What Is the Relative Atomic Mass of an Atom? Ar and Mr Explained
The relative atomic mass of an atom (symbol Ar) tells you how heavy that element’s atoms are compared with one twelfth of a carbon-12 atom. It is an average, because almost every element is a mixture of isotopes with different masses, and the average is weighted by how common each isotope is. Carbon-12 was given the value of exactly 12, so everything else is measured against it. Ar has no units — it is a comparison, not a measurement.
That one paragraph answers the exam definition. But the definition is not what sends students to Google at eleven at night. These are:
- Why is the relative atomic mass of chlorine 35.5 when no chlorine atom actually weighs 35.5?
- What is the difference between relative atomic mass and mass number? They look like the same thing.
- What is the relative mass of a proton, a neutron and an electron, and why does the electron get ignored?
- What is Mr, and is relative formula mass the same as relative molecular mass?
- How do you work backwards — given Ar, find the abundances?
Most pages on this topic answer the first one and stop. This page answers all of them, with every number worked through so you can follow the arithmetic rather than trust it. There are four drawings, worked examples you can cover up and attempt yourself, a table of the Ar values you will actually be asked for, and the mistakes that cost marks on this topic every single year.
What “relative” actually means
Before any formula, sort out the word that causes the trouble: relative.
Atoms are far too small to put on a balance. A single carbon atom weighs about 0.00000000000000000000000002 kilograms. Nobody wants to write that down, and nobody wants to multiply by it. So chemists did what you would do if you had no ruler: they picked one thing, called it the standard, and measured everything else against it.
The thing they picked is the carbon-12 atom, and they sliced it into twelve. One of those twelfths is the unit. Here is the whole idea in one picture.
Scroll sideways to see the whole drawing
So when a data booklet says the relative atomic mass of magnesium is 24.3, it is saying: a magnesium atom is 24.3 times heavier than one twelfth of a carbon-12 atom. That is all. There is no gram, no kilogram and no “amu” in that sentence, because dividing a mass by a mass cancels the units out. A ratio has no units.
Relative atomic mass answers one question: how many times heavier than one twelfth of a carbon-12 atom?
Why carbon-12 and not hydrogen, which is lighter and would seem simpler? Hydrogen was the standard originally, and oxygen after that. The problem was that physicists and chemists were quietly using two slightly different oxygen scales and their numbers disagreed. In 1961 both sides agreed to switch to carbon-12: it is a single, common, stable isotope that is easy to get hold of and easy to measure in a mass spectrometer, and choosing 12 for it kept almost every existing value nearly unchanged. One scale, one set of numbers, argument over.
The definition, in plain words
Here is the version you write in an exam, and then the version that actually explains it.
The exam definition
The relative atomic mass of an element is the weighted mean mass of its atoms, relative to one twelfth of the mass of a carbon-12 atom.
What that sentence is saying
Take a normal sample of the element. Work out the average mass of its atoms, counting the common isotopes more heavily than the rare ones. Then divide by one twelfth of a carbon-12 atom.
Three words in that definition are doing all the work, and each one is worth a mark on its own.
- Weighted. Not a plain average. A 75–25 mixture does not sit in the middle; it sits three quarters of the way towards the common one. Write “average” instead of “weighted mean” and you can drop a mark.
- Mean mass of its atoms. Of all the atoms, across every isotope. This is why the answer is a decimal: no single atom has that mass, the mixture does.
- Relative to one twelfth of a carbon-12 atom. Leave this out and you have described an average mass, not a relative atomic mass. This is the clause students forget most often.
Why does relative atomic mass have no units?
Because it is one mass divided by another mass. Kilograms divided by
kilograms leaves you with a bare number, exactly as “twice as tall” has
no units. Writing Ar of chlorine = 35.5 g is
wrong and markers do take the mark off. You may see the symbol
u or the name atomic mass unit attached to
isotope masses in some textbooks — that is the actual mass of an
atom, a closely related but different quantity, and it is covered
further down.
