Safety and evidence boundary
Use supplied numerical isotope data and simulations only.
Explicit science instruction
Periodic-table atomic mass is usually a weighted average, not the mass number of one atom. Each isotope contributes according to both its isotopic mass and its fractional abundance.
The calculation is Σ(mass × fractional abundance). Percentages must be converted to decimal fractions or divided by 100 before multiplying.
A weighted average should lie between the contributing isotope masses when all abundances are positive and sum to one. Use that as a sanity check.
Vocabulary: weighted average; fractional abundance; relative atomic mass; isotopic mass; sanity check.
Worked example with reasoning
Synthetic element X: 75.0% X-35 and 25.0% X-37. Average mass = 35(0.750)+37(0.250)=26.25+9.25=35.50 u. The answer is closer to 35 because that isotope is more abundant.
Guided question
Calculate the weighted average for isotopes 10 u at 80% and 11 u at 20%, then explain why a simple arithmetic mean would be inappropriate.
Independent work
- Solve three two-isotope weighted-average problems.
- For each result, write an expected range before calculating.
- Create one inverse problem and estimate which isotope must be more abundant.
Misconception check
Do not average isotope masses by simply adding and dividing by the number of isotopes unless their abundances are equal.
Formative understanding check
Why can a periodic-table atomic mass be non-integer even though a particular isotope has a whole-number mass number?
Reveal worked response
Because the table value is an abundance-weighted average across isotopes, whereas mass number counts protons plus neutrons in one nucleus.
Public self-check only.
Mentor evidence conference
Ask Archaemenes to verify your abundance conversion, arithmetic, and whether the final value passes the between-isotopes sanity check.
Teacher guidance
Foundation: Use a two-row weighted-average organizer.
Core: Calculate and interpret weighted averages with percentage abundance.
Extended: Solve an inverse abundance problem and state the assumptions behind it.