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 fraction u (negligible) fraction u (negligible) 0 Exam Tip 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 (ν_e) Electron antineutrino (ν_e) Same (≈ 0) Both neutral Positron The antiparticle of the electron.
It has the same mass as an electron but a positive charge (+e). Symbol: e^+ or \ ^0_+1e Important 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 (ν_e) is emitted In β⁺ decay : an electron neutrino (ν_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 Point The 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 FIG 11.9: Alpha Particle Energy Spectrum 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 FIG 11.10: Beta Particle Energy Spectrum 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 Tip If 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_2He The parent nucleus loses 4 nucleons (2 protons + 2 neutrons) and its charge decreases by 2 .
FIG 11.11: Alpha Decay of Uranium-238 Uranium-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_2He Check conservation: Nucleon number: 238 = 234 + 4 ✓ Proton number: 92 = 90 + 2 ✓ Example: Alpha Decay of Americium-241 Americium-241 (used in smoke detectors) decays by alpha emission to form neptunium-237: \ ^241_95Am -> ^237_93Np + ^4_2He Check: 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 p + e^- + ν_e The nuclear equation form is: \ ^A_ZX -> ^A_Z+1Y + ^0_-1e + ν_e The nucleon …
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