One last piece of housekeeping, because it costs marks every year. The symbol is Ar: a capital A with a lower-case r, and the r is a subscript. Not “AR”, not “ar”, not “Ar” sitting on the line. The r stands for relative. In handwriting, drop the r below the line clearly — written on the line it reads as argon.
Why Ar is hardly ever a whole number
Look up chlorine in any data booklet and you get 35.5. That number bothers students, and it should, because of this:
The reason is isotopes. Atoms of the same element always have the same number of protons — that is what makes them that element — but they can carry different numbers of neutrons. Chlorine comes in two sorts: 35Cl, with 17 protons and 18 neutrons, and 37Cl, with 17 protons and 20 neutrons. Both are chlorine. Both react in exactly the same way. One is simply two neutrons heavier.
In any real sample of chlorine, roughly 75 per cent of the atoms are the light sort and 25 per cent are the heavy sort. That ratio is remarkably steady wherever on Earth you take your sample from. So “the mass of a chlorine atom” has no single answer, and the honest thing to quote is the average — weighted so that the common isotope counts for more.
Here is that average being built, one atom at a time.
Scroll sideways to see the whole drawing
Notice what would have gone wrong with a plain average. Adding 35 and 37 and halving gives 36, which is the answer you would get if the two isotopes were equally common. They are not. Three quarters of the atoms are light, so the true average sits three quarters of the way down towards 35. That is the whole meaning of the word weighted.
Plain average — wrong
(35 + 37) ÷ 2 = 36
Treats both isotopes as equally common. They are not.
Weighted mean — right
(35 × 75 + 37 × 25) ÷ 100 = 35.5
Counts each isotope as often as it actually turns up.
This also explains a pattern you can see across the whole periodic table. Where an element has one overwhelmingly dominant isotope, its Ar sits very close to a whole number: fluorine is 19.0, sodium is 23.0, phosphorus is 31.0, because those elements are effectively one isotope only. Where an element is a genuine mixture, the decimal appears: chlorine 35.5, copper 63.5, boron 10.8. A decimal in the data booklet is a signpost telling you the element has more than one common isotope.
Mass number is not relative atomic mass. The mass number of an isotope is a whole number — protons plus neutrons for that one particular atom, such as 35 for 35Cl. The relative atomic mass is the weighted average across the whole mixture, which is why it can be 35.5. If a question gives you a single isotope, use its mass number. If it gives you an element, use Ar.
The relative atomic mass formula
Everything above turns into one line. This is the relative atomic mass equation, and it is the only one you need for this topic.
Multiply every isotope’s mass by its percentage, add the lot up, divide by 100.
Some textbooks write the same thing with a sigma, as Ar = Σ(mass × abundance) ÷ 100. The Σ just means “add them all up”. It is the same instruction.
There is one version of the formula that is safer, and it is worth learning instead of the one above, because it also handles the questions where the abundances are not percentages:
This version never lets you down, whatever the question throws at you.
Why the second one is better: when abundances are given as percentages, “total number of atoms” is 100 and the two formulas are identical. But mass spectrometry questions often give abundances as peak heights in centimetres, or as plain ratios like 3 : 2, and then the total is not 100. Students who memorised “divide by 100” divide by 100 anyway and lose the question. Students who learned “divide by the total” simply add the numbers up and divide by that. There is more on this below.
Total mass, divided by total atoms. Learn that sentence and you can forget the rest.
How to work out relative atomic mass, step by step
Four steps, the same four every time, whether the element has two isotopes or six.
- List the isotopes with their masses and abundances. Write them in a column. Half the errors on this topic come from reading the wrong number out of the question.
- Multiply each mass by its abundance. One line per isotope. Do not round yet.
- Add those products together. This is the total mass of the whole sample.
- Divide by the total abundance. That is 100 if you were given percentages, or whatever the heights add up to if you were not.
