Nuclear decay — Eduqas A-Level Physics

Nuclear decay is the process by which unstable atomic nuclei lose energy by emitting radiation. This topic is central to nuclear physics and covers the three main types of decay: alpha, beta, and gamma. Each type involves different particles and has distinct properties, such as ionising power and penetration depth. Understanding nuclear decay is essential for explaining natural radioactivity, nuclear reactions, and applications like medical imaging and carbon dating.

In the WJEC A-Level Physics syllabus, nuclear decay builds on atomic structure and introduces key concepts such as decay equations, half-life, and the random nature of decay. You will learn to write balanced nuclear equations, calculate decay constants, and use exponential decay models. This topic also links to energy-mass equivalence (E=mc²) and the stability of nuclei, providing a foundation for more advanced topics like nuclear fission and fusion.

Mastering nuclear decay is not just about memorising facts; it requires applying mathematical models to real-world scenarios. For example, you might calculate the age of an archaeological sample using carbon-14 dating or determine the activity of a radioactive source. These skills are highly valued in exams and demonstrate a deep understanding of how the physical world operates at the nuclear level.

• →Alpha decay: emission of an alpha particle (helium nucleus, 2 protons + 2 neutrons), resulting in a daughter nucleus with atomic number decreased by 2 and mass number decreased by 4.
• →Beta-minus decay: a neutron converts into a proton, emitting an electron and an antineutrino; atomic number increases by 1, mass number unchanged.
• →Gamma decay: emission of high-energy photons from an excited nucleus, often following alpha or beta decay; no change in atomic or mass number.
• →Half-life: the time taken for half the radioactive nuclei in a sample to decay; it is constant for a given isotope and independent of initial quantity.
• →Exponential decay law: N = N₀ e^(-λt), where N is the number of undecayed nuclei, λ is the decay constant, and t is time.

• Definition of simple harmonic motion as a statement in words
• Mathematical defining equation a = -ω²x
• Graphical representation of acceleration vs displacement
• Solution x = A cos(ωt + φ)
• Definitions of frequency, period, amplitude, and phase
• Period T = 1/f or T = 2π/ω
• Velocity v = -Aω sin(ωt + φ)
• Period of a system with stiffness k and mass m: T = 2π√(m/k)
• Period of a simple pendulum: T = 2π√(l/g)
• Energy interchange between kinetic and potential energy
• Free oscillations and the effect of damping
• Importance of critical damping in systems like vehicle suspensions
• Forced oscillations and resonance
• Variation of amplitude with driving frequency and the effect of damping on resonance curves
• Practical examples of useful resonance (e.g., circuit tuning) and avoidable resonance (e.g., bridge design)

• 💡Always ensure your calculator is in the correct mode (radians or degrees) when using trigonometric functions for SHM equations
• 💡When drawing graphs of displacement, velocity, or acceleration against time, ensure the phase relationships are correct
• 💡Use fiducial markers when timing oscillations to improve accuracy
• 💡Remember that the area under a force-extension graph represents energy stored
• 💡Be prepared to explain the importance of critical damping in real-world applications like car suspensions
• 💡Always write balanced nuclear equations with correct notation: superscript for mass number, subscript for atomic number. For example, ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He. Check that mass and atomic numbers balance on both sides.
• 💡When calculating half-life from a graph, use the exponential decay curve. Pick a point where the activity or count rate is exactly half of an earlier value, and read the time difference. Avoid using the initial point if the graph is noisy.
• 💡For questions involving decay constant λ, remember the relationship λ = ln2 / t₁/₂. Ensure units are consistent (e.g., λ in s⁻¹ if half-life is in seconds). Show all working, including the substitution into the exponential decay formula.

• Confusing the period of a simple pendulum with that of a mass-spring system
• Incorrectly applying the small angle approximation for pendulums
• Failing to account for the phase difference between displacement and velocity graphs
• Misinterpreting the effect of damping on the sharpness of resonance curves
• Confusing free oscillations with forced oscillations
• Misconception: Alpha particles are the most dangerous because they have the most mass. Correction: While alpha particles are highly ionising, they are easily stopped by a sheet of paper or skin. They are only dangerous if ingested or inhaled, as they can cause significant internal damage.
• Misconception: Half-life means the time for all nuclei to decay. Correction: Half-life is the time for half the nuclei to decay, not all. After two half-lives, one quarter remains, and so on. The decay continues indefinitely, though the number becomes negligible.
• Misconception: Beta particles are electrons from the electron cloud. Correction: Beta particles are electrons emitted from the nucleus during beta decay, not from the electron cloud. They are produced when a neutron transforms into a proton.