Mass spectrometry of elements

A mass spectrometer takes a sample, turns its atoms into ions, and sorts those ions by mass — then counts how many land at each mass. The picture it produces is a mass spectrum: a set of vertical peaks. The horizontal position of a peak is the mass of a particle; the height of a peak is how common that particle is, its relative abundance.

For a pure element, every peak is one isotope. Isotopes are atoms of the same element — same number of protons, so same identity — that differ in their number of neutrons, and therefore in mass. Chlorine, for example, comes in two natural isotopes: chlorine-35 and chlorine-37. So chlorine's spectrum has exactly two peaks.

The payoff is the number printed on the periodic table. The average atomic mass of an element is not a measurement of one atom — it is the weighted average of its isotope masses, each weighted by how abundant that isotope is. The mass spectrum is where that weighted average comes from.

Every mass-spectrum question is some combination of these four reads. Do them in order and the weighted average falls out at the end.

1. Count the peaks. One peak per isotope. Two peaks means two isotopes; three peaks, three isotopes. The number of peaks never tells you protons or electrons — only how many isotopes the element has.
2. Read each peak's position as a mass. The horizontal axis is mass (technically the mass-to-charge ratio m/z, but the ions carry a +1 charge, so the number is just the isotope's mass). A peak at 37 is a chlorine-37 atom, not 37% of anything.
3. Read each peak's height as an abundance. The taller the peak, the more common the isotope. Convert a percent abundance to a fractional abundance by dividing by 100: 75.8% becomes 0.758.
4. Weight, then add. Multiply each isotope's mass by its fractional abundance, then sum every term. That sum is the average atomic mass: average mass = Σ (isotope mass × fractional abundance).

A fast sanity check before you compute: the weighted average must land between the lightest and heaviest isotope, and closer to whichever peak is taller. If your answer falls outside that range, you weighted something backwards.

Quick reference card. Keep straight what sits on each axis and which number gets weighted.

Question. Chlorine's mass spectrum shows chlorine-35 (mass 34.97) at 75.8% abundance and chlorine-37 (mass 36.97) at 24.2% abundance. What is chlorine's average atomic mass?

Step 1 — convert percents to fractional abundances. Divide each by 100: 75.8% → 0.758 and 24.2% → 0.242. As a check, they add to 1.000.

Step 2 — weight each isotope's mass. Chlorine-35 contributes 34.97 × 0.758 = 26.51. Chlorine-37 contributes 36.97 × 0.242 = 8.95.

Step 3 — add the weighted terms. 26.51 + 8.95 = 35.45 g/mol, exactly the chlorine value on the periodic table.

Sanity check. The answer sits between 35 and 37, and much closer to 35 — which is right, because chlorine-35 is the far more abundant isotope. Notice no chlorine atom actually weighs 35.45; every real atom is either 35 or 37. The 35.45 is a bookkeeping average, not a description of any single atom.