P4: Nuclear Physics, Radioactivity and Thermal Physics

Year 1 / ASYear 2 / A-Level All Boards (AQA, Edexcel, OCR, WJEC, CCEA) AQA

Radioactive decay law, binding energy, nuclear fission/fusion, ideal gas laws, kinetic theory, specific heat capacity.

Exam Board:

📋 Key Definitions and Core Concepts

Binding Energy: Energy required to disassemble a nucleus into its constituent protons and neutrons (E = Δm c²).

Decay Law: Activity A = λN; N(t) = N₀ e^{-λt}; half-life t_{1/2} = ln 2 / λ.

Rutherford scattering: evidence for tiny, dense, positively charged nucleus.
Ideal gas equation: pV = nRT = NkT; Kinetic theory: pV = ⅓Nm(c_rms)²; mean KE = ³/₂kT.
Thermal energy: Q = mcΔθ (heating) and Q = mL (phase change).

Exam-Style Question

Question:

Calculate the binding energy per nucleon of Helium-4 (mass defect Δm = 0.0304 u, 1 u = 931.5 MeV).

Model Solution & Mark Scheme:

Total binding energy = 0.0304 × 931.5 MeV = 28.32 MeV.
4 nucleons => Binding energy per nucleon = 28.32 / 4 = 7.08 MeV/nucleon.

Q1: Carbon-14 has half-life 5730 years. A sample has 25% original activity. Find age.

Show Model Answer

Answer: 25% = (½)² => 2 half-lives elapsed = 2 × 5730 = 11,460 years.

Q2: Calculate the root-mean-square speed of nitrogen molecules (m = 4.65 × 10⁻²⁶ kg) at 300 K (k = 1.38 × 10⁻²³ J/K).

Show Model Answer

Answer: ½m(c_rms)² = ³/₂kT => c_rms = √(3kT/m) = √(3 × 1.38×10⁻²³ × 300 / 4.65×10⁻²⁶) = 517 m/s.

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