WACE Chemistry
Mass Spectrometry: Isotopes, Spectra and Relative Atomic Mass
Many students lose marks on mass spectrometry questions not because they cannot do the arithmetic, but because they misread the spectrum before they even start calculating. Confusing the tallest peak with the heaviest isotope, or forgetting to convert percentages to fractions, are the kinds of slips that WACE markers see every year. This guide walks through exactly what you need to know for the ATAR course examination, with worked examples drawn directly from the syllabus content.
What the syllabus asks
For Unit 1 of WACE Chemistry, you need to understand mass spectrometry in terms of three things: how ions are produced, how they are separated, and how the resulting spectrum lets you determine isotopic composition and calculate relative atomic mass. You are not required to know the internal workings of the instrument in detail, so do not spend time memorising the mechanics of the machine itself.
The idea, explained
How a mass spectrometer works (the three stages)
A mass spectrometer processes a sample in three stages.
- Ionisation. Atoms in the sample are converted to positive ions, most commonly by knocking off one electron from each atom.
- Separation. The resulting ions are separated according to their mass-to-charge ratio, written as m/z.
- Detection. The instrument records the relative number of ions arriving at each m/z value.
Because most ions produced from elements carry a single positive charge (z = 1), the m/z value is effectively equal to the mass of the isotope. Each peak in the spectrum therefore corresponds to one isotope of the element.
Reading the mass spectrum
The output is a graph with m/z on the x-axis and relative abundance (or percentage abundance) on the y-axis. From this graph you can read off two things directly:
- Which isotopes are present, from the m/z values where peaks appear.
- The relative abundance of each isotope, from the height of each peak (normalised so all peaks together sum to 100%).
Calculating relative atomic mass
Relative atomic mass (Ar) is the weighted average of all isotopic masses, weighted by their fractional abundances:
Ar = sum of (isotope mass x fractional abundance)
Or, if you are working with percentage abundances directly:
Ar = sum of (isotope mass x percentage abundance) / 100
Worked example 1: chlorine (two isotopes)
A mass spectrum of chlorine shows two peaks: m/z 35 at 75.77% and m/z 37 at 24.23%.
Ar = (35 x 0.7577) + (37 x 0.2423) Ar = 26.520 + 8.965 Ar = 35.49
This is very close to the periodic table value of approximately 35.45. Notice that the answer is a decimal, not a whole number. That is because naturally occurring chlorine is always a fixed mixture of these two isotopes, so the average mass falls between them.
Worked example 2: magnesium (three isotopes)
Magnesium has peaks at m/z 24 (78.99%), m/z 25 (10.00%) and m/z 26 (11.01%).
Ar = (24 x 0.7899) + (25 x 0.1000) + (26 x 0.1101) Ar = 18.958 + 2.500 + 2.863 Ar = 24.32
Working backwards: finding abundances from Ar
If the relative atomic mass is given and the element has exactly two isotopes, you can calculate the abundance of each. Let x be the fractional abundance of the lighter isotope; then (1 - x) is the fractional abundance of the heavier one.
Worked example: boron
Boron has two isotopes, mass 10.01 (B-10) and mass 11.01 (B-11). Its Ar is 10.81.
10.81 = (10.01 x x) + (11.01 x (1 - x)) 10.81 = 10.01x + 11.01 - 11.01x 10.81 - 11.01 = -1.00x -0.20 = -1.00x x = 0.20
So B-10 is 20% abundant and B-11 is 80% abundant.
What the exam asks
In the ATAR course examination, mass spectrometry questions typically ask you to:
- Read m/z values and percentage abundances from a given spectrum.
- Calculate the relative atomic mass using the weighted average formula.
- Identify which peak represents the most abundant isotope and which represents the heaviest isotope (these are not always the same peak).
- Work backwards from a known Ar to find the percentage abundances of two isotopes.
Show every step of your working. WACE markers award marks for method, so a small arithmetic error will cost you far fewer marks if your working is clear.
Common mistakes
- Confusing the tallest peak with the heaviest isotope. The tallest peak is the most abundant isotope. The peak at the highest m/z value is the heaviest isotope. These are often different peaks.
- Forgetting to convert percentages to fractions. If you use percentage abundances directly without dividing by 100, your Ar will be roughly 100 times too large. Always convert to decimals first, or use the divide-by-100 version of the formula.
- Assuming Ar equals the mass of the most abundant isotope. Ar is pulled towards the other isotopes in proportion to their abundances. It will be close to the most abundant isotope's mass but rarely equal to it.
- Not checking that abundances sum to 100%. Before calculating, confirm the percentages add up to 100. If they do not, you have misread the spectrum.
- Rounding too early. Carry at least four significant figures through each multiplication before adding, then round the final answer. Rounding intermediate steps introduces errors that WACE markers will notice.
If you want to practise these calculations with immediate feedback and step-by-step explanations tailored to the WACE syllabus, Avocado's AI-native tutoring service has you covered. Work through the Mass Spectrometry lesson at your own pace and see exactly where your working goes right, and where it needs a small correction.