Physics › Particles › The conserved quantities
The conserved quantities
An interaction can occur only if charge, baryon number, the two lepton numbers and, in a strong interaction, strangeness are all conserved. Beta-minus decay is a down quark becoming an up and beta-plus an up becoming a down.
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Conservation laws, part 1 of 2. Part 2 is Energy, momentum and particle tracks.
Builds on Quarks and the hadrons built from them and Stable and unstable nuclei.
IN THIS TOPIC
- Describe the quark character change in β− and β+ decay.
- Check interactions against conservation of charge, baryon number, lepton number and strangeness.
COMMON MISCONCEPTION
In particle physics, anything can happen.
Not every reaction is allowed: a particle interaction can only happen if charge, baryon number and each lepton number are conserved, and strangeness is also conserved in strong interactions.
Beta decay as a change of flavour
Both beta decays are single-quark events. In β− a down quark becomes an up, d → u, with the W− carrying off the charge and turning into e− plus an electron antineutrino. In β+ an up becomes a down, u → d, via a W+ that gives a positron and an electron neutrino. A complete answer states the quark change and names the W boson.
Checking a proposed interaction
For each proposed interaction, check conservation of charge, baryon number, lepton number, energy and momentum. Lepton number must balance for the electron family and the muon family separately. Strangeness is conserved in strong interactions, but may change by 0 or ±1 in weak ones.
Describe the drawing
The interaction antineutrino plus proton to neutron plus positron audited line by line: charge, baryon number, electron lepton number and strangeness each show the same total before and after, with a cyan tick on every row. Passing the four quantum-number checks is necessary; energy and momentum must also be possible.
Work in columns, one quantum number at a time, totalling each side of the arrow. For any particle outside the familiar set, the necessary data will be provided in the question, so this is careful checking and nothing to recall. A single failed line means the interaction cannot occur, and no exception to these conservation laws has been observed.
WORKED EXAMPLE
A check that fails, and the fix
A student writes neutron decay as n → p + e−, with no third product. Check it against the conservation laws.
Charge runs 0 → +1 − 1 = 0, which passes. Baryon number runs 1 → 1 + 0, which passes.
Lepton number runs 0 → 0 + 1. That fails. One failed line is enough, so the decay cannot happen as written.
The fix is an electron antineutrino, lepton number −1, giving n → p + e− + e and balancing every line. The failed check both rejected the equation and identified the missing particle.
GUIDED PRACTICE
A neutrino interaction
Check the interaction νμ + n → μ− + p against charge, baryon number, and both lepton numbers. Run all four lines.
Show the working
Charge runs 0 + 0 → −1 + 1 = 0. Baryon number runs 0 + 1 → 0 + 1. Muon lepton number runs 1 + 0 → 1 + 0. Electron lepton number is zero throughout.
All four pass, so no conservation law forbids the interaction; with enough incident energy for energy and momentum to balance as well, it happens. Detectors identify muon neutrinos in exactly this way.
The two laws that always apply has moved to the next part of this lesson.
Reading particle tracks, an Edexcel skill has moved to the next part of this lesson.
ASSESSMENT FOCUS
- Set the working out as a table: one row per quantum number, totals on both sides, and a verdict on each row. Show the table even when the answer is “not allowed”, since the failed row is the reason.
- Lepton numbers are checked per family. An interaction turning a muon neutrino into an electron fails on the two families separately even when the grand total balances.
- Strangeness carries a conditional rule, conserved in strong interactions and free to change by 0 or ±1 in weak ones. Say which interaction is being checked before applying it.
- For an unfamiliar particle, the question prints its quantum numbers. Read them, and never guess from the symbol.
- A complete beta-decay answer names the quark change and the W boson: d → u with a W− for β−, u → d with a W+ for β+. The two spectator quarks are unchanged and saying so costs nothing.
CHECK YOURSELF
A student proposes the interaction π− + p → K0 + Λ0, a strong interaction. The K0 has strangeness +1 and baryon number 0; the Λ0 has strangeness −1 and baryon number +1; the pion and the proton have strangeness 0. Audit charge, baryon number and strangeness, and give a verdict.
Show a hint
One row per quantum number, totals on both sides. Which rule applies to strangeness in a strong interaction?
Show the answer
Charge runs −1 + 1 = 0 → 0 + 0 = 0 ✓.
Baryon number runs 0 + 1 = 1 → 0 + 1 = 1 ✓.
Strangeness runs 0 + 0 = 0 → +1 − 1 = 0 ✓, and in a strong interaction strangeness must be conserved exactly, which it is.
Every row passes, so no conservation law forbids it, and with enough incident energy it happens. The two strange particles are made together for exactly this reason: strange particles are produced in pairs.
Check conservation of charge, baryon number, lepton number and strangeness.
One failed row is enough to forbid an interaction, and it is also the reason to quote.
WORKBOOK
Printable practice for this topic: original exam-style questions with room to work, and a fully worked answer book. Free to use; please do not redistribute or sell.
Or read them with their mark schemes on the conserved quantities questions page.
USED LATER IN
CHECK YOUR PROGRESS
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- Describe the quark character change in β− and β+ decay.
- Check interactions against conservation of charge, baryon number, lepton number and strangeness.
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