Subatomic Particles, Ions, and Isotopes: Why Atomic Masses Aren't Whole Numbers
60 min · SC.912.P.8.2
Objective
Students will identify the location, charge, and relative mass of protons, neutrons, and electrons; distinguish atoms from ions and isotopes; and calculate weighted average atomic mass from isotope abundance data.
Content
Carbon's atomic mass on the periodic table is listed as 12.011 amu, even though a carbon atom must have a whole number of protons and neutrons. Almost all carbon in the human body is carbon-12 (6 protons, 6 neutrons), but a tiny fraction is carbon-14 (6 protons, 8 neutrons). Both are carbon — same element, same chemistry — but one is heavier and slightly radioactive. Archaeologists use carbon-14's radioactive decay to date bones, mummies, and artifacts like the Shroud of Turin. The 12.011 on the periodic table is a weighted average across these isotopes.
Delivery
Open by asking students: "Why does the periodic table say carbon's mass is 12.011 amu when a carbon atom must have a whole number of protons and neutrons?" Let 2–3 students guess. Then tell them that by the end of class they'll be able to calculate that number themselves.
Optional video:search YouTube for“Subatomic Particles, Ions, and Isotopes: Why Atomic Masses Aren't Whole Numbers”
Preview it yourself before class to make sure it fits and is classroom-appropriate.
- 6m
The three subatomic particles: location, charge, mass
Content
Every atom is built from three subatomic particles. Protons sit in the nucleus, carry a +1 charge, and have a mass of about 1 amu. Neutrons also sit in the nucleus, carry 0 charge, and have a mass of about 1 amu. Electrons live in a cloud around the nucleus, carry a −1 charge, and have a mass of only about 1/1836 amu — so small that we usually treat electron mass as negligible when calculating atomic mass. The nucleus is tiny but holds essentially all the mass; the electron cloud is huge in volume but contributes almost nothing to mass. The atomic number (Z) equals the number of protons, and Z is what defines the element — change Z and you've changed elements entirely.
Delivery
Walk through the labeled atom diagram particle by particle, naming charge and mass each time. Emphasize the mass contrast: 'A proton is about 1836 times heavier than an electron — that's why almost all the mass is in the nucleus.' Ask students to predict: 'If I told you an atom has 6 protons, what element is it?' (Carbon — no exceptions.) Pre-empt the misconception that electrons contribute meaningful mass — they don't, which is why we can approximate mass number as just protons + neutrons.
- 5m
Atomic number vs. mass number — reading the periodic table cell
Content
Every periodic table cell shows two numbers. The atomic number (Z) is the whole number, usually shown above the element symbol — it's the count of protons. The atomic mass is the decimal number below the symbol — it's the weighted average atomic mass in amu. Mass number (A) is different from atomic mass: A is protons + neutrons in ONE specific atom, and it's always a whole number. For a neutral atom, the number of electrons equals the number of protons. To find neutrons: neutrons = A − Z. For example, an atom with A = 23 and Z = 11 (sodium-23) has 11 protons, 11 electrons, and 23 − 11 = 12 neutrons.
Delivery
Point out the zoomed-in periodic table cell and explicitly label which number is which. Emphasize the difference between the two 'mass' terms — this is the #1 confusion point. Mass number = whole number, one specific atom. Atomic mass = decimal, average across all isotopes. Work the sodium-23 example on the board slowly: 'How many protons? 11. How many electrons in a neutral atom? Also 11. How many neutrons? 23 minus 11 equals 12.' Have students do fluorine-19 (Z=9) as a quick check: 9p, 9e, 10n.
- 5m
Isotopes: same element, different neutron count
Content
Isotopes are atoms of the same element that have different numbers of neutrons. Because they have the same number of protons, they are still the same element and behave the same chemically — but they have different mass numbers. The classic example is uranium: ²³⁵U and ²³⁸U both have 92 protons (both are uranium), but ²³⁵U has 143 neutrons and ²³⁸U has 146 neutrons. Only ²³⁵U is used as nuclear fuel because its nucleus is fissile. Most isotopes in nature are perfectly stable — carbon-12, oxygen-16, and iron-56 are all stable isotopes. Radioactive isotopes exist, but 'isotope' does not automatically mean 'radioactive.'
Delivery
Use the ²³⁵U vs ²³⁸U side-by-side comparison to anchor the definition — same protons, different neutrons, still uranium. Directly attack the misconception: 'Isotopes are NOT automatically radioactive. The carbon in your body is 99% carbon-12, a stable isotope. Radioactivity is a separate property that only SOME isotopes have.' Quick check: 'If I have an atom with 6 protons and 7 neutrons, what element is it, and is it an isotope of anything?' (Carbon-13, an isotope of carbon.)
