Average Atomic Mass Calculator

The number printed under each symbol on the periodic table is not the mass of any real atom. It is an abundance-weighted mean over the isotopes present in a normal terrestrial sample, computed by multiplying each isotope mass by its fractional abundance and summing. The weighting is what makes chlorine 35.45 despite having no isotope anywhere near that mass: Cl-35 at 34.9689 u supplies about 75.8 percent and Cl-37 at 36.9659 u the remaining 24.2 percent. Each isotope contributes in proportion to how likely a randomly drawn atom is to be that isotope, which is what makes the average the right quantity for converting bulk mass to moles. Fractional abundances must sum to 1, or percentages to 100. Copper at 63.546 and bromine at 79.904 sit near the midpoint between two isotopes, while carbon at 12.011 barely departs from 12 because C-13 is only about 1.1 percent abundant. Two caveats matter. First, individual isotope masses are themselves non-integral because of nuclear binding energy, so even a monoisotopic element such as fluorine has an atomic weight of 18.998 rather than 19; carbon-12 is the sole exception, exactly 12 u by definition. Second, abundances are not universal constants. Physical and biological processes fractionate isotopes, so the atomic weight of an element genuinely varies with its source. IUPAC now publishes interval values rather than single numbers for elements including hydrogen, lithium, boron, carbon, nitrogen, oxygen, silicon, sulfur, chlorine, bromine, magnesium and thallium; boron ranges roughly from 10.806 to 10.821 depending on provenance. Commercially processed lithium and enriched or depleted uranium can fall far outside natural ranges.

The idea that an element could be a mixture of masses arose from the radioactive decay chains studied in the first decade of the twentieth century, where chemically inseparable substances showed different radioactive behaviour. Frederick Soddy proposed the concept in 1913 and adopted the word isotope, from Greek for same place, which had been suggested to him by the Scottish physician and writer Margaret Todd. In the same period J. J. Thomson used positive-ray parabolas to show that neon consisted of species at mass 20 and mass 22, the first demonstration that a stable, non-radioactive element is isotopically mixed. Francis Aston turned the observation into measurement with his mass spectrograph from 1919 onward, determining isotope masses and abundances for most elements and receiving the 1922 Nobel Prize in Chemistry. Once abundances were known, the long-standing atomic weights determined by painstaking gravimetric chemistry, above all by Theodore Richards at Harvard, who won the 1914 Nobel Prize for that work, could be reinterpreted as weighted averages rather than fundamental constants. Responsibility for the tabulated values has rested since 1899 with the international commission that is now the IUPAC Commission on Isotopic Abundances and Atomic Weights, which revises the table roughly every two years. In 2009 the commission took the significant step of replacing single values with intervals for elements whose isotopic composition varies measurably in nature, and it extended that treatment to bromine and magnesium in the 2010s.