IB Chemistry HLTopic 1 — The Nuclear AtomPaper 1 & 2Core skill~13 min read
Isotopes
Look up chlorine and the periodic table says 35.45. No chlorine atom has ever weighed 35.45 — they come in two sizes, 35 and 37. That number is an average, and understanding why it is not a whole number is most of this page.
📚 What you need to know
Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons.
They therefore have the same atomic number but different mass numbers.
Isotopes have identical chemical properties, because they have identical electron arrangements.
They have slightly different physical properties — mass, density, melting and boiling point, rate of diffusion.
Relative atomic mass (Ar) is the weighted average mass of an element’s atoms compared with 1/12 of the mass of a carbon-12 atom.
Ar = Σ(% abundance × isotopic mass) ÷ 100.
Ar values are rarely whole numbers because they are averages, not the mass of any real atom.
Same element, different mass
Change the number of protons and you have changed the element. Change the number of neutrons and you have not — you have made an isotope. The atom is heavier or lighter, but chemically it is the same substance.
Hydrogen is the only element whose isotopes get their own names. For everything else you just say the mass number: carbon-12, carbon-14, uranium-235.
Why chemical properties are identical
This follows in one step. Chemical reactions involve electrons — sharing them, transferring them, rearranging them. Isotopes have the same number of protons, therefore the same number of electrons in a neutral atom, therefore the same electron configuration. Same electrons, same chemistry.
Physical properties are a different matter, because many of them depend on mass. A heavier isotope moves more slowly at a given temperature, so it diffuses more slowly, and it has a slightly higher density, melting point and boiling point.
This is the basis of a useful exam sentence. “Isotopes have identical chemical properties because they have the same electron configuration, but differ in physical properties that depend on mass.” That one line answers a large family of questions.
Relative atomic mass
Because an element is a mixture of isotopes in fixed proportions, its useful mass is a weighted average: each isotope contributes in proportion to how common it is.
Relative atomic mass
Ar = Σ(% abundance × isotopic mass) ÷ 100
If the two isotopes were equally abundant the average would sit at 36, dead centre. It sits at 35.45 because chlorine-35 outnumbers chlorine-37 by roughly three to one.
Two things follow from Ar being an average. First, no single atom has that mass — asking for “the mass of a chlorine atom” as 35.45 is a category error. Second, the value is closer to the more abundant isotope, which gives you a free sanity check: if your answer lands nearer the rarer isotope, you have made an arithmetic slip.
WORKED EXAMPLE
Silicon has three isotopes: 28Si (92.23%), 29Si (4.67%) and 30Si (3.10%). Calculate the relative atomic mass of silicon to 2 decimal places.
Check the abundances first92.23 + 4.67 + 3.10 = 100.00They should always total 100. If they do not, you have misread the question.Multiply each mass by its abundance(92.23 × 28) + (4.67 × 29) + (3.10 × 30)= 2582.44 + 135.43 + 93.00 = 2810.87Divide by 1002810.87 ÷ 100 = 28.1087Ar = 28.11Sanity checkOver 92% of the atoms are 28Si, so the answer should sit just above 28. It does.
WORKED EXAMPLE
Gallium has a relative atomic mass of 69.72 and consists of only two isotopes, 69Ga and 71Ga. Calculate the percentage abundance of each.
Set up one unknownLet x be the percentage of 69Ga. Since there are only two isotopes, the other must be (100 − x).Write the Ar expression[69x + 71(100 − x)] ÷ 100 = 69.72Expand and solve69x + 7100 − 71x = 6972−2x = −128, so x = 6464% 69Ga and 36% 71GaCheck it works[(64 × 69) + (36 × 71)] ÷ 100 = 69.72And it passes the sense test: Ar is nearer 69 than 71, so the lighter isotope should be the more common one.
WORKED EXAMPLE
Explain why 35Cl and 37Cl react identically with sodium, but diffuse through a gas at different rates. Estimate how much faster the lighter isotope diffuses.
Why the chemistry is identicalBoth have 17 protons and therefore 17 electrons in the same arrangement. Reactions involve electrons only, so both isotopes form chloride ions in exactly the same way.same electron configuration, same chemistryWhy diffusion differsDiffusion depends on how fast the particles move. At the same temperature both isotopes have the same average kinetic energy, so the heavier one must travel more slowly.Estimate the differencespeed ratio = √(37 ÷ 35) = √1.057 = 1.028about 2.8% fasterA tiny difference, but a real one — repeated over thousands of diffusion stages it is enough to separate isotopes industrially.
💡 Exam tip
Define isotopes using same protons, different neutrons — both halves are needed.
Justify identical chemistry by naming the same electron configuration.
Check that abundances add to 100 before calculating anything.
Round only at the very end, and to the number of decimal places asked for.
Sanity check: Ar lies nearer the more abundant isotope.
For a two-isotope problem, let one abundance be x and the other 100 − x.
⚠️ Common mix-up
Saying isotopes have different numbers of electrons. They do not; that would make them ions.
Taking a simple average of the isotopic masses instead of weighting by abundance.
Claiming a real atom has the periodic table’s mass, when that value is an average.
Rounding partway through and losing the required decimal places.
Saying isotopes have different chemical properties because they have different masses.
Forgetting the second isotope is (100 − x) in a reverse calculation.
Up next: Interpreting Mass Spectra — every abundance on this page had to be measured somehow. The next page is the instrument that measures them, and how to read its output.
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