- 5m
Ions: same element, different electron count
Content
An ion is an atom that has gained or lost electrons, giving it a net electric charge. The proton count never changes — if it did, the element would change. A cation is positive (lost electrons); an anion is negative (gained electrons). Neutral sodium has 11 protons and 11 electrons; Na⁺ still has 11 protons but only 10 electrons, so it's +1 overall. Neutral chlorine has 17 protons and 17 electrons; Cl⁻ has 17 protons and 18 electrons, so it's −1 overall. Notice: neither one is a different element, and neither one is an isotope — neutron count didn't change, only electron count did.
Delivery
Use the atom vs cation vs anion three-panel comparison to walk through Na → Na⁺ and Cl → Cl⁻. Emphasize what stays the same (protons — so it's still sodium, still chlorine) and what changes (electrons — so the charge changes). Hit the misconception head-on: 'Adding or removing an electron does NOT change the element. Only changing protons does that.' Summary table: change protons → new element; change neutrons → isotope; change electrons → ion.
- 4m
Weighted average atomic mass — the math
Content
The atomic mass on the periodic table is a weighted average of all naturally occurring isotopes of that element. 'Weighted' means the more common isotopes count more heavily. The formula is: average atomic mass = (mass₁ × abundance₁) + (mass₂ × abundance₂) + …, where abundances are written as decimals (percent ÷ 100). Worked example — chlorine: ³⁵Cl has mass 34.97 amu and abundance 75.77%; ³⁷Cl has mass 36.97 amu and abundance 24.23%. Average = (34.97)(0.7577) + (36.97)(0.2423) = 26.50 + 8.96 = 35.46 amu. That's why chlorine's periodic table mass is 35.45, not a nice whole number — most chlorine is ³⁵Cl, but enough ³⁷Cl exists to pull the average up.
Delivery
Walk through the chlorine calculation step by step. Emphasize: convert percentages to decimals BEFORE multiplying. Sanity-check the answer — the weighted average must fall between the two isotope masses, and closer to the more abundant one. If a student gets 35.97, they averaged without weighting. Tell them the next activity has them do this calculation with beans instead of chlorine — but the math is identical.
- 25m
Beanium Lab: Modeling Isotope Abundance and Weighted Average MassLab
Setup (before class): Prepare one cup per lab group containing ~30–40 total beans mixed from three varieties — roughly 60% pinto, 30% black, 10% lima (vary slightly per cup so groups get different answers, but stay near this ratio). Each group gets: 1 cup of 'beanium,' 1 electronic balance, 3 weigh boats, and the handout below. Tell students: 'These beans are three isotopes of a made-up element called Beanium. Each variety is one isotope. Your job is to find Beanium's average atomic mass.' Run-of-show: 2 min introduce and distribute materials; 15 min groups work; 5 min share results and discuss; 3 min debrief. Walk around and check: (1) Are they zeroing the balance with the weigh boat on it? (2) Are they converting percentages to decimals before multiplying? (3) Are they computing average mass per bean (total mass ÷ count) for each isotope, NOT just using the mass of one bean? Student handout: Beanium Lab — Finding the Average Atomic Mass of an Element Your cup contains three isotopes of Beanium (Be*): pinto-beanium, black-beanium, and lima-beanium. Each variety is one isotope. Your job is to determine Beanium's weighted average atomic mass — in beans, 1 amu = 1 gram for this lab. Part 1 — Sort and count 1. Pour your cup onto a weigh boat and separate the beans into three piles by variety. 2. Count each pile and record below. - Pinto beans: - Black beans: - Lima beans: - Total beans: Part 2 — Find the mass of each isotope Zero the balance with an empty weigh boat on it. Then, for each variety: 1. Place the entire pile on the weigh boat. 2. Record the total mass. 3. Divide by the number of beans to get average mass per bean. - Pinto: total mass = g, average per bean = g - Black: total mass = g, average per bean = g - Lima: total mass = g, average per bean = g Part 3 — Find the abundance of each isotope Abundance (%) = (number of that isotope ÷ total beans) × 100 - Pinto abundance: % → as decimal: - Black abundance: % → as decimal: - Lima abundance: % → as decimal: Check: your three decimals should add to 1.00 (allowing for rounding). Part 4 — Calculate the weighted average atomic mass of Beanium Use: average mass = (mass₁ × abundance₁) + (mass₂ × abundance₂) + (mass₃ × abundance₃) Show your work: Weighted average atomic mass of Beanium = g Part 5 — Analysis questions 1. Is your weighted average closer to the mass of the most abundant bean or the least abundant bean? Why does that make sense? 2. Two lab groups might get different answers for Beanium's average mass. Does that mean one is wrong? Explain using the idea of natural abundance. 3. In the real world, why does chlorine's periodic table mass (35.45 amu) sit closer to 35 than to 37? Do NOT eat the beans. They are lab materials.
Materials
- electronic balances
- mixed dried beans of 2-3 varieties (pinto, lima, black)
- weigh boats
- plastic cups
Example outputs
- A group with 20 pinto (0.35 g each), 12 black (0.20 g each), and 4 lima (0.80 g each) out of 36 total: pinto 55.6% → 0.556; black 33.3% → 0.333; lima 11.1% → 0.111. Average = (0.35)(0.556) + (0.20)(0.333) + (0.80)(0.111) = 0.194 + 0.0666 + 0.0888 = 0.35 g.
