Nuclear equations
Section: Particle Physics | Syllabus: Cambridge AS Level Physics (9702)
Types of Nuclear Radiation
Unstable nuclei emit radiation to become more stable. The main types of nuclear radiation are alpha (α), beta-minus (β⁻), beta-plus (β⁺), and gamma (γ).
| Property | α (alpha) | β⁻ (beta-minus) | β⁺ (beta-plus) | γ (gamma) |
|---|---|---|---|---|
| Composition | 2 protons + 2 neutrons (helium nucleus) | Electron | Positron | Electromagnetic radiation (photon) |
| Symbol | \ ^4_2He or \ ^4_2α | \ ^0_-1e or \ ^0_-1β | \ ^0_+1e or \ ^0_+1β | γ |
| Charge | +2e | -e | +e | 0 |
| Relative mass | 4 u | (1/1836) u (negligible) | (1/1836) u (negligible) | 0 |
Remember: α-particles are the same as helium nuclei (\ ^4_2He). They have the highest mass and charge of all common radiations.
Antiparticles
Antiparticle A particle with the same mass as its corresponding particle but with opposite charge (and other quantum numbers reversed).Key antiparticles you must know:
| Particle | Antiparticle | Mass | Charge |
|---|---|---|---|
| Electron (e^-) | Positron (e^+) | Same | Opposite (+e vs -e) |
| Electron neutrino (_e) | Electron antineutrino (_e) | Same (≈ 0) | Both neutral |
When a particle meets its antiparticle, they annihilate, converting their mass into energy (usually gamma rays).
Neutrinos and Antineutrinos
Neutrinos are fundamental particles with extremely small (nearly zero) mass and no charge. They interact very weakly with matter.
Role in Beta Decay
- In β⁻ decay: an electron antineutrino (_e) is emitted
- In β⁺ decay: an electron neutrino (_e) is emitted
Neutrinos are essential for conserving energy and momentum in beta decay. Without them, the observed energy distribution of beta particles could not be explained.
Key PointThe existence of neutrinos was first proposed to explain why beta particles have a continuous energy spectrum rather than discrete energies. The neutrino carries away varying amounts of energy.
Energy of Emitted Particles
Alpha Particles - Discrete Energies
α-particles are emitted with discrete (specific) energies.
- Each α-particle from a particular nuclear transition has a well-defined energy
- This is because only two particles result from α-decay (the daughter nucleus and the α-particle)
- Energy and momentum conservation uniquely determine the α-particle energy
Graph with "Number of alpha particles" on y-axis and "Energy" on x-axis showing sharp, discrete peaks at specific energy values. This illustrates that all alpha particles from a given decay have the same energy. Each peak corresponds to a specific nuclear transition.
Beta Particles - Continuous Energy Spectrum
β-particles are emitted with a continuous range of energies, from zero up to a maximum value.
- This continuous spectrum initially puzzled physicists - it appeared to violate conservation of energy
- Wolfgang Pauli proposed that another particle was being emitted: the neutrino
- Three particles result from β-decay: the daughter nucleus, the β-particle, and the (anti)neutrino
- The available energy is shared between the β-particle and the neutrino in varying proportions
Graph with "Number of beta particles" on y-axis and "Energy" on x-axis showing a smooth, continuous curve starting from zero, rising to a peak, then falling to zero at maximum energy. The continuous spectrum demonstrates that energy is shared variably between the beta particle and the neutrino.
Exam TipIf asked why β-particles have a continuous energy spectrum, always mention the emission of a neutrino (or antineutrino) that shares the decay energy with the β-particle. The total energy released is constant, but it is distributed variably between these particles.
Radioactive Decay Equations
When writing decay equations, ensure that both nucleon number (A) and charge/proton number (Z) are conserved.
Alpha (α) Decay
In α-decay, the nucleus emits an α-particle (helium nucleus):
\ ^A_ZX -> ^A-4_Z-2Y + ^4_2HeThe parent nucleus loses 4 nucleons (2 protons + 2 neutrons) and its charge decreases by 2.
FIG 11.11: Alpha Decay of Uranium-238Uranium-238 nucleus (²³⁸₉₂U with 92 protons, 146 neutrons) on the left, with an arrow showing decay products: thorium-234 nucleus (²³⁴₉₀Th with 90 protons, 144 neutrons) plus an alpha particle (⁴₂He shown as 2 protons + 2 neutrons). Nuclide notation labelled for each particle.
Example: Alpha Decay of Uranium-238 \ ^238_92U -> ^234_90Th + ^4_2HeCheck conservation:
- Nucleon number: 238 = 234 + 4 ✓
- Proton number: 92 = 90 + 2 ✓
Americium-241 (used in smoke detectors) decays by alpha emission to form neptunium-237:
\ ^241_95Am -> ^237_93Np + ^4_2HeCheck: Nucleon number: 241 = 237 + 4 ✓ | Proton number: 95 = 93 + 2 ✓
Beta-minus (β⁻) Decay
In β⁻ decay, a neutron transforms into a proton, emitting an electron and an electron antineutrino. The decay equation at the nucleon level is:
n arrow p + e^- + _eThe nuclear equation form is:
\ ^A_ZX -> ^A_Z+1Y + ^0_-1e + _eThe nucleon number stays the same, but the proton number increases by 1.
FIG 11.12: Beta-minus Decay at Nucleon LevelA neutron (n, charge 0) transforms into a proton (p, charge +e), emitting an electron (e⁻, charge −e) and an electron antineutrino (ν̄ₑ, charge 0). Arrows show particles being emitted. The equation n → p + e⁻ + ν̄ₑ is illustrated.
Example: Beta-minus Decay of Carbon-14Carbon-14 is used in archaeology for radiocarbon dating:
\ ^14_6C -> ^14_7N + ^0_-1e + _eCheck conservation:
- Nucleon number: 14 = 14 + 0 + 0 ✓
- Charge: 6 = 7 + (-1) + 0 ✓
Strontium-90 (used as spacecraft fuel) undergoes β⁻ decay:
\ ^90_38Sr -> ^90_39Y + ^0_-1e + _eThe daughter nucleus is yttrium (Y, atomic number 39).
Beta-plus (β⁺) Decay
In β⁺ decay, a proton transforms into a neutron, emitting a positron and an electron neutrino. The decay equation at the nucleon level is:
p arrow n + e^+ + _eThe nuclear equation form is:
\ ^A_ZX -> ^A_Z-1Y + ^0_+1e + _eThe nucleon number stays the same, but the proton number decreases by 1.
Example: Beta-plus Decay of Sodium-22 \ ^22_11Na -> ^22_10Ne + ^0_+1e + _eCheck conservation:
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