TL;DR:
Isotopes of an element have the same number of protons but different numbers of neutrons.
The mass number is protons plus neutrons. The atomic mass on the periodic table is a weighted average over the isotopes.
Chlorine:
0.7576 × 34.969 + 0.2424 × 36.966 = 35.45, which is why no chlorine atom actually has a mass of 35.45.
Look up chlorine on the periodic table and you find an atomic mass of about 35.45. But atoms come in whole numbers of protons and neutrons, so how can any atom weigh 35.45? None does. The number is an average, and working out where it comes from is a short calculation.
Same protons, different neutrons
The number of protons, the atomic number Z, defines the element. Every chlorine atom has 17 protons. But the number of neutrons can vary. Atoms of the same element with different neutron counts are isotopes.
The mass number A is the total of protons and neutrons. Isotopes are named by element and mass number: chlorine-35 has 17 protons and 35 − 17 = 18 neutrons, and chlorine-37 has 17 protons and 37 − 17 = 20 neutrons. Both have 17 electrons when neutral, so they have the same chemistry. They differ in mass.
Why the periodic table shows an average
A real sample of chlorine contains a mix of its isotopes in fixed proportions. The atomic mass on the table is the weighted average of the isotope masses, with each weighted by its natural abundance (the fraction of atoms that are that isotope). Masses are in atomic mass units, u.
The formula is: average mass = (fraction₁ × mass₁) + (fraction₂ × mass₂) + ..., and the fractions must add up to 1.
Worked example: chlorine
Isotope | Mass (u) | Abundance (as a fraction) |
|---|---|---|
Chlorine-35 | 34.969 | 0.7576 |
Chlorine-37 | 36.966 | 0.2424 |
Check the fractions:
0.7576 + 0.2424 = 1.0000.Weight the first isotope:
0.7576 × 34.969 = 26.49.Weight the second isotope:
0.2424 × 36.966 = 8.96.Add:
26.49 + 8.96 = 35.45 u.
That matches the periodic table value. Note that 35.45 sits between 34.969 and 36.966, and closer to the lighter isotope, because the lighter isotope is more abundant. If your average falls outside the range of the isotope masses, something is wrong.
You can also run the problem backward. Suppose an element has two isotopes with masses 10.0 and 11.0 and an average of 10.8. Let the fraction of the heavier be x. Then 10.0 (1 − x) + 11.0 x = 10.8, so 10.0 + x = 10.8 and x = 0.8. The heavier isotope is 0.8 of the atoms and the lighter is 0.2. Check: 0.2 × 10.0 + 0.8 × 11.0 = 2.0 + 8.8 = 10.8.
A quick shortcut for estimating
Before computing, estimate. About three quarters of chlorine atoms are chlorine-35, so the average should sit close to 35. With a quarter of the atoms two units heavier, estimate 35 + 0.25 × 2 = 35.5. The exact answer, 35.45, fits.
What isotopes are used for
Dating. Carbon-14 is radioactive, and its decay is used to date organic remains, as in half-life and radioactive decay.
Medicine. Radioactive isotopes can be used as tracers in medical imaging, where detectors follow where the isotope goes in the body.
Research. Heavier or lighter isotopes act as labels, letting scientists follow atoms through chemical reactions and biological processes.
Energy. Certain isotopes of uranium are used as nuclear fuel.
Radioactive isotopes: Most isotopes, including chlorine-35 and chlorine-37, are stable and harmless in ordinary use. Radioactive ones are handled only by trained people with proper shielding and monitoring. Never open or tamper with any device that carries a radioactive source.
Some isotopes can be shown in notation with the mass number as a superscript and the atomic number as a subscript to the left of the symbol. For chlorine-35 that is ³⁵₁₇Cl. The top number is protons plus neutrons, 17 + 18 = 35, and the bottom number is protons alone. Reading the notation back is a quick check: top minus bottom gives neutrons, 35 − 17 = 18.
A mass spectrometer is the instrument that measures isotope masses and abundances. It sorts charged atoms by mass, so each isotope shows up as a separate peak, and the height of each peak tells you its relative abundance. The averaging step then works exactly as in the chlorine example.
How to check your answer
Range. The average lies between the lightest and heaviest isotope masses.
Fractions. They add to 1 (or the percentages add to 100 and are converted first).
Lean. The average is nearer the more abundant isotope.
Neutrons. Neutrons equal mass number minus atomic number.
Mistakes that cost marks
Taking the plain mean of the two masses,
(34.969 + 36.966) / 2 = 35.97, which ignores abundance.Using percentages as if they were fractions without dividing by 100.
Confusing mass number (a whole number) with atomic mass (an average).
Saying isotopes have different numbers of protons or electrons.
Rounding masses too early.
Where you will use it next
The averaged mass is the molar mass you use in the mole, explained with a dozen, which is why chlorine's molar mass is 35.45 g/mol. The charge on the nucleus also feeds the ideas in electron configurations and the periodic table.
Frequently asked questions
Do isotopes react differently?
Almost not at all, because chemistry depends on electrons. Heavier isotopes react slightly slower in some cases, but the differences are small.
Why is the mass not exactly the mass number?
Protons and neutrons have slightly different masses, and some mass is released as binding energy when a nucleus forms, so the exact mass is not a whole number.
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