The actual masses of atoms are far too small to use conveniently, so chemists compare them with a standard. This gives relative values that make isotope and element masses easier to describe.

The carbon-12 standard

Chemists need a consistent reference point when discussing atomic masses. Instead of writing extremely small masses in kilograms or grams for individual atoms, they compare atomic masses with a standard atom. The chosen standard is carbon-12.

A carbon-12 atom is assigned a mass of exactly 12 on the relative scale. All other atomic masses are then measured relative to one-twelfth of the mass of a carbon-12 atom.

Textbook figure/context explaining the atomic mass unit definition based on carbon-12, i.e., $1\ \mathrm{amu} = \frac{1}{12}$ of the mass of one $^{12}\mathrm{C}$ atom. This anchors the “carbon-12 scale” as a consistent reference for comparing isotopic masses and weighted mean atomic masses. Source

This means the scale is based on comparison, not on the direct mass of atoms in everyday units.

Because these values are relative, they do not have units such as g or kg. They are numbers that show how heavy an atom is compared with the carbon-12 reference.

Relative isotopic mass

Relative isotopic mass refers to the mass of a single atom of one particular isotope on this scale. It is important that this term applies to one isotope only, not to an element as a whole.

This definition focuses on one specific isotope, such as one isotope of chlorine, magnesium, or copper. Different isotopes of the same element have different relative isotopic masses because they contain different numbers of neutrons.

Relative isotopic mass is often close to the isotope’s mass number, but the two ideas are not identical. Mass number is simply the total number of protons and neutrons, so it is always a whole number. Relative isotopic mass is an experimentally measured comparison on the carbon-12 scale, so it is not always a whole number.

A common mistake is to treat relative isotopic mass as an average value for an element. It is not. It describes the mass of one isotope only.

Relative atomic mass

Most elements exist as a mixture of isotopes. Because of this, the value given for an element on the Periodic Table is usually not the mass of any one atom. Instead, it represents the average mass of the atoms of that element, taking account of the different isotopes present.

The phrase weighted mean is essential.

Mass spectrum of a chloroethane sample showing the two molecular-ion peaks produced by $^{35}\mathrm{Cl}$ and $^{37}\mathrm{Cl}$. The \sim3:1 peak-height ratio provides a direct visual cue that isotopes occur in different abundances, which is why the elemental average is weighted rather than a simple mean. Source

It means that each isotope contributes to the final value according to how abundant it is. An isotope present in a larger proportion has a greater effect on the relative atomic mass than an isotope present in a smaller proportion.

This is why relative atomic mass is often not a whole number. It is usually somewhere between the relative isotopic masses of the isotopes of that element. It may be closer to one isotope than another if that isotope is more abundant.

How weighted mean affects $A_r$

If all isotopes of an element were present in equal amounts, the relative atomic mass would lie halfway between their isotope masses only when there were two isotopes. In real samples, isotopes are rarely present in exactly equal proportions, so the value of $A_r$ depends on their abundances.

You should understand what this equation shows even when no calculation is required. The formula emphasizes that relative atomic mass is an average based on both isotope mass and isotope abundance.

The denominator allows for abundance values to be written as percentages or as other relative amounts. The key idea is that more abundant isotopes affect the final value more strongly.

Distinguishing the two terms

Students often confuse relative isotopic mass and relative atomic mass because both use the carbon-12 scale. The difference is the level being described.

• Relative isotopic mass describes one isotope.

• Relative atomic mass describes the overall element.

• Relative isotopic mass does not consider abundance.

• Relative atomic mass does consider abundance.

• Relative isotopic mass is linked to a specific atom type within an element.

• Relative atomic mass is the weighted mean value usually shown for the element in the Periodic Table.

When answering exam questions, look carefully for the words isotope, element, and weighted mean. These words usually show which term is required.