Worked example 1 — bromine, two isotopes
Bromine exists as 79Br (50.7%) and 81Br (49.3%). Calculate the relative atomic mass of bromine to one decimal place.
Step 1 — list them
mass 79 → 50.7%
mass 81 → 49.3%
Step 2 — multiply each one
79 × 50.7 = 4005.3
81 × 49.3 = 3993.3
Step 3 — add them
4005.3 + 3993.3 = 7998.6
Step 4 — divide by the total abundance (100)
7998.6 ÷ 100 = 79.986
Ar(Br) = 80.0
Sense check: the two isotopes are almost equally common, so the answer should land almost exactly halfway between 79 and 81. It does.
Worked example 2 — neon, three isotopes
Three isotopes instead of two changes nothing except the number of lines. Students panic at this and they should not.
A sample of neon contains 90.5% 20Ne, 0.3% 21Ne and 9.2% 22Ne. Calculate the relative atomic mass of neon to one decimal place.
Step 2 — multiply each one
20 × 90.5 = 1810.0
21 × 0.3 = 6.3
22 × 9.2 = 202.4
Step 3 — add them
1810.0 + 6.3 + 202.4 = 2018.7
Step 4 — divide by 100
2018.7 ÷ 100 = 20.187
Ar(Ne) = 20.2
Sense check: 20Ne is the overwhelming majority, so the answer must sit very close to 20. It does. Notice also that the three percentages add to 100, which is a free check that you copied them correctly.
In the neon question, dividing by 3 because there are three isotopes gives 672.9, which is heavier than lead. The divisor is the total abundance, never the number of isotopes. If your answer does not sit between the lightest and the heaviest isotope mass, you have divided by the wrong thing.
When the numbers do not add up to 100
Relative atomic masses are measured on a mass spectrometer. The machine strips an electron off each atom to make a positive ion, accelerates the ions, and sorts them by mass. What comes out is a chart with a peak for each isotope. The position of a peak gives the mass. The height of a peak gives how common that isotope is.
The catch is that peak heights are measured in whatever units the chart uses — centimetres, millimetres, arbitrary units — and they do not have to add up to 100. This is exactly where “divide by the total” earns its keep.
The mass spectrum of gallium shows two peaks: one at m/z 69 of height 3.0 cm, and one at m/z 71 of height 2.0 cm. Calculate the relative atomic mass of gallium.
Total abundance = 3.0 + 2.0 = 5.0 (not 100)
69 × 3.0 = 207
71 × 2.0 = 142
207 + 142 = 349
Divide by the total, which is 5.0
349 ÷ 5.0 = 69.8
Ar(Ga) = 69.8
Divide by 100 here and you get 3.49, which is lighter than lithium. An answer that absurd is your warning that the divisor was wrong.
If you prefer to convert to percentages first, you can, and you get the same answer. The heights are in the ratio 3 : 2, so the first isotope is 3⁄5 of the sample, which is 60%, and the second is 2⁄5, which is 40%. Then (69 × 60 + 71 × 40) ÷ 100 = 6980 ÷ 100 = 69.8. Two routes, one answer. Use whichever you trust yourself with under pressure.
The horizontal axis of a mass spectrum is m/z, mass divided by charge, not mass. For the ordinary 1+ ions this makes no difference, because dividing by 1 changes nothing. But occasionally a 2+ ion forms, and it lands at half its real mass. A tiny peak at m/z 31.5 in a spectrum of copper is not a mystery isotope — it is 63Cu2+. GCSE questions will not do this to you. A-level ones will.
Working backwards: finding the abundance from Ar
This is the question that separates the grades, and it is the one almost no revision page covers. Instead of giving you the abundances and asking for Ar, the question gives you Ar and asks for the abundances.
