Understand nuclear stability, decay modes and the role of neutrinos
AQA A-Level Physics 2
🗺️Describe the N-Z stability curve
💪Explain the strong nuclear force and its properties
⬇️Write and balance alpha decay equations
⚡Write and balance beta-minus and beta-plus decay equations
👻Explain the role of neutrinos and antineutrinos
🎯Predict which decay mode a given nucleus will undergo
The Strong Nuclear Force
The nucleus contains positively charged protons packed closely together. The electrostatic (Coulomb) repulsion between them would blow the nucleus apart — so there must be another force holding it together.
Strong nuclear force: A short-range attractive force that acts between all nucleons (proton-proton, neutron-neutron, proton-neutron). It is responsible for holding the nucleus together.
Key properties of the strong nuclear force:
Attractive at distances of ~1–3 fm (femtometres, 10⁻¹⁵ m)
Repulsive at very short range (<0.5 fm) — prevents nucleons from merging
Acts equally on all nucleons regardless of charge
Very short range — negligible beyond ~3 fm
For large nuclei (many protons), the electrostatic repulsion between protons acts across the whole nucleus, while the strong force only acts between neighbouring nucleons. Beyond ~82 protons, no stable nuclei exist.
The N-Z Stability Curve
If we plot neutron number N against proton number Z for all known stable nuclei, the points follow a curved band called the line of stability (or N-Z curve).
For light nuclei (Z < 20): Stable nuclei have approximately equal numbers of protons and neutrons (N ≈ Z). They lie close to the N = Z line.
For heavier nuclei (Z > 20): Extra neutrons are needed to provide additional strong nuclear force without adding to electrostatic repulsion. The stability curve bends away from N = Z towards N > Z.
Nuclei that lie off the stability curve are unstable and undergo radioactive decay:
Position on N-Z plot
Too many...
Decay mode
Above curve
Neutrons
Beta-minus (β⁻) decay
Below curve
Protons
Beta-plus (β⁺) decay or electron capture
Z > 82 (very heavy)
Nucleons
Alpha (α) decay
Alpha Decay
An alpha particle (⁴₂He nucleus: 2 protons + 2 neutrons) is emitted from a heavy nucleus. This reduces both Z and N, moving the nucleus towards stability.
General: ᴬ_Z X → ᴬ⁻⁴_(Z−2) Y + ⁴₂He
Example: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He
Conservation laws in alpha decay: Mass number A is conserved (238 = 234 + 4). Proton number Z is conserved (92 = 90 + 2). Charge is conserved.
Alpha particles are emitted with discrete kinetic energies (monoenergetic), confirming the energy levels of the nucleus are quantised.
Beta Decay and Neutrinos
There are two types of beta decay. Both convert a nucleon from one type to another.
Beta-minus (β⁻) decay: A neutron turns into a proton. An electron and an antineutrino are emitted. Occurs when N is too high (too many neutrons).
n → p + e⁻ + ν̄_e
Example: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̄_e
Beta-plus (β⁺) decay: A proton turns into a neutron. A positron and a neutrino are emitted. Occurs when Z is too high (too many protons).
p → n + e⁺ + ν_e
Example: ²²₁₁Na → ²²₁₀Ne + ⁰₊₁e + ν_e
The neutrino was proposed by Pauli (1930) because beta particles have a continuous energy spectrum — meaning the decay energy is shared between the beta particle and the (anti)neutrino. Without the neutrino, energy and momentum would not be conserved.
Neutrinos have negligible mass and zero charge. They interact very weakly with matter, making them extremely difficult to detect.
Thorium-228 undergoes alpha decay. Write the full nuclear equation and identify the daughter nucleus.
3Z = 39 → Yttrium (Y); also emit β⁻ particle (⁰₋₁e) and antineutrino
⁹⁰₃₈Sr → ⁹⁰₃₉Y + ⁰₋₁e + ν̄_e
A nucleus ²²₁₁Na undergoes β⁺ decay. Write the equation and explain why this nucleus is unstable.
1β⁺ decay: A stays the same, Z decreases by 1
2Z_new = 11 − 1 = 10 → Neon (Ne)
3²²₁₁Na → ²²₁₀Ne + ⁰₊₁e + ν_e
4Stability: Na-22 has Z=11, N=11. For Z=11 the N-Z curve is close to N=Z, but Na-22 lies slightly below the curve (too many protons relative to neutrons) → β⁺ decay moves it up towards stability.
²²₁₁Na → ²²₁₀Ne + ⁰₊₁e + ν_e
Explain why the existence of the neutrino was proposed and what evidence supported it.
1In beta decay, if only an electron were emitted, it would carry away all the decay energy → electrons would all have the same kinetic energy (monoenergetic)
2Experiment showed beta particles have a continuous energy spectrum — electrons can have any energy from zero up to a maximum
3This violates conservation of energy unless another particle (the neutrino/antineutrino) carries away the remaining energy
The continuous beta energy spectrum is evidence that decay energy is shared between the beta particle and the (anti)neutrino
1. Which decay mode occurs when a nucleus has too many neutrons?
Too many neutrons → above the stability curve → β⁻ decay converts a neutron to a proton, reducing N and increasing Z.
2. In alpha decay, by how much does the mass number A change?
An alpha particle ⁴₂He has A=4 and Z=2, so A decreases by 4 and Z decreases by 2 in alpha decay.
3. What is emitted alongside a positron in beta-plus decay?
β⁺ decay: p → n + e⁺ + ν_e. A neutrino (ν_e) is emitted. β⁻ decay emits an antineutrino (ν̄_e).
4. The strong nuclear force between two nucleons becomes repulsive below approximately what distance?
The strong force is repulsive below ~0.5 fm, attractive between ~0.5–3 fm, and negligible beyond ~3 fm.
5. ²¹⁰₈₃Bi undergoes beta-minus decay. What is the daughter nucleus? Write the nuclide notation.
1. Radium-226 decays by alpha emission to radon, then radon undergoes further alpha decay. Write both nuclear equations and state the final nucleus.
2. Explain why heavy nuclei (Z > 82) are all unstable, referring to the properties of the strong nuclear force and electrostatic repulsion.
The strong nuclear force is short-range (effective only to ~3 fm), so a nucleon only "feels" the attraction from its nearest neighbours. However, the electrostatic repulsion between protons is long-range — each proton repels every other proton across the whole nucleus. As Z increases, the cumulative repulsion grows, while the strong force cannot increase proportionally (it saturates). Beyond Z = 82, even adding extra neutrons (which provide strong-force attraction but no extra repulsion) cannot stabilise the nucleus. All nuclei with Z > 82 are therefore unstable.
3. A student claims that beta particles from a radioactive source should all have the same kinetic energy if energy is conserved. Explain why this claim is incorrect and what this reveals about the nature of beta decay.
The student's claim would be correct if only the beta particle were emitted. However, beta particles have a continuous energy spectrum — they can have any energy from zero up to a maximum (the Q-value of the decay). This indicates that a third particle (antineutrino in β⁻, neutrino in β⁺) is also emitted and shares the decay energy in varying proportions. The antineutrino has negligible mass and zero charge and was not observed at the time, but its existence was necessary to conserve energy and momentum. This was confirmed experimentally by Cowan and Reines in 1956.