Why atomic mass is almost never a whole number
Open a periodic table and a question jumps out: why is chlorine’s atomic mass 35.45 u and not a tidy whole number? The answer is isotopes — atoms of the same element with the same number of protons but different numbers of neutrons. The number you read on the table is the abundance-weighted average of every naturally occurring isotope.
Use the calculator above to pick an element (chlorine, boron, or copper), then slide the abundance of its two isotopes. The two abundances always sum to 100%, the weighted average updates live, and it is compared against the real value stored in our element dataset.
Mass number vs. atomic mass
Two “mass” ideas get confused, so keep them separate:
- Mass number (A) counts protons + neutrons in one atom. It is always a whole number. Chlorine-35 has 17 protons and 18 neutrons, so A = 35.
- Atomic mass (or atomic weight) is the average mass of an element’s atoms, measured in unified atomic mass units (u). Because it averages over a mix of isotopes, it is rarely whole.
The protons set the element’s identity — its atomic number — and they anchor the Bohr model and the valence electrons that drive chemistry. Neutrons change only the mass.
The weighted-average formula
For an element with isotopes of mass m and fractional abundance f:
atomic mass = (m₁ × f₁) + (m₂ × f₂) + …
For chlorine: (34.969 u × 0.7577) + (36.966 u × 0.2423) ≈ 35.45 u. Because Cl-35 makes up about three-quarters of all chlorine atoms, the average sits much closer to 35 than to 37. Try the same logic for copper (Cu-63 and Cu-65 → 63.55) and boron (B-10 and B-11 → 10.81).
What the slider reveals
Drag an abundance to an extreme and the average snaps to one isotope’s mass — proof that the periodic-table value is a mixture, not a measurement of any single atom. Nudge the abundances back to their natural values (the “Use real abundances” button) and the average lands on the published figure. This is the same averaging idea behind broader periodic trends; even the unreactive noble gases follow it.
Using this with a class
Project the calculator and ask students to predict whether the average will be closer to the lighter or heavier isotope before they slide — then check. Have them reproduce 35.45 by hand with the formula, then verify on the widget. It is free to embed on your site or LMS with the snippet below.