How to explain isotopes and relative atomic mass

Two ideas in the atomic structure chapter are joined at the hip, and understanding one makes the other obvious: isotopes and relative atomic mass. Once you see that relative atomic masses are averages, and that they are averages precisely because isotopes exist, a whole set of exam marks opens up. This guide explains both in plain terms and then shows the calculation step by step.

What an isotope is

Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. Because the proton number (the number of protons, which defines the element) is the same, they are the same element and sit in the same place on the Periodic Table. But because the neutron number differs, their nucleon number, the total of protons and neutrons, also called the mass number, is different, so they have slightly different masses.

Chlorine is the standard example. Chlorine-35 has 17 protons and 18 neutrons; chlorine-37 has 17 protons and 20 neutrons. Both are chlorine, both have 17 electrons arranged 2.8.7, so both react in exactly the same way. Carbon behaves the same: carbon-12, carbon-13 and carbon-14 all have 6 protons but 6, 7 and 8 neutrons. You can revise the full definition and notation at our isotope glossary entry.

Why isotopes matter, same chemistry, different mass

This is the key exam point. Isotopes of an element have the same chemical properties, because chemical reactions involve electrons, and isotopes have identical electron arrangements. What differs is their physical properties, mass, and anything that depends on mass such as density and rate of diffusion, because the extra neutrons make one isotope heavier than the other. If a question asks why two isotopes react identically, the answer is always “same number of valence electrons / same electron arrangement.” If it asks why they differ physically, the answer is “different number of neutrons, so different mass.”

What relative atomic mass means

A real sample of chlorine is a mixture of chlorine-35 and chlorine-37 atoms. When we weigh a huge number of chlorine atoms, we are weighing a mixture, so the average mass per atom sits between 35 and 37. That average is the relative atomic mass.

Formally, the relative atomic mass (Ar) of an element is the average mass of one atom of the element compared with one-twelfth of the mass of one atom of carbon-12. Carbon-12 is the agreed standard, and comparing to one-twelfth of it means hydrogen comes out near 1 and oxygen near 16, which is why the numbers feel familiar. The term itself is defined at relative atomic mass.

This also answers a question students often ask: why is the relative atomic mass of chlorine 35.5 and not a whole number? Because it is an average of two isotopes weighted by how common each one is, no single chlorine atom has a mass of 35.5.

How to calculate relative atomic mass

Use the weighted-average method:

1. Write each isotope’s mass and its percentage abundance.
2. Multiply each mass by its percentage.
3. Add those products together.
4. Divide by 100.

Worked example, chlorine. A sample of chlorine contains 75% chlorine-35 and 25% chlorine-37. Find its relative atomic mass.

• Products: (35 × 75) + (37 × 25) = 2625 + 925 = 3550.
• Divide by 100: 3550 ÷ 100 = 35.5.

That is exactly the value printed on the Periodic Table, and now you know where it comes from.

A second worked example. Suppose a sample of copper contains 70% copper-63 and 30% copper-65. Then Ar = [(63 × 70) + (65 × 30)] ÷ 100 = (4410 + 1950) ÷ 100 = 6360 ÷ 100 = 63.6. The method never changes; only the numbers do. You can drill more of these at relative atomic mass calculation.

The mistakes to avoid

Three slips catch students out. First, confusing proton number and nucleon number, isotopes share the proton number and differ in nucleon number, never the other way round. Second, saying isotopes have different chemical properties; they do not, because chemistry is decided by electrons. Third, forgetting to divide by 100 at the end, which gives an answer a hundred times too big. A quick sanity check is that your answer must lie between the two isotope masses, 35.5 sits neatly between 35 and 37.

Isotopes and relative atomic mass sit early in Form 4 but feed directly into every mole calculation later, so it pays to make them solid now. You can see how they fit the wider topic on our matter and the atomic structure chapter page. If you would like a teacher to check your explanations are using the exact exam wording, our online one-to-one lessons with our experienced SPM Chemistry teachers give that feedback, from RM50 an hour with a paid one-hour trial.