How this instrument works
Every element occurs in nature as a mix of isotopes — atoms with the same number of protons but different numbers of neutrons, and therefore different masses. The atomic mass printed on the periodic table is not the mass of any one isotope; it's the abundance-weighted average across all of them, which is why chlorine's atomic mass (35.45) isn't a whole number even though every individual chlorine atom has a whole-number mass in atomic mass units. This instrument computes that weighted average for the common case of an element with two significant stable isotopes.
The weighting matters enormously. An isotope that makes up 75% of natural samples pulls the average toward its own mass three times harder than one making up 25%, so the weighted average sits much closer to the more abundant isotope's mass than to a simple unweighted midpoint. Chlorine's two stable isotopes, 35Cl and 37Cl, differ by about 2 atomic mass units, but because 35Cl makes up roughly three-quarters of natural chlorine, the weighted average comes out at 35.45 — much nearer 35 than 37, precisely because of that abundance imbalance.
Isotopic abundances aren't universal physical constants in the way that, say, the speed of light is — they're measured values, published and periodically re-evaluated by the Commission on Isotopic Abundances and Atomic Weights (CIAAW) under IUPAC. This instrument uses whatever isotope masses and abundances you supply, so it works equally well for reproducing a textbook element's standard atomic weight or for exploring how the average would shift if the abundances were different.
- Enter Isotope 1 mass (u) and Isotope 1 abundance (%) — the atomic mass and natural abundance of the more common (or first-listed) isotope.
- Enter Isotope 2 mass (u) and Isotope 2 abundance (%) for the second isotope.
- Read Weighted average atomic mass (u) directly — this is the figure that would appear on a periodic table for a two-isotope element.
- The two abundance percentages should sum to 100% for a physically meaningful result, since together they should account for all naturally occurring atoms of the element.
- For an element with three or more significant isotopes, extend the same weighted-average logic by hand: multiply each isotope's mass by its fractional abundance and sum every term.
Worked example — chlorine's two stable isotopes
Chlorine occurs naturally as two stable isotopes: 35Cl, with a mass of 34.96885 u and an abundance of 75.77%, and 37Cl, with a mass of 36.9659 u and an abundance of 24.23%. Enter 34.96885 into Isotope 1 mass (u), 75.77 into Isotope 1 abundance (%), 36.9659 into Isotope 2 mass (u), and 24.23 into Isotope 2 abundance (%); Weighted average atomic mass (u) reads 35.452735215.
That figure — 35.45 u once rounded to the periodic table's usual precision — is chlorine's official IUPAC standard atomic weight. It sits much closer to 35Cl's mass than to 37Cl's, which is exactly what the roughly 3-to-1 abundance ratio between the two isotopes predicts.
Questions
Why isn't an element's atomic mass a whole number?
Because it's a weighted average across multiple isotopes, each with its own whole-number-ish mass (technically not exactly whole, due to nuclear binding energy), rather than the mass of a single atom. Chlorine's atomic mass of 35.45 doesn't correspond to any real chlorine atom — every actual atom is either close to 35 u (35Cl) or close to 37 u (37Cl) — it's the abundance-weighted blend of the two that lands on the periodic table.
What does it mean for an isotope to have 75.77% abundance?
It means that if you sampled a large number of naturally occurring chlorine atoms from anywhere on Earth, about 75.77% of them would be the 35Cl isotope and the remaining 24.23% would be 37Cl. Natural isotopic abundances are remarkably consistent across terrestrial sources, which is why they're published as standard reference values rather than needing to be re-measured for every sample.
Do the two abundance percentages have to add up to 100%?
For the result to represent a real element's standard atomic weight, yes — the two abundances should account for all the naturally occurring atoms, summing to 100%. This instrument will still compute a weighted average if they don't sum to 100%, but the result no longer corresponds to a physically meaningful standard atomic weight; it becomes a differently-weighted blend instead.
Can this instrument handle an element with more than two isotopes?
Not directly — it's built for the common two-isotope case. For an element with three or more significant stable isotopes, such as oxygen or magnesium, extend the same formula by hand: multiply each isotope's mass by its fractional abundance (abundance percent divided by 100) and add every term together, the same weighted-sum logic this instrument uses for two terms.
Where do isotope masses and abundances come from?
They're measured experimentally — mass spectrometry for the isotope masses, and analysis of terrestrial samples for the natural abundances — then compiled, evaluated, and periodically updated by the Commission on Isotopic Abundances and Atomic Weights (CIAAW) under IUPAC. The periodic table's standard atomic weights are the published output of that evaluation process, not derived quantities calculated from first principles.