Mass Spectrometry

1.2 Mass Spectra

Real mass spectra for all 84 elements that occur with a natural isotopic composition, drawn from NIST data. Point at a peak to read its m/z and abundance, and switch the axis between base-peak and percent scaling to see the weighted average atomic mass build up term by term.

Isotopesm/z PeaksRelative AbundanceAvg Atomic Mass

Topic 1.2

Mass Spectra of Elements

Explain the quantitative relationship between the mass spectrum of an element and the masses of the element’s isotopes.

A mass spectrometer ionizes a sample, accelerates the ions, and separates them by mass-to-charge ratio (m/z). For a sample of a single element, each peak is one isotope: same number of protons (so same element, same chemistry) but different numbers of neutrons, and therefore different mass.

Two readings come off the spectrum directly:

Peak position → the mass of that isotope.
Peak height → the relative natural abundance of that isotope.

The average atomic mass printed on the periodic table is the abundance-weighted average of those isotope masses. Because it is weighted, the average always sits closer to the more abundant isotope. Chlorine averages 35.45 amu — much nearer ³⁵Cl (75.8%) than ³⁷Cl (24.2%).

Run the logic backward and a spectrum becomes an identification tool: compute the weighted average, then find the element on the periodic table with that atomic mass.

Key points

Peak position gives mass; peak height gives abundance. Never swap them.
Average atomic mass = Σ (fractional abundance × isotope mass), and it always lies between the lightest and heaviest isotope.
Isotopes of an element are chemically near-identical because chemistry is set by electrons, not neutrons.

Equations

$\overset{ˉ}{A} = i \sum f_{i} m_{i}$
not on the sheetNot printed on the equation sheet — you are expected to know the idea of a weighted average.
- $\overset{ˉ}{A}$ average atomic mass (amu)
- $f_{i}$ fractional abundance of isotope i (0–1)
- $m_{i}$ mass of isotope i (amu)

Common mistakes

Convert percentages to decimals before multiplying, and confirm the fractions sum to 1.
Do not take a plain average of the isotope masses — that only works if the abundances happen to be equal.
Isotopes differ in neutrons, not protons. A different proton count is a different element entirely.
Mass number ≠ average atomic mass. Mass number is a whole-number count of protons + neutrons for one isotope.

Worked example

An element X shows peaks at m/z = 62.93 (69.17%) and m/z = 64.93 (30.83%). Identify X.

Ā = (0.6917)(62.93) + (0.3083)(64.93)
Ā = 43.53 + 20.02 = 63.55 amu

63.55 amu is copper. The two peaks are ⁶³Cu and ⁶⁵Cu.

Check the weighting: the average is much closer to 62.93 than to 64.93, matching the 69% abundance of the lighter isotope.

Full notes for topic 1.2 →