Nuclear Physics Revision for IB & AQA | IB与AQA物理核物理考点精讲

📚 Nuclear Physics Revision for IB & AQA | IB与AQA物理核物理考点精讲

Nuclear physics is a core topic for both IB and AQA A‑level Physics, covering the structure of the nucleus, radioactive decay, half‑life, mass–energy equivalence, nuclear binding energy, fission and fusion. This revision guide walks you through every essential concept, with worked examples and exam tips, to help you master the syllabus.

核物理是 IB 和 AQA A‑level 物理的核心模块，涉及原子核结构、放射性衰变、半衰期、质能等价、结合能、裂变与聚变等。本文梳理全部关键考点，配例子和应试技巧，帮助你系统掌握大纲要求。

1. The Atomic Nucleus | 原子核结构

An atom consists of a tiny, dense nucleus containing nucleons (protons and neutrons), surrounded by electrons. The proton number (atomic number) Z determines the element, while the nucleon number (mass number) A gives the total number of nucleons. An isotope has the same Z but a different N = A – Z.

原子由一个极小、致密的原子核（内含质子和中子，统称核子）以及核外电子构成。质子数（原子序数）Z 决定元素种类，核子数（质量数）A 为总核子数。同位素具有相同的 Z 但不同的中子数 N = A – Z。

Proton mass ≈ 1.673 × 10⁻²⁷ kg, charge +e; neutron mass ≈ 1.675 × 10⁻²⁷ kg, no charge.

质子质量约 1.673 × 10⁻²⁷ kg，带 +e 电荷；中子质量约 1.675 × 10⁻²⁷ kg，不带电。

Radius of a nucleus R = R₀ A^(¹⁄³) with R₀ ≈ 1.2 fm. This shows that nuclear density is roughly constant for all nuclei.

原子核半径 R = R₀ A^(¹⁄³)，R₀ ≈ 1.2 fm。这表明所有核的核密度大致恒定。

Exam tip: convert between atomic mass units (1 u = 1.661 × 10⁻²⁷ kg) and energy (931.5 MeV) using E = mc².

考试提示：熟练运用原子质量单位（1 u = 1.661 × 10⁻²⁷ kg）与能量（931.5 MeV）的换算，利用 E = mc²。

2. The Strong Nuclear Force | 强核力

The strong nuclear force binds protons and neutrons together in the nucleus, overcoming the electrostatic repulsion between protons. It is a short‑range force that is attractive up to about 3 fm, repulsive at very short distances (< 0.5 fm), and negligible beyond 3 fm.

强核力将质子和中子束缚在原子核内，克服质子间的静电斥力。它是一种短程力：在约 3 fm 内表现为吸引，极短距离 (< 0.5 fm) 表现为排斥，超过 3 fm 可忽略。

It acts between all nucleons (p‑p, n‑n, p‑n) with the same strength.

强核力对任意核子对（p‑p、n‑n、p‑n）作用强度相同。

The stability of a nucleus depends on the balance between the strong force and Coulomb repulsion. Heavier nuclei need extra neutrons to provide more strong‑force binding without adding electrostatic repulsion.

核的稳定性取决于强力与库仑斥力的平衡。重核需要更多中子参与强相互作用而不增加静电斥力。

3. Radioactive Decay | 放射性衰变

An unstable nucleus spontaneously emits particles or electromagnetic radiation to become more stable. The three main types are alpha (α), beta (β) and gamma (γ) decay. The activity A of a sample is the number of decays per unit time, measured in becquerels (Bq), where 1 Bq = 1 decay per second.

不稳定核自发发射粒子或电磁辐射以趋于稳定，主要衰变类型为 α、β 和 γ。样品的活度 A 是单位时间衰变次数，单位为贝克勒尔 (Bq)，1 Bq = 1 次衰变/秒。

Nature of emissions: α is a helium nucleus (²⁴He²⁺), β⁻ is an electron, β⁺ is a positron, γ is a high‑energy photon.

发射体本质：α 为氦核（²⁴He²⁺），β⁻ 为电子，β⁺ 为正电子，γ 为高能光子。

General decay equation for a parent nucleus X to daughter Y: A ᶻX → ᴬ⁻⁴ ᶻ⁻²Y + ²⁴α (α decay); A ᶻX → ᴬ ᶻ₊₁Y + e⁻ + ν̄ (β⁻ decay).

衰变通式：母核 X 变为子核 Y，α 衰变 A ᶻX → ᴬ⁻⁴ ᶻ⁻²Y + ²⁴α；β⁻ 衰变 A ᶻX → ᴬ ᶻ₊₁Y + e⁻ + ν̄。

4. Alpha Decay | α 衰变

Alpha decay occurs in heavy, neutron‑rich nuclei (Z > 82). An alpha particle is ejected, reducing the mass number by 4 and the atomic number by 2. The alpha particle has a discrete kinetic energy specific to the transition.

α 衰变发生在重核、富中子核（Z > 82）中。释放一个 α 粒子，质量数减 4，原子序数减 2。α 粒子的动能是特定核转变的离散值。

Example: ²³⁸₉₂U → ²³⁴₉₀Th + ²⁴He + Q (Q ≈ 4.27 MeV).

例：²³⁸₉₂U → ²³⁴₉₀Th + ²⁴He + Q（Q ≈ 4.27 MeV）。

Alpha particles are highly ionising but have a very short range in matter (a few cm in air).

α 粒子电离本领强但穿透力弱，空气中射程仅几厘米。

5. Beta Decay | β 衰变

Beta decay is the emission of an electron (β⁻) or positron (β⁺) to change a neutron into a proton or a proton into a neutron, respectively, preserving the nucleon number but shifting Z by ±1. A neutrino or antineutrino is also emitted to conserve energy and momentum.

β 衰变通过释放电子（β⁻）或正电子（β⁺）使中子变质子或质子变中子，核子数不变，Z 改变 ±1。同时放出一个中微子或反中微子以保证能量和动量守恒。

β⁻ decay: n → p + e⁻ + ν̄ₑ. Occurs in neutron‑rich nuclei.

β⁻ 衰变：n → p + e⁻ + ν̄ₑ，发生在富中子核。

β⁺ decay: p → n + e