- Analysis Q1: The average is closest to pinto because pinto is the most abundant — it 'weighs' the most in the calculation. Q2: Different groups get different answers because they scooped slightly different abundances by chance; in the real world, natural abundances are fixed, which is why every carbon atom sample on Earth averages to 12.011 amu.
An atom has a mass number of 31 and an atomic number of 15. How many protons, neutrons, and electrons does the neutral atom have?
short answer15 protons, 16 neutrons, 15 electrons. (Z = 15 gives protons; A − Z = 31 − 15 = 16 gives neutrons; neutral atom → electrons = protons.)Which of the following pairs are isotopes of each other?
- A)⁴⁰Ca and ⁴⁰Ar
- B)³⁵Cl and ³⁷Cl
- C)Na and Na⁺
- D)O and O²⁻
multiple choiceB) ³⁵Cl and ³⁷Cl. Both have 17 protons (same element) but different mass numbers due to different neutron counts. A is two different elements (different Z). C and D are ion/atom pairs, not isotope pairs.Copper has two naturally occurring isotopes: ⁶³Cu (mass 62.93 amu, 69.17% abundant) and ⁶⁵Cu (mass 64.93 amu, 30.83% abundant). Calculate the weighted average atomic mass of copper.
calculationAverage = (62.93)(0.6917) + (64.93)(0.3083) = 43.53 + 20.02 = 63.55 amu (Matches the periodic table value for Cu.)A magnesium ion has 12 protons, 12 neutrons, and 10 electrons. What is its charge, and is it a cation or an anion?
short answerCharge = +2 (12 protons − 10 electrons = +2). It is a cation, written Mg²⁺. Losing electrons made it positive.True or false: An atom with 8 protons and 10 neutrons is a different element from an atom with 8 protons and 8 neutrons. Explain.
short answerFalse. Both atoms have 8 protons, so both are oxygen. They are isotopes of each other (¹⁸O and ¹⁶O). Only a change in proton count changes the element.
- proton
- Positively charged subatomic particle (+1) in the nucleus; mass ≈ 1 amu. Its count (atomic number, Z) defines the element.
- neutron
- Neutral subatomic particle (0 charge) in the nucleus; mass ≈ 1 amu. Its count can vary within one element, producing isotopes.
- electron
- Negatively charged subatomic particle (−1) in the electron cloud; mass ≈ 1/1836 amu. Its count can change to form ions.
- atomic number (Z)
- Number of protons in the nucleus. Same for every atom of an element.
- mass number (A)
- Total number of protons + neutrons in one specific atom. Always a whole number.
- isotope
- Atoms of the same element (same Z) with different numbers of neutrons, giving different mass numbers. Example: ²³⁵U and ²³⁸U.
- ion
- An atom that has gained or lost electrons, giving it a net electric charge. Proton count stays the same.
- cation
- Positively charged ion formed when an atom loses electrons (e.g., Na⁺: 11 protons, 10 electrons).
- anion
- Negatively charged ion formed when an atom gains electrons (e.g., Cl⁻: 17 protons, 18 electrons).
- atomic mass unit (amu)
- Unit of mass for atoms; 1 amu ≈ mass of one proton or one neutron.
- weighted average atomic mass
- The average mass of an element's atoms, weighted by the natural abundance of each isotope. This is the decimal number on the periodic table.
- 'Isotopes are radioactive.' Most isotopes are stable — carbon-12, oxygen-16, and iron-56 are the most common forms of those elements and are not radioactive. Being an isotope just means 'has a different neutron count than another atom of the same element.' Radioactivity is a separate property that only some isotopes have.
- 'The atomic mass on the periodic table is the mass of one atom.' It's actually a weighted average across all naturally occurring isotopes of that element. That's why the number is a decimal — no single atom has a mass of 12.011 amu, but the average of all carbon atoms does.
- 'Mass number and atomic mass are the same.' Mass number (A) is a whole number that counts protons + neutrons in ONE specific atom. Atomic mass (on the table) is a decimal that averages across isotopes. They almost never match exactly.
- 'Adding or removing electrons changes what element you have.' Only the proton count defines the element. Losing an electron turns Na into Na⁺, but it's still sodium — just a sodium cation. Changing neutrons makes an isotope; changing electrons makes an ion; only changing protons makes a new element.
- 'Electrons contribute meaningful mass to an atom.' An electron is about 1/1836 the mass of a proton, so we treat electron mass as negligible. Nearly all of an atom's mass is in the nucleus.
- Electronic balances (1 per group)
- Mixed dried beans of 2–3 varieties: pinto, lima, black (~30–40 beans per group, pre-mixed roughly 60/30/10)
- Weigh boats (3 per group)
- Plastic cups (1 per group, to hold pre-mixed 'beanium')
- Beanium lab handout (1 per student)
- Calculators
- Periodic table (1 per student)