Short on time? This page is the recap. For explanations, both figures and the worked examples, use the full study guide.
Recap
- The strong force acts between nucleons, dominates at nuclear distances (about 10⁻¹⁵ m) and is negligible beyond a few of those distances.
- Fusion: small nuclei join into a larger one (plus particles). Fission: a nucleus splits into smaller nuclei (plus particles, usually neutrons).
- Either process releases energy when the products have a higher binding energy per nucleon. The peak of the curve is near iron.
- Some heavy nuclei fission spontaneously; others need an energy input, such as absorbing a neutron.
- Released energy appears as kinetic energy of the products or as photons.
- Decay is random for one nucleus. Probability makes a large sample predictable.
- Half-lives range from fractions of a second to billions of years. You are given them; you do not memorise them.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| ΣA before = ΣA after; ΣZ before = ΣZ after | A = nucleon number, Z = charge number | find a missing product |
| E = mc², Q = Δm c² | c = 3.00 × 10⁸ m/s | find energy released from a mass decrease |
| 1 u = 1.66 × 10⁻²⁷ kg = 931 MeV/c² | 1 MeV = 1.60 × 10⁻¹³ J | convert mass in u straight to MeV |
| p_before = p_after | from rest: equal and opposite p | share energy: K ∝ 1/m for two products |
| λ = ln 2 / t½ | λ in s⁻¹ (or h⁻¹, etc.) | link the decay constant and half-life |
| N = N₀e^(−λt) = N₀(½)^(t/t½) | N = undecayed nuclei | predict the amount left or, with logs, an age |
Assumptions behind the numbers
- The sample is large, so the actual number left is very close to the predicted value.
- Count rates have the background subtracted before you use them.
- Reactants start at rest unless the question says otherwise.
Mistakes to avoid
- Calling mass conserved. Nucleon number is conserved; mass decreases when energy is released.
- Treating binding energy as stored energy. It is the energy needed to pull the nucleus apart.
- “Two half-lives = all gone.” It leaves ¼.
- Mixing time units. λ in h⁻¹ needs t in hours.
- Sharing energy equally. The lighter product gets more kinetic energy.
- Forgetting neutrons when balancing a fission equation.
Quick self-check
- What fraction of a sample is left after 3 half-lives? (⅛)
- A source has a half-life of 10 s. What is λ? (0.0693 s⁻¹)
- A reaction loses 0.0100 u of mass. How much energy is released? (9.31 MeV)
- Balance: ¹₀n + ²³⁵₉₂U → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + ? (3 ¹₀n)
Next: practice questions.