The trick is that with two isotopes there is really only one unknown, not two. If x per cent of the atoms are the light isotope, then the rest — 100 − x — must be the heavy one. There is nowhere else for them to go. So you write the normal formula with x in it and solve.
Boron has two isotopes, 10B and 11B, and a relative atomic mass of 10.8. Calculate the percentage abundance of each isotope.
Let x = percentage of the light isotope, so (100 − x) is the heavy one
[10x + 11(100 − x)] ÷ 100 = 10.8
Multiply both sides by 100 to clear the fraction
10x + 11(100 − x) = 1080
Expand the bracket
10x + 1100 − 11x = 1080
Collect the x terms
−x + 1100 = 1080
−x = −20
x = 20
10B = 20% and 11B = 80%
Always check by putting the answer back in: (10 × 20 + 11 × 80) ÷ 100 = 1080 ÷ 100 = 10.8. It works, so the answer is right. That check takes fifteen seconds and catches every sign error.
The thirty-second shortcut
There is a much faster way, and once you see it you will never do the algebra again. Picture the two isotope masses as the two ends of a line, and Ar as a point somewhere along it. The closer Ar sits to one end, the more of that isotope there is. The fractions are simply the distances, swapped over.
Then the light isotope is whatever is left over.
Boron again: Ar is 10.8, the ends are 10 and 11. The gap from 10 up to 10.8 is 0.8, and the whole span is 1, so the heavy isotope is 0.8 of the sample, which is 80%, and the light one is 20%. Same answer, no algebra, one line of working.
Copper has two isotopes, 63Cu and 65Cu, and a relative atomic mass of 63.5. Find the abundance of each, using the shortcut.
gap from the light end: 63.5 − 63 = 0.5
whole span: 65 − 63 = 2
fraction of the heavy isotope: 0.5 ÷ 2 = 0.25
65Cu = 25% and 63Cu = 75%
Check: (63 × 75 + 65 × 25) ÷ 100 = 6350 ÷ 100 = 63.5. Correct.
One warning about the shortcut: it only works when the element has exactly two isotopes. With three or more there are two unknowns and the question has to give you one of them, at which point you are back to writing the full equation out. Read the question before you reach for the shortcut.
Relative mass of a proton, a neutron and an electron
This is a different question from the one above, and the two get muddled constantly. Relative atomic mass is about whole atoms of an element. Relative mass of a particle is about the three things an atom is built from. Same word, different scale.
The numbers here are worth memorising outright, because they turn up in the first question of almost every atomic structure paper.
Scroll sideways to see the whole drawing
| Particle | Relative mass | Relative charge | Where it is | Actual mass in kg |
|---|---|---|---|---|
| Proton | 1 | +1 | In the nucleus | 1.673 × 10−27 |
| Neutron | 1 | 0 | In the nucleus | 1.675 × 10−27 |
| Electron | 1⁄1836, about 0.0005 often written as “negligible” | −1 | In shells outside the nucleus | 9.11 × 10−31 |
Read the relative mass column and one fact jumps out. A proton and a neutron weigh essentially the same as each other, and an electron weighs almost nothing by comparison. Divide the proton’s mass by the electron’s and you get 1836. If a proton were a bag of sugar, the electron would be about half a grain of rice.
That single fact explains three things students are asked to justify:
- Why mass number counts only protons and neutrons. The electrons are there, but adding them in would change the total by less than a rounding error.
- Why nearly all of an atom’s mass is in the nucleus. Everything heavy is in there; the rest of the atom is electrons and empty space.
- Why an ion has virtually the same mass as its atom. A sodium ion has lost an electron, so it is lighter — by about 0.0005 out of 23. Nothing you could measure in a school lab.
If a question asks for the relative mass of a proton, the answer is 1. If it asks for the relative atomic mass of hydrogen, the answer is 1.0, and the reason it is so close to 1 is that a hydrogen-1 atom is one proton plus one almost weightless electron. They look like the same question and they are not. Watch for the words “atomic” and “of an atom”.
