The relative atomic mass, often referred to as atomic weight, is a dimensionless physical quantity that represents the average mass of atoms of a particular element. This value is determined by the relative abundance of the different isotopes of that element.

The formula for calculating the relative atomic mass can be expressed as the sum of the product of the isotope abundance and the isotope mass number for all isotopes of the element. Specifically, the calculation can be described mathematically as:

To clarify these concepts further, let’s break down the terms involved. An isotope is a variant of a chemical element that has the same number of protons but a different number of neutrons, resulting in different mass numbers. The isotope abundance refers to the proportion or percentage of each isotope present naturally in a sample of the element. The isotope mass number is the total count of protons and neutrons in the nucleus of a specific isotope.

To calculate the relative atomic mass of an element, you multiply the isotope abundance of each isotope by its respective mass number, and then sum these products. This process yields a weighted average that accounts for both the mass numbers of the isotopes and their natural abundance.

For instance, consider chlorine, which has two primary isotopes: Cl-35 and Cl-37. If we assume that $75\%$ of chlorine atoms are Cl-35 and $25\%$ are Cl-37, we can calculate the relative atomic mass as follows:

This result indicates that, on average, a chlorine atom has a mass close to $35.5$ atomic mass units.

It is important to note that the relative atomic mass is a dimensionless quantity. This means it has no units, as it serves as a comparison or ratio of the average mass of one atom of an element to one-twelfth of the mass of an atom of carbon-12.