The atomic mass on the periodic table is almost never a whole number — carbon is 12.01, chlorine is 35.45. That's strange, since protons and neutrons each have a mass of about 1 unit. The reason is that not all atoms of an element are identical: they can have different numbers of neutrons, and the periodic table reports the average mass of a natural sample. Knowing which isotopes an element has, and how common each one is, matters well beyond the exam: it is how nuclear reactors are fuelled, how hospitals image organs, and how archaeologists date bones. In this lesson you will learn to read isotope notation, count the particles in any atom or ion, and calculate an average atomic mass in both directions.
Protons, neutrons, and isotopes
- Atomic number () = number of protons. This defines the element — change it and you change the element.
- Mass number () = number of protons + number of neutrons. This is a whole number, unique to each isotope.
- Isotopes are atoms of the same element (same , same protons) with different numbers of neutrons (different ).
| Isotope | Protons | Neutrons | Natural abundance | Stable? |
|---|---|---|---|---|
| Hydrogen-1 (protium) | 1 | 0 | ≈ 99.98% | Yes |
| Hydrogen-2 (deuterium) | 1 | 1 | ≈ 0.02% | Yes |
| Hydrogen-3 (tritium) | 1 | 2 | Trace | No — radioactive |
| Carbon-12 | 6 | 6 | ≈ 98.9% | Yes |
| Carbon-13 | 6 | 7 | ≈ 1.1% | Yes |
| Carbon-14 | 6 | 8 | Trace | No — radioactive |
Why do isotopes behave the same chemically? Reactions are about electrons being shared or transferred, and every isotope of an element has the same number of protons, so the same number of electrons arranged the same way. Neutrons add mass but no charge, so they change mass-dependent physical properties only slightly. Heavy water, , made with deuterium, is about 11% denser than ordinary water and boils at about 101.4 °C. Ontario's CANDU nuclear reactors use heavy water to slow neutrons down. Some isotopes have unstable nuclei and break down over time, giving off radiation — these are radioisotopes. Carbon-14 is used to date once-living material, cobalt-60 (produced in Ontario reactors) sterilizes medical equipment and treats cancer, and technetium-99m is the most widely used tracer in medical imaging.
Weighted average atomic mass
Because isotopes of an element have (almost) identical chemical behaviour — chemistry is controlled by electrons, not neutrons — a natural sample of any element is a mix of its isotopes in fixed proportions. The periodic table's atomic mass is a weighted average of all naturally occurring isotopes, weighted by how abundant (common) each one is.
This also means the average atomic mass will always be closer to the mass of the more abundant isotope. For chlorine (75.77% Cl-35, 24.23% Cl-37), the average of 35.45 sits much closer to 35 than to 37 — because Cl-35 is far more common.
Why multiply by the fraction? Picture a sample of exactly 100 chlorine atoms. About 76 of them have a mass near 35 and about 24 have a mass near 37. The total mass is , and dividing by 100 atoms gives an average of about 35.5 per atom. Multiplying by 0.76 and 0.24 is the same calculation done in one step. A simple average of 35 and 37 would give 36, which is wrong because it pretends the two isotopes are equally common. Atomic masses are measured in atomic mass units (u), defined so that one carbon-12 atom has a mass of exactly 12 u. A proton or a neutron has a mass of about 1 u, which is why mass numbers and isotope masses are so close.
Working backward: finding the abundance
Exam questions come in two directions, and you should recognise which one you face before you calculate. If you are given every isotope's mass and abundance, multiply and add (forward). If you are given the average atomic mass and must find an abundance, you have an unknown: for two isotopes, let one fractional abundance be and the other , because the fractions must add to 1. Substitute into the weighted-average equation and solve. With three isotopes and one unknown abundance, first subtract the known percents from 100%. Always sanity-check: the answer must be between 0% and 100%, and the more abundant isotope must be the one whose mass is nearer the average.