Relative charge, and why an atom has no overall charge
Charge works on exactly the same comparison trick as mass. The real charge on a proton is 1.60 × 10−19 coulombs, which is unpleasant to carry through a calculation, so chemists call that +1 and measure everything against it. An electron carries the same size of charge the other way, so it is −1. A neutron carries none, which is where its name comes from: it is neutral.
Now the question thousands of students type into Google every month: what is the overall charge of an atom?
Zero. An atom has no overall charge, because it contains the same number of protons as electrons. Every +1 is matched by a −1 and they cancel exactly. This is not a coincidence or an approximation — it is the definition of an atom. The moment the numbers stop matching, it is no longer an atom. It is an ion.
Work it through with sodium. A sodium atom has 11 protons, so it has 11 electrons. The charge is (+11) + (−11) = 0. Lose one electron and you have 11 protons against 10 electrons, giving +1: that is the Na+ ion. Gain one and you would be at −1. The charge on an ion is simply the protons-versus-electrons scoreboard.
Atom
protons = electrons
overall charge = 0
written as Na
Ion
protons ≠ electrons
overall charge = not 0
written as Na+ or Cl−
One thing to be careful about: the nucleus on its own is not neutral. It holds the protons and the neutrons, so its charge is positive and equal to the number of protons. A carbon nucleus has a charge of +6. It is the electrons outside, added in, that bring the whole atom to zero. Questions do ask for the charge on the nucleus specifically, and answering “zero” there costs the mark.
Atomic number, mass number and “relative atomic number”
Every periodic table square has two numbers on it, and knowing which is which is half of this topic. Here is the full set of terms, including the one that does not exist.
| Term | Symbol | What it counts | Whole number? |
|---|---|---|---|
| Atomic number also: proton number | Z | Protons. This is what decides which element it is | Always |
| Mass number also: nucleon number | A | Protons + neutrons, for one particular isotope | Always |
| Relative atomic mass | Ar | The weighted average mass across all the isotopes of the element | Usually not |
| Relative isotopic mass | — | The mass of one single isotope, on the same carbon-12 scale | Near enough, at this level |
| Relative atomic number | — | Nothing. There is no such quantity | Not a real term |
That last row is not a joke. “Relative atomic number” is not a thing in chemistry, and thousands of students search for it every month. It happens because two correct terms get spliced together. If you have been asked for it, the question almost certainly wants one of these two:
- Atomic number — the number of protons, a whole number, the small number on the periodic table square. Carbon is 6.
- Relative atomic mass — the weighted average, usually a decimal, the larger number on the square. Carbon is 12.0.
Use the words your exam board uses, write them out in full once in your answer, and the ambiguity disappears.
Reading an isotope symbol
Isotopes are written with both numbers stacked to the left of the symbol: the mass number on top, the atomic number underneath. For chlorine-35 that is 3517Cl. From those two numbers you can read off everything about the atom.
For 3517Cl
protons = Z = 17
electrons = Z = 17 (because it is a neutral atom)
neutrons = A − Z = 35 − 17 = 18
Neutrons are the only one you have to work out, and the sum is always the same: mass number minus atomic number. Students get it backwards and end up with a negative number of neutrons, which is a clear signal the subtraction went the wrong way round.
The argon and potassium puzzle
Here is a detail that catches people out and makes the difference between the two numbers very clear. Look up argon and potassium:
- Argon: atomic number 18, Ar = 39.9
- Potassium: atomic number 19, Ar = 39.1
Argon comes first in the periodic table even though it is heavier. That looks like a mistake in the table, and it is not. The periodic table is ordered by atomic number, never by mass. Argon happens to be mostly the heavy 40Ar isotope while potassium is mostly 39K, so the averages cross over. Mendeleev ran into exactly this problem and trusted chemical behaviour over mass; he turned out to be right, for a reason nobody understood until protons were discovered. Tellurium and iodine do the same thing.
