An unstable nucleus often decays into another unstable one, and a decay chain ends only when a stable nucleus is reached. Each alpha decay lowers the atomic number by 2 and the mass number by 4; each beta decay raises the atomic number by 1 and leaves the mass number alone. Uranium-238 reaches stable lead-206 after eight alpha and six beta decays.
A grain of uranium doesn't decay once. It sets off a chain of fourteen steps, passing through radon, a gas that seeps into some basements, and ends as lead. How can you follow it?
You know alpha and beta decay and half-life. Now put them in a row.
Engage: Commit to a prediction before you test anything. A wrong guess is fine: it shows you what to look for.
Explore: Try it on the board and compare what happens with your prediction.
Explain: Use the particle model to explain what you saw.
Elaborate: Use the same idea in a new context.
Evaluate: Look back at your first ideas and what changed.
WidthMore contexts, same idea.
Make your prediction first. Help opens once you've locked it in.
EngageCommit to a prediction before you test anything. A wrong guess is fine: it shows you what to look for.
Engage: where does it end?
ExploreTry it on the board and compare what happens with your prediction.
Explore: follow the chain
Use Alpha decay or Beta decay at each step. The board tells you whether that is how the isotope really decays.
Each step changes the atomic number and the mass number. Keep an eye on both.
Try it yourselfYour edits are saved in this browser.
Radon-222 is unstable. Decay it step by step until the isotope is stable.
Use the board. This ticks when you get there.
Start from uranium-238 and follow the chain to the end. It has eight alpha decays and six beta decays.
Use the board. This ticks when you get there.
ExplainUse the particle model to explain what you saw.
Explain: tracking numbers
In your book: write the first four steps of the uranium-238 chain as nuclei, for example ²³⁸U → ²³⁴Th + α. Show the atomic and mass number after each step.
Uranium-238 has atomic number 92. After one alpha decay, what is the new atomic number?
And the new mass number, after the alpha decay from mass number 238?
Thorium-234 (atomic number 90) then decays by beta emission. What is the new atomic number?
Uranium-238 ends as lead-206. By how much does the mass number fall in total?
Only alpha decays change the mass number, by 4 each time. How many alpha decays are in the chain?
Elaborate TypicalUse the same idea in a new context.
Elaborate: radon in the home
Elaborate WiderUse the same idea in a new context.
Elaborate: missing mass
EvaluateLook back at your first ideas and what changed.
Evaluate: look back
Write one sentence: "At first I thought… Now I think… because…"
Revision summary
A decay chain is a series of decays that ends only at a stable nucleus.
Alpha decay: atomic number −2, mass number −4. Beta decay: atomic number +1, mass number unchanged.
Uranium-238 ends as lead-206 after 8 alpha and 6 beta decays.
Alpha decays make the nucleus smaller and beta decays fix its balance of neutrons to protons, until it is stable.
For teachers
Students trace a decay sequence, track atomic and mass numbers at each step, and explain how the sequence ends at a stable nucleus (AC9S9U06, node 5, an integration node). About 22 minutes.
I can follow a decay chain from an unstable isotope to a stable one.
I can work out the atomic and mass numbers after each alpha or beta decay.
I can say why a chain stops.
Before class
A short integration tutorial that follows the half-life lesson. Set the width with ?width=minimum, typical (default) or wider.
The decay board stops at a stable isotope and says whether each step is how the isotope really decays, so students can't wander into impossible chains. The uranium-238 chain used here is the main series: eight alpha and six beta decays, with a few side branches in the full chart that are left out.
Board notes: the board counts alpha (x) and beta (y) decays. Half-lives vary from a fraction of a second to billions of years and aren't shown here.
Running the lesson
Engage: tally the predictions. Ask the 'stable lead' group what makes a nucleus stable.
Explore: ask what is the same about every alpha step, and every beta step.
Explain: the number questions and 'why it stops' are the success criteria.
In your own words: the first four steps of the chain.
The hard part (on purpose)
Keeping two numbers in step. When a student changes only one of the atomic or mass numbers, ask what each particle carried away.
When students get stuck
A student subtracts 4 from the atomic number for alpha. Ask: How many protons does an alpha particle carry? Fix: Two, so the atomic number falls by 2; the mass number falls by 4.
A student changes the mass number in beta decay. Ask: What changes in the nucleus in beta decay? Fix: A neutron becomes a proton: the atomic number rises by 1 and the mass number stays the same.
Stretch and support
Stretch: Thorium-232 decays by 6 alpha and 4 beta decays to a stable lead isotope. Which isotope? (232 − 24 = 208; 90 − 12 + 4 = 82: lead-208.)
Support: Give a two-column table (Alpha, Beta) with the change to atomic and mass number filled in, and ask students to tick the right column at each step on the board.
Where it leads
Next: word equations and balancing equations.
In class: draw the decay series on a large wall chart with a bar for each isotope's half-life; ask students to colour the alpha and beta steps.
What each step is for
Engage: where does it end?: Students expect decay to end after one step. The node's point is that each step often leaves another unstable nucleus, so the chain continues until the nucleus is stable: alpha decays shrink it, beta decays fix its balance of neutrons and protons.
Explore: follow the chain: Choosing alpha or beta at each step from the atomic and mass numbers, and watching the nucleus change element, makes the bookkeeping rule something students use, not recite.
Explain: tracking numbers: Applying the two rules to one step, to a whole chain and then to the question of why it stops covers the three success criteria.
Elaborate: radon in the home: Radon is the best-known step in the chain, because it is a gas and shows why the order of the steps matters in the real world.
Elaborate: missing mass: The energy released in decay links to mass, which is the idea behind nuclear power.
Now you can
Follow a decay chain from an unstable isotope to a stable one.
Work out the atomic and mass numbers after each alpha or beta decay.