How to calculate relative atomic mass from a mass spectrum
Each peak is one isotope: its m/z is the isotope's mass and its height is how common it is. Multiply each m/z by its abundance, add the products and divide by the total abundance. With percentages that total is 100; when the tallest peak is set to 100, divide by the sum of the peak heights instead. Answers are right when they match the key to the decimal places asked.
Pick your course first. GCSE and A-level sets use whole-number m/z values and ask for 1 decimal place; A-level adds relative abundance spectra, Cl₂ and Br₂ molecular ions (Edexcel) and time of flight (AQA); untick the ones your course leaves out under Question types. IB sets ask for 2 decimal places. AP Chemistry and US sets use isotope masses in amu to 3 decimals and call the answer the average atomic mass. AP students can also practise photoelectron spectra (AP 1.6).
Example: magnesium
In set MGJ224 (GCSE), the spectrum has peaks at m/z 24 (79.0%), 25 (10.0%) and 26 (11.0%). Aᵣ = (24 × 79.0 + 25 × 10.0 + 26 × 11.0) ÷ 100 = 2432 ÷ 100 = 24.3. Open set MGJ224
Questions
How do you calculate relative atomic mass from a mass spectrum?
Multiply the m/z of each peak by its abundance, add the products, then divide by the total abundance. With percentages the total is 100. For magnesium at 79.0%, 10.0% and 11.0%: (24 × 79.0 + 25 × 10.0 + 26 × 11.0) ÷ 100 = 24.3.
What if the peaks are relative abundances, not percentages?
Some spectra set the tallest peak to 100. Work out the products the same way, but divide by the sum of the peak heights instead of 100. Chlorine at 100 and 31.9 gives (35 × 100 + 37 × 31.9) ÷ 131.9 = 35.48.
How do you find the percentage abundance from the relative atomic mass?
For two isotopes, call one x% and the other (100 − x)%. Then (m1 × x + m2 × (100 − x)) ÷ 100 = Ar. If a copper spectrum worked from the mass numbers 63 and 65 gives Ar = 63.62: 63x + 65(100 − x) = 6362, so x = 69.0% copper-63.
Why does chlorine give peaks at 70, 72 and 74 in the ratio 9:6:1?
Chlorine is about 3/4 chlorine-35 and 1/4 chlorine-37. A Cl2 molecule pairs two atoms at random: 35 + 35 has a chance of 9/16, 35 + 37 of 6/16 (either way round) and 37 + 37 of 1/16. Bromine, about half and half, gives 1:2:1 at 158, 160 and 162.
Why is my answer not exactly the periodic table value?
Exam spectra use whole-number m/z values and rounded abundances, so the answer can differ slightly from the periodic table. Always work from the numbers on the spectrum. AP and US sets use isotope masses to 3 decimals, which land closer to the table.
What happens in a time of flight mass spectrometer?
Atoms are ionised, then accelerated so every ion has the same kinetic energy. Lighter ions move faster and reach the detector first: from KE = ½mv² and v = d ÷ t, the time of flight grows with the square root of the mass.
Can I give my class the same questions?
Yes. Share with class copies a link with the set code, and everyone who opens it gets the same spectra and numbers. To stop copying, print a class set: each copy asks the same kinds of question in the same order with different elements, and each has its own key.
Sources, read October 27, 2026: CIAAW isotopic compositions of the elements 2024, CIAAW atomic masses (AME2020) and abridged atomic weights; AQA GCSE Chemistry 8462 4.1.1.6; AQA A-level Chemistry 7405 3.1.1.2; OCR A-level Chemistry A H432 2.1.1; Pearson Edexcel A-level Chemistry 9CH0 Topic 1; College Board AP Chemistry course and exam description 1.2.