S1.2 The nuclear atomIB Chemistry HL: Revision notes

Atoms have a small, dense, positive nucleus of protons and neutrons (nucleons), with negative electrons occupying the space around it. In the nuclear symbol $^{A}_{Z}\mathrm{X}$, A is the mass number and Z the atomic number.

• protons = Z; neutrons = A − Z; electrons = Z − ionic charge.
• Example: $^{79}_{34}\mathrm{Se}^{2-}$ has 34 p, 45 n and 36 e.

Isotopes are atoms of the same element with different numbers of neutrons. They share chemical properties (same electron arrangement) but differ in mass-dependent physical properties such as density.

Relative atomic mass Ar is the weighted mean: Ar = Σ(isotopic mass × % abundance) ÷ 100. For two isotopes, abundances can be found by letting the fractions be x and (1 − x).

A mass spectrometer turns atoms into positive ions and separates them by mass-to-charge ratio (m/z). The output, a mass spectrum, shows a peak for each ion; the peak height (or area) gives the relative abundance.

For singly charged ions, m/z equals the mass of the ion, so each peak for an element identifies an isotope by its mass number. The number of peaks gives the number of isotopes.

1. Read the m/z of each peak: these are the isotopes' masses.
2. Read each relative abundance (convert to percentages if heights are given).
3. Calculate Ar = Σ(m/z × abundance) ÷ Σ abundance.

Example: neon peaks at 20 (90.5 %), 21 (0.3 %) and 22 (9.2 %) give Ar = 20.19.

Small peaks at fractional or halved m/z come from 2+ ions: ²⁴Mg²⁺ appears at m/z 12. Diatomic elements also give molecular ion peaks: chlorine gives Cl₂⁺ at 70, 72 and 74 in a 9 : 6 : 1 ratio because ³⁵Cl is three times as abundant as ³⁷Cl.

Samples of the same element from different sources can have slightly different isotopic compositions. Two samples can have the same Ar but different isotope abundances, so the full spectrum is more informative than Ar alone. Comparing individual abundances or isotope ratios (e.g. ²⁰⁷Pb/²⁰⁶Pb) can trace the origin of lead, confirm the origin of food, or detect enriched isotopes. Conclusions are limited by measurement uncertainty and by the number of possible sources tested.