Relative formula mass and relative molecular mass
Once you can handle one atom, compounds are easy, because Mr is nothing more than a shopping list. Add up the relative atomic mass of every atom in the formula and you are finished.
No averaging, no dividing. Just addition.
Here is sulfuric acid taken apart, so you can see where each number comes from.
Scroll sideways to see the whole drawing
Is relative formula mass the same as relative molecular mass?
You calculate them in exactly the same way, and they share the symbol Mr. The difference is only about what the substance is made of, and it matters because one of the two phrases is wrong for ionic compounds.
Relative molecular mass
For substances that really are made of separate molecules: water, carbon dioxide, ammonia, oxygen gas. There is a genuine particle you can point at and weigh.
H2O, CO2, NH3, O2
Relative formula mass
For anything at all, molecules included. It is the only correct phrase for ionic compounds, which are giant lattices with no molecules in them.
NaCl, MgO, CaCO3, and also H2O
Sodium chloride is the example that makes the point. A grain of salt is a three-dimensional lattice of alternating sodium and chloride ions, going on for millions of ions in every direction. There is no such thing as an NaCl molecule. “NaCl” is the simplest whole-number ratio of the ions, which is why it is called a formula unit rather than a molecule. So “the relative molecular mass of sodium chloride” is a phrase a marker can penalise, while “the relative formula mass of sodium chloride” is always safe.
Relative formula mass is never wrong. Relative molecular mass is only right when the substance has molecules.
This is why most GCSE specifications use “relative formula mass” for everything, and simply avoid the other phrase. At A-level and IB you are expected to know both and to pick the right one.
Working out Mr, step by step
Three steps. The whole difficulty is in step one, reading the formula correctly.
- Count how many of each atom there are. Small numbers below the line multiply the symbol in front of them. Brackets multiply everything inside.
- Multiply each count by that element’s Ar. Take the Ar from your periodic table, not from memory.
- Add the results. That total is Mr. No units, for the same reason Ar has none.
The examples below all use these values: H = 1.0, C = 12.0, N = 14.0, O = 16.0, Na = 23.0, S = 32.1, Cl = 35.5, Ca = 40.1, Cu = 63.5. Your own periodic table may round differently; use yours.
The straightforward ones
| Compound | Atoms in it | The sum | Mr |
|---|---|---|---|
| Water H2O | 2 × H, 1 × O | (2 × 1.0) + 16.0 | 18.0 |
| Carbon dioxide CO2 | 1 × C, 2 × O | 12.0 + (2 × 16.0) | 44.0 |
| Sodium chloride NaCl | 1 × Na, 1 × Cl | 23.0 + 35.5 | 58.5 |
| Sulfuric acid H2SO4 | 2 × H, 1 × S, 4 × O | (2 × 1.0) + 32.1 + (4 × 16.0) | 98.1 |
When there are brackets
A bracket with a small number outside it multiplies everything inside, not just the last symbol. This is where most Mr marks are lost.
Calculate the relative formula mass of calcium hydroxide, Ca(OH)2.
The 2 applies to BOTH the O and the H inside the bracket
Ca : 1 × 40.1 = 40.1
O : 2 × 16.0 = 32.0
H : 2 × 1.0 = 2.0
Add them up
40.1 + 32.0 + 2.0
Mr = 74.1
The common wrong answer is 57.1, which comes from multiplying only the H by 2 and forgetting the O. If your answer is suspiciously small, check the bracket first.
Calculate the relative formula mass of ammonium sulfate, (NH4)2SO4.
Inside the bracket: 1 N and 4 H. The 2 outside doubles both
N : 2 × 1 × 14.0 = 28.0
H : 2 × 4 × 1.0 = 8.0
S : 1 × 32.1 = 32.1
O : 4 × 16.0 = 64.0
Add them up
28.0 + 8.0 + 32.1 + 64.0
Mr = 132.1
Note that the O4 at the end is outside the bracket, so it is not doubled. There are 4 oxygens in total, not 8. Read the formula slowly: the bracket closes before the S.
