Average atomic mass is weighted by isotope abundance
You will be able to: Calculate a weighted isotope mean and infer a two-isotope abundance.
Why is the periodic-table mass usually not a whole number?
If a bag contains three 10 g tokens for every one 14 g token, its average token mass is closer to 10 g. An isotope average follows the same weighting idea, but the masses are in atomic mass units.
A useful starting point: Read isotope identity and abundance from a mass spectrum →
Words and symbols before equations
- Atomic mass unit u
- A unit of mass for individual atoms; also called amu.
- Weighted mean
- Sum of each value multiplied by its fraction of the population.
- Mass number A
- Integer proton-plus-neutron count; it differs from a measured isotope mass.
What this picture assumes
Fictional two-isotope sample with simplified masses 20 and 22 u. These are isotope masses for this model, not exact measured natural-isotope data. Fractions sum to one.
Read the picture in three steps
- Identify the chemical species and the quantities each label or axis represents. Read the units and any scale assumptions before comparing values.
- Weighted mean = 20.4 u; lighter-isotope fraction = 0.8.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the chemistry
The average mass is Σfᵢmᵢ. Fractions must sum to 1; percent values must first be divided by 100.
For two isotopes, one fraction is f and the other is 1−f. A measured average can then be used to solve for f. The mean must lie between the isotope masses.
The mean describes a population. It does not require an atom with that exact mass. Real isotope masses are not exactly their mass numbers, and natural isotope proportions can vary between samples. Our integer masses are explicitly simplified.
A worked example, step by step
A teaching sample is 80% 20 u atoms and 20% 22 u atoms. Find its average mass.
- Convert percentages to 0.80 and 0.20.
- Calculate contributions: 0.80(20) = 16.0 u and 0.20(22) = 4.4 u.
- Add: average = 20.4 u.
- It lies between 20 and 22 u and is nearer the more common 20 u isotope.
Do not use an unweighted mean unless the isotope abundances are equal.
Can a 20 u/22 u mixture have a 23 u average?
Compare with an explanation
No. A weighted mean with nonnegative fractions stays between the component values.
Predict. Change one thing. Explain.
Move the lighter-isotope fraction from 0% to 100%. Predict both endpoints and the location of the average.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Weighted mean = 20.4 u; lighter-isotope fraction = 0.8.
Fictional two-isotope sample with simplified masses 20 and 22 u. These are isotope masses for this model, not exact measured natural-isotope data. Fractions sum to one.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use particle counts, mass or charge balance, electron structure, or nuclear attraction to justify your prediction. Separate an observation from an explanation.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionA fictional two-isotope element has masses 30.0 u and 32.0 u and average 30.5 u. Set up and solve for both abundances, then explain why no 30.5 u isotope is required.
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Compare with the answer and four-point rubric
- 1 point: Let f be the fraction of 30.0 u atoms: 30f+32(1−f)=30.5.
- 1 point: 32−2f=30.5 gives f=0.75, or 75%.
- 1 point: The other abundance is 25%.
- 1 point: The average is over the population; individual atoms are one isotope or the other.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1Why use fractional abundances?
They weight the contribution of each isotope to the population average.
RECALL 2Where must a weighted average lie?
Between the smallest and largest component masses.
RECALL 3Is the average necessarily an isotope mass?
No.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Average atomic mass is weighted by isotope abundance
- Average mass = Σfᵢmᵢ.
- For two isotopes: average = fm₁ + (1−f)m₂.
- Mass number counts nucleons; isotope mass measures mass.
Remember: Do not use an unweighted mean unless the isotope abundances are equal.
Conditions: Fictional two-isotope sample with simplified masses 20 and 22 u. These are isotope masses for this model, not exact measured natural-isotope data. Fractions sum to one.
Refresh Kid · AP Chemistry Unit 1 · Objectives 1.2.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 1.2, objectives 1.2.A. CED effective Fall 2024, current official file checked September 16, 2026, together with the published clarifications. This is Unit 1: Atomic Structure and Properties, Topics 1.1–1.8. The topic mapping identifies a framework area; focused lesson titles are our own teaching sequence. Molecular-formula scaling is an application of empirical composition. Models explicitly distinguish atom counts, molecule counts, mass fractions and electron structure. Spectra marked schematic are not measured data. Mass spectra here use single-element, singly charged monatomic ions. Configurations avoid Aufbau exceptions and individual quantum-number assignments. Qualitative attraction and size indices are not exact atomic predictions. The optional NaCl-type spatial block supplements complete charge-balance explanations. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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