Short on time? This page is the recap. For explanations and worked examples, use the full study guide.
Recap
- Isotopes are atoms of the same element (same number of protons) with different numbers of neutrons, so they have different masses.
- A mass spectrometer turns atoms into +1 ions, separates them by mass-to-charge ratio (m/z) and counts them.
- For a sample of one element: number of peaks = number of isotopes; m/z of each peak = isotope mass (amu); peak height = relative abundance.
- The average atomic mass on the periodic table is a weighted average of the isotope masses. It is also the molar mass in g mol⁻¹.
Key relationships
| Relationship | Meaning | Use it to |
|---|---|---|
| fraction = % ÷ 100 | all fractions add up to 1 | prepare abundances for the weighted average |
| fraction = height ÷ (sum of all heights) | heights scaled with the tallest = 100 | convert relative heights into fractions |
| average = Σ (mass × fraction) | weighted average | find the average atomic mass from a spectrum |
| m₁(1 − x) + m₂x = average | two isotopes, x = fraction of isotope 2 | find abundances from an average atomic mass |
Assumptions
- Each peak comes from a singly charged ion of one atom, so m/z equals the isotope’s mass. (Spectra with molecules, 2+ ions or several elements are outside this topic’s assessment.)
- The sample is one pure element.
- The periodic-table value assumes the natural mix of isotopes; a sample with a different mix has a different average.
Mistakes to avoid
- Simple mean instead of weighted average. Weight each mass by its abundance.
- Relative heights used as percentages. If the tallest peak is 100, divide each height by the total of all heights.
- Forgetting ÷ 100. 75.76% is 0.7576.
- Mixing up height and position. Height = how many; position = how heavy.
- Thinking an atom has the average mass. Each atom is one isotope; the average is for the whole sample.
- Skipping the check. An answer outside the range of isotope masses is always wrong.
Quick self-check
- Chlorine is 75.76% ³⁵Cl (34.969 amu) and 24.24% ³⁷Cl (36.966 amu). What is its average atomic mass? (35.45 amu)
- An element has peaks at m/z 20.0 (90.0%) and 22.0 (10.0%). What is its average atomic mass? (20.2 amu)
- Two peaks have relative heights 100 and 50. What are the percentage abundances? (66.7% and 33.3%)
- In question 1, how tall is the ³⁷Cl peak if the ³⁵Cl peak is drawn at 100? (32.0)
Next: practice questions.