When there is a dot in the formula
Some salts trap water molecules inside their crystals. These are called hydrated salts and the trapped water is written after a dot. The dot does not mean multiply — it means “and this much water is in there too”. You add the water in like any other part of the formula.
Calculate the relative formula mass of hydrated copper(II) sulfate, CuSO4·5H2O.
First the salt itself
Cu : 63.5
S : 32.1
O : 4 × 16.0 = 64.0
Then the five waters. One water is 18.0
5 × 18.0 = 90.0
Add the lot
63.5 + 32.1 + 64.0 + 90.0
Mr = 249.6
Leaving the water out gives 159.6, and every calculation built on it — moles, percentage yield, water of crystallisation — then comes out wrong. If a formula has a dot in it, the part after the dot is not decoration.
Relative mass against real mass in kilograms
Everything so far has been comparisons. At some point you will be asked for the actual mass of an atom, in kilograms or grams, and the two are connected by one number.
That number is the atomic mass unit, written u (older books use “amu” or “Da”). It is defined as exactly one twelfth of the mass of a carbon-12 atom — the same yardstick from the start of this page, now given a name and weighed:
The mass of one twelfth of a carbon-12 atom, in real kilograms.
So to turn a relative mass into a real one, multiply by that. A carbon-12 atom has a relative mass of 12, so:
The mass of one atom of carbon-12
12 × 1.661 × 10−27 kg
= 1.993 × 10−26 kg
which is 0.00000000000000000000000001993 kg
Now you can see why nobody works in kilograms. Writing 12 is quicker than writing that, and when you divide one atom’s mass by another’s, all those powers of ten cancel anyway. That is the entire argument for the relative scale.
The link to moles
There is one more connection, and it is the reason this topic sits at the front of every chemistry course. Take the relative atomic mass of any element and weigh out that many grams. You will have exactly one mole of it, which is 6.02 × 1023 atoms.
- Ar of carbon is 12.0, so 12.0 g of carbon is one mole of carbon atoms.
- Ar of sodium is 23.0, so 23.0 g of sodium is one mole of sodium atoms.
- Mr of water is 18.0, so 18.0 g of water is one mole of water molecules — about one and a half tablespoons.
This is why getting Ar and Mr right matters so much. Every mole calculation, every titration, every percentage yield and every empirical formula question is built on top of these two numbers. Get the Mr wrong at the start and the whole question falls over, no matter how good the rest of your method is.
The Ar values you will be asked for
In an exam these are printed on your periodic table, so there is no need to memorise them. Knowing the first twenty by heart still saves time and lets you spot a nonsense answer straight away. Values are rounded to one decimal place, which is what most exam boards use.
Quick answers
Which element has an Ar of 35.5? Chlorine.
What is the Ar value for Na? 23.0, sodium.
Relative atomic mass of oxygen? 16.0.
Relative atomic mass of chlorine? 35.5.
Watch the capital letters
Co is cobalt, one element, Ar 58.9. CO is carbon monoxide, a compound, Mr 28.0. One capital letter, a completely different answer. Element symbols are always a capital, optionally followed by a lower-case letter.
A note on precision. Some data booklets give chlorine as 35.45 rather than 35.5, and oxygen as 15.999 rather than 16.0. Both are correct; the first is the internationally agreed value and the second is the rounded version your exam board has chosen. Use the values printed on the periodic table you are given, and keep them consistent through a question. Mixing 35.45 from memory with 16.0 from the booklet is how answers end up half a mark outside the acceptable range.
Where the marks get lost
Nine mistakes account for nearly every dropped mark on this topic. None of them is about understanding. All of them are about reading carefully.
- Dividing by the number of isotopes instead of the total abundance. Three isotopes does not mean divide by 3. Divide by 100, or by whatever the abundances add up to.
