Isotopes and Relative Atomic Mass

Isotopes of the same element share the same number of protons (Z) but differ in neutron number. Since chemical behaviour is determined by the number and arrangement of electrons (which equals protons in neutral atoms), isotopes have virtually identical chemical properties. They do differ in:

• Physical properties: slightly different mass → slightly different density, melting/boiling points, reaction rates (kinetic isotope effect)
• Nuclear stability: some isotopes are radioactive (unstable nucleus) while others are stable

Isotopes are atoms of the same element with the same proton number (Z) but different neutron numbers. They have virtually identical chemical properties (chemistry depends on electron configuration, which is the same) but differ in mass, density, BP, and nuclear stability (some are radioactive). Examples: ¹H, ²H, ³H; ¹²C, ¹³C, ¹⁴C; ³⁵Cl, ³⁷Cl.

Pause, copy the highlighted isotope definition into your book before moving on.

We just saw that isotopes of the same element can be stable or radioactive. That raises a question: structurally, what actually makes one isotope stable and another unstable? This card answers it → the neutron-to-proton (N:Z) ratio, covered by the syllabus dot point on investigating the basic structure of stable and unstable isotopes (CH11-8 dot point 5).

Inside the nucleus, two forces compete. The strong nuclear force attracts all nucleons (protons and neutrons) to each other over very short range, holding the nucleus together. The electrostatic force repels protons from each other (like charges repel) and acts over a longer range. Whether a nucleus is stable depends on the balance between these two forces, which in turn depends on the ratio of neutrons to protons (N:Z).

Plotting the number of neutrons (N) against the number of protons (Z) for every stable isotope traces out a narrow curve called the band of stability. Isotopes that fall on this band are stable. Isotopes with too many or too few neutrons for their proton number fall outside the band, their combination of forces cannot hold the nucleus together indefinitely, and they are radioactive (unstable), they spontaneously decay, releasing particles and energy, in a process that moves them back toward the band of stability.

Nuclear stability depends on the neutron-to-proton (N:Z) ratio, the balance between the short-range strong nuclear force (attracts all nucleons) and the longer-range electrostatic force (repels protons from each other). Light stable nuclei have N:Z ≈ 1:1; heavy stable nuclei need progressively more neutrons, up to N:Z ≈ 1.5:1. Plotting N against Z for all stable isotopes traces the band of stability; isotopes outside this band are unstable (radioactive) and decay to move back toward it.

Pause, copy the highlighted N:Z ratio rule and band-of-stability definition into your book before moving on.

The relative atomic mass (Ar) is the weighted average of all isotopic masses, weighted by their fractional abundance. The standard reference is ¹²C = exactly 12.

Mass Spectrometry and Isotope Data

A mass spectrometer ionises atoms and accelerates them through a magnetic field. Heavier ions deflect less, lighter ions more, they separate by mass. A detector measures the relative number of ions at each mass value, producing a mass spectrum showing peaks at each isotope's mass, with peak height proportional to abundance.

We just saw that isotopes have the same chemical behaviour but different masses. That raises a question: since elements have multiple isotopes with different masses, how is the single "atomic mass" value on the periodic table calculated? This card answers it → it is the weighted average of all naturally occurring isotopic masses, using fractional abundance as the weighting.

Relative atomic mass (Ar) = weighted average of all naturally occurring isotopic masses, on the scale where a carbon-12 atom is defined as exactly 12 (that is, relative to 1/12 the mass of a carbon-12 atom). Formula: Ar = Σ(isotopic mass × fractional abundance). Always convert percentage abundances to fractions (÷ 100). Example: for neon, Ar = (20 × 0.9048) + (21 × 0.0027) + (22 × 0.0925) ≈ 20.18.

Add the highlighted Ar formula to your notes before the check below.

We just saw how Ar is calculated from fractional abundances. That raises a question: how do chemists actually measure isotopic composition experimentally? This card answers it → mass spectrometry separates ions by mass and measures their relative abundance, producing a spectrum where peak height equals abundance.

A mass spectrum shows peaks at each isotope's mass-to-charge ratio (m/z), with peak height proportional to relative abundance. More abundant isotopes produce taller peaks. Mass spectrometry is the primary method for determining isotopic composition and calculating Ar. A spectrum with two peaks at m/z 35 and 37 (ratio 3:1) gives Ar = (35 × 0.75) + (37 × 0.25) = 35.5.

Pause, write the highlighted mass spectrum rule into your book.

We just saw how mass spectra reveal isotopic composition. That raises a question: how do you write full-mark exam answers on isotopes, Ar calculations, and mass spectra? This card answers it → for each question type, follow the structured method: define, calculate (showing working), and interpret from the data given.

For exam answers on isotopes: state that isotopes have virtually identical chemical properties (same Z, same electron configuration) but different physical properties (different mass, density). For Ar calculations: convert % to fractions, multiply each isotopic mass by its fraction, then sum, always show the calculation. For mass spectra: peak position = mass number, peak height ∝ relative abundance.

Pause, copy the highlighted exam strategy into your book before moving on.