Relative atomic mass (Ar) is the average mass of the naturally occurring atoms of an Element, measured on a scale in which the mass of one atom of carbon-12 (¹²₆C) is defined as exactly 12 — that is, all masses are compared to 1/12 of the mass of a carbon-12 atom. It is an average because most elements exist as a mixture of isotopes, each with its own mass number and natural abundance, so the Ar reflects both how heavy each isotope is and how common it is. This weighting explains why many Ar values on the Periodic Table are not whole numbers: chlorine, a roughly 3:1 mixture of chlorine-35 and chlorine-37, has an Ar of 35.5 even though no individual chlorine atom has that mass. Being a ratio of masses, Ar has no units, and it is the foundation of all quantitative chemistry — it feeds directly into Relative Molecular Mass and the mole calculations covered in Relative Masses and Moles. Interpreting the isotope data used in these calculations relies on Nuclide Notation and the ideas in Atomic Structure.

Definition and Formula

Relative atomic mass (Ar) is the average mass of naturally occurring atoms of an element on a scale where the carbon-12 atom has a mass of exactly 12 units. Equivalently, it is the average atomic mass compared with 1/12 of the mass of a carbon-12 atom.

For an element with several isotopes:

$A_r=\sum (\text{isotope mass}\times \text{fractional abundance})$

where the fractional abundance is the percentage abundance divided by 100 (so all fractions sum to 1). An equivalent form using percentages is:

$A_r=\frac{\sum (\text{isotope mass}\times \%\text{ abundance})}{100}$

At IGCSE level the mass of each isotope is taken to be its mass number.

Chlorine Example

Naturally occurring chlorine contains two isotopes:

$A_r(\text{Cl})=(35\times 0.75)+(37\times 0.25)=26.25+9.25=35.5$

The result, 35.5, lies between 35 and 37 but closer to 35 because chlorine-35 is three times more abundant. A quick sanity check for any Ar calculation is that the answer must fall between the lightest and heaviest isotope masses, weighted towards the more abundant one.

Further Examples

The same method extends to any number of isotopes: multiply each mass by its fractional abundance and add the results.

Isotopes and Chemical Properties

Isotopes of the same element have the same chemical properties because they have the same electronic configuration — the same number of electrons arranged in the same electron shells, and in particular the same number of valence electrons, which govern bonding and reactivity. They differ only in neutron number, which affects mass but not chemistry. This is why a single Ar value can be used for an element in Reacting Masses and other calculations even though its atoms are a mixture of isotopes: chlorine-35 and chlorine-37 form identical compounds in identical ratios, differing only in physical properties such as density and rate of Diffusion that depend on mass.

Sources

• Cambridge IGCSE Chemistry 0620 Syllabus (2023-2025) — Section 2.3 Supplement 3–4, Cambridge Assessment International Education

Common Misconceptions