- Forgetting to divide at all. You multiply, you add, you write down 3550 and move on. Chlorine is not 3550. Always finish the last step.
- Dividing by 100 when the abundances were peak heights. If the heights add to 5.0, the divisor is 5.0. Check what the numbers add up to before you divide.
- Putting units on Ar or Mr. They are ratios. No grams, no kilograms, no u.
- Not multiplying everything inside a bracket. Ca(OH)2 has two oxygens as well as two hydrogens.
- Ignoring the water after the dot. CuSO4·5H2O is 249.6, not 159.6.
- Using mass number where Ar was wanted. One isotope gets a whole number; an element gets the weighted average.
- Rounding part-way through. Round once, at the end, to whatever the question asks for. Rounding 79.986 to 80 and then using it in a further calculation will drift your final answer out of range.
- Defining Ar without the carbon-12 clause. “The average mass of the atoms of an element” is only half the definition and usually only half the marks. The phrase “relative to one twelfth of the mass of a carbon-12 atom” is where the rest of them are.
Before you write your final answer, ask one question: does it sit between the lightest and the heaviest isotope? If chlorine comes out as 3550, or 36.2, or 2.7, something has gone wrong in the arithmetic. An average can never be outside the range of the things it averages. This one check catches almost every error on this page.
The whole thing on one card
Photograph this the night before the paper.
Relative atomic mass — quick reference
- Ar = total mass ÷ total atoms. Divide by 100 only when the abundances were percentages.
- The scale is one twelfth of a carbon-12 atom. Leave that clause out of a definition and you lose marks.
- No units, ever. Ar and Mr are ratios.
- Decimals come from isotopes. Chlorine is 35.5 because three in four chlorine atoms are 35Cl.
- Proton 1, neutron 1, electron 1⁄1836. Charges +1, 0, −1.
- An atom’s overall charge is zero, because protons and electrons match. A nucleus on its own is positive.
- Mr is just addition. Brackets multiply everything inside; the part after a dot still counts.
- Two isotopes, Ar given? Heavy fraction = (Ar − light) ÷ (heavy − light).
- Sanity check: your answer must land between the lightest and heaviest isotope.
- Ar in grams = one mole = 6.02 × 1023 particles.
If you want the rest of atomic structure in the same shape, bonding and the periodic table included, our IB Chemistry revision notes cover it topic by topic at both SL and HL.
Frequently asked questions
What is the relative atomic mass of an atom?
What is the relative atomic mass formula?
How do you calculate relative atomic mass?
How do you work out relative atomic mass from a mass spectrum?
Why does relative atomic mass have no units?
What is Ar in chemistry?
What is Mr in chemistry?
What is the difference between relative atomic mass and mass number?
What is the relative mass of a proton?
What is the relative mass of a neutron?
What is the relative mass of an electron?
What is the relative charge of an electron?
What is the overall charge of an atom?
What is relative formula mass?
How do you calculate relative formula mass?
Is relative formula mass the same as relative molecular mass?
What is the relative atomic mass of chlorine, and why is it 35.5?
What is the relative atomic mass of oxygen?
What is the Ar value for Na?
Which element has an Ar value of 35.5?
What is relative mass?
Is there such a thing as relative atomic number?
Why is carbon-12 used as the standard?
What is the mass of an atom of carbon?
Can relative atomic mass be a whole number?
Stuck on the calculations rather than the idea?
Most students understand what relative atomic mass means within a few minutes. What costs the marks is the arithmetic under time pressure, and that only improves with someone watching you work. Our tutors teach IB and A-level chemistry and will sit with your own past papers rather than a generic worksheet.
Book a free 30-minute meetingRevising the whole of atomic structure? Start with our IB revision notes. Writing a chemistry investigation? See our guide to IB internal assessments, or read about IB Diploma tutoring and the people who teach it.