Mass number is the total number of protons and neutrons in one particular atom, so it is always a whole number. Relative atomic mass is the weighted mean mass of all the atoms of an element, taking account of how common each isotope is — which is why it is often not a whole number.
What is mass number?
The mass number, symbol A, counts the particles in the nucleus of a single atom:
mass number = number of protons + number of neutrons
Because you cannot have half a proton or half a neutron, a mass number is always a whole number. It belongs to one specific atom, or to one isotope of an element.
Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons. Chlorine, for example, exists as chlorine-35 (17 protons, 18 neutrons) and chlorine-37 (17 protons, 20 neutrons). Those two numbers, 35 and 37, are mass numbers.
What is relative atomic mass?
The relative atomic mass, symbol Ar, is the average mass of the atoms of an element, compared with one twelfth of the mass of a carbon-12 atom — and crucially it is a weighted average, so a more abundant isotope counts for more.
A real sample of chlorine is not made of chlorine-35 atoms alone. It is roughly 75% chlorine-35 and 25% chlorine-37. A single average value has to represent that mixture, so it lands between 35 and 37, closer to 35 because chlorine-35 is the more common isotope. That value is 35.5.
How do the two compare?
| Mass number (A) | Relative atomic mass (Ar) | |
|---|---|---|
| What it describes | One atom of one isotope | All the atoms of an element, as a mixture |
| How it is found | Count protons + neutrons | Weighted mean of the isotope masses |
| Whole number? | Always | Usually not |
| Appears on the periodic table? | No | Yes — the larger of the two numbers |
| Example for chlorine | 35 and 37 | 35.5 |
| Used for | Working out neutrons, writing isotope symbols | Calculating Mr, moles and reacting masses |
The most useful line in that table is the fourth. The bigger number printed beside an element on the periodic table is the relative atomic mass, not the mass number, and calling it the mass number is the single most common slip in this topic.
How do you calculate relative atomic mass from abundances?
Multiply each isotope's mass number by its percentage abundance, add the results, then divide by 100:
$$A_r = \frac{\sum (\text{mass number} \times \text{percentage abundance})}{100}$$
Worked example — chlorine. Chlorine is 75% chlorine-35 and 25% chlorine-37.
Ar = (75 × 35 + 25 × 37) ÷ 100 Ar = (2625 + 925) ÷ 100 Ar = 3550 ÷ 100 = 35.5
Worked example — boron. Boron is 20% boron-10 and 80% boron-11.
Ar = (20 × 10 + 80 × 11) ÷ 100 Ar = (200 + 880) ÷ 100 Ar = 1080 ÷ 100 = 10.8
Worked example — three isotopes. Magnesium is 79% magnesium-24, 10% magnesium-25 and 11% magnesium-26.
Ar = (79 × 24 + 10 × 25 + 11 × 26) ÷ 100 Ar = (1896 + 250 + 286) ÷ 100 Ar = 2432 ÷ 100 = 24.32, which rounds to 24.3
A quick sanity check every time: the answer must sit between the smallest and largest isotope mass, and nearer the mass of the most abundant one. If your answer for chlorine came out as 36, or as 40, you have made an arithmetic error.
Where does the difference actually matter?
Finding the number of neutrons. Neutrons = mass number − atomic number. You must use the mass number of a specific isotope, not the relative atomic mass. Chlorine-35 has 35 − 17 = 18 neutrons. Using 35.5 would suggest 18.5 neutrons, which is impossible — a good demonstration of why the two quantities are not interchangeable.
Calculating relative formula mass (Mr) and moles. Here you use relative atomic mass, because you are working with real samples containing the natural mixture of isotopes. The Mr of NaCl is 23 + 35.5 = 58.5, not 58.
Writing isotope symbols. The notation places the mass number above the atomic number, so ³⁵Cl and ³⁷Cl describe two specific isotopes.
Why are most relative atomic masses close to whole numbers?
Because most elements have one isotope that is overwhelmingly the most common. Carbon is about 99% carbon-12, so its Ar of 12.011 is usually rounded to 12 at GCSE. Chlorine is the classic exception, with two isotopes in a roughly 3:1 ratio, so its Ar of 35.5 sits noticeably between whole numbers. Bromine is another, at 79.9, because bromine-79 and bromine-81 are present in almost equal amounts.
Common mistakes to avoid
- Calling the periodic table's larger number the mass number. It is the relative atomic mass.
- Using Ar to find neutrons. Use the mass number of the isotope named in the question.
- Forgetting to divide by 100 at the end of a weighted-mean calculation.
- Averaging the isotope masses without weighting them. For chlorine that would give (35 + 37) ÷ 2 = 36, which ignores the abundances entirely.
- Confusing atomic number with mass number. Atomic number counts protons only, and it is what defines the element.
Frequently asked questions
Does relative atomic mass have units?
No. It is a relative quantity — a ratio of one mass to another — so the units cancel out. Relative atomic mass compares the average mass of an element's atoms with one twelfth the mass of a carbon-12 atom, which is why carbon-12 has a value of exactly 12 and why the whole scale has no units attached. The same applies to relative formula mass.
If abundances are given as decimals or fractions rather than percentages, does the method change?
The method is the same — multiply each isotope mass by its abundance and add — but the final division changes. If abundances are given as percentages, divide by 100. If they are given as decimals adding to 1 (such as 0.75 and 0.25), no division is needed, because the weights already sum to one. If they are given as raw counts of atoms, divide by the total number of atoms. In every case you are dividing by the sum of the weights.
Can two different elements have the same mass number?
Yes. Argon-40 and calcium-40 both have a mass number of 40, but argon has 18 protons and calcium has 20, so they are entirely different elements with different chemistry. What identifies an element is its atomic number — its proton count — never its mass number. This is also why the periodic table is ordered by atomic number.
Do isotopes of the same element react differently?
Chemically they behave essentially identically, because chemical reactions involve electrons, and isotopes of an element have the same number of electrons arranged in the same way. The extra neutrons change the mass of the atom and can make some isotopes unstable and radioactive, but they do not change which reactions the atom takes part in. That is why an element's chemical properties can be discussed without specifying an isotope.
For Socratic GCSE chemistry with Professor Curie — who builds the picture of the atom before reaching for any formula — visit aitutors.me.