What is relative atomic mass?

AQA's GCSE Chemistry specification puts it simply: the relative atomic mass of an element is an average value that takes account of the abundance of the isotopes of the element. It is the number shown on the periodic table, usually the larger of the two numbers for each element.

Relative atomic mass definition

At A-level, the definition is more exact. Relative atomic mass is the weighted mean mass of an atom of an element, compared with one twelfth of the mass of an atom of carbon-12:

Because it divides one mass by another, the units cancel, so relative atomic mass has no units. IUPAC also calls it the atomic weight. Carbon-12 was chosen as the standard, and one twelfth of its mass is the atomic mass unit.

Why isn't relative atomic mass a whole number?

Most elements are a mixture of isotopes: atoms of the same element whose nuclei hold different numbers of neutrons, which gives them different masses. Chlorine is a mixture of chlorine-35 and chlorine-37. The relative atomic mass is an average of the two, weighted by how common each one is, so it falls between them, nearer to the more common one. That is why chlorine's A_r is 35.5, even though no single chlorine atom has a mass of 35.5.

How to calculate relative atomic mass

Multiply each isotope's mass by its percentage abundance, add the results, then divide by 100:

Example 1: chlorine

Chlorine is about 75% chlorine-35 and 25% chlorine-37.

Example 2: copper

Copper has two isotopes: copper-63 (69%) and copper-65 (31%). A_r = (63 × 69 + 65 × 31) ÷ 100 = (4,347 + 2,015) ÷ 100 = 63.62. The periodic table gives 63.5, slightly lower, because the precise values use the isotopes' exact masses rather than their mass numbers, and more exact abundances.

Example 3: three isotopes

Magnesium is 78.99% magnesium-24, 10.00% magnesium-25 and 11.01% magnesium-26. A_r = (24 × 78.99 + 25 × 10.00 + 26 × 11.01) ÷ 100 = 24.32. The method is the same however many isotopes there are.

Try one yourself, then press Mark to check it in our Atomic Structure course.

Example 4: working backwards to an abundance

An element has two isotopes with masses 69 and 71, and its A_r is 69.8. What percentage is the lighter isotope? Call its fraction x, so the other is 1 − x.

So 71 − 2x = 69.8, which gives 2x = 1.2 and x = 0.6. The lighter isotope makes up 60%, and the heavier one 40%. A quick check: 69.8 is nearer 69 than 71, so the lighter isotope should be the more common one.

Relative atomic mass from a mass spectrum (A-level)

A mass spectrometer measures the masses of an element's isotopes and how common each is. The spectrum shows a peak for each isotope: its position on the horizontal axis is the mass-to-charge ratio (m/z), which equals the isotope's mass for ions with a 1+ charge, and its height is the relative abundance. To find A_r, multiply each m/z by its abundance, add them, and divide by the total abundance. If the abundances are given as peak heights rather than percentages, divide by the sum of the heights, not by 100.

Where the values on the periodic table come from

An international committee, the IUPAC Commission on Isotopic Abundances and Atomic Weights, reviews the measurements and publishes the standard atomic weights that periodic tables use. For a few elements, such as hydrogen, carbon and chlorine, the mix of isotopes varies slightly depending on where a sample comes from, so the commission gives a range rather than one number. School periodic tables round these to a single convenient value, like 35.5 for chlorine.

Relative atomic mass and relative formula mass

Add the relative atomic mass of every atom in a formula and you get the relative formula mass, M_r. For water, H₂O, M_r = 2 × 1 + 16 = 18. Our guides to relative formula mass and the mole take this further, and the Molar Mass Calculator does the adding for any formula.

Common mistakes

• Taking a plain average of the isotope masses. Weight each one by its abundance.
• Forgetting to divide by 100 when abundances are percentages, or by the total when they are peak heights.
• Confusing A_r with mass number. Mass number belongs to one atom and is a whole number. A_r is an average.
• Giving units. Relative atomic mass has none. Molar mass, in g/mol, has the same number but does have units.
• An answer outside the isotope range. A_r must lie between the lightest and heaviest isotope masses.

Read next

Chemistry · Atoms and the periodic tableRelative isotopic mass: definition and examplesRelative isotopic mass for A-level Chemistry: the carbon-12 definition, how it differs from mass number and relative atomic mass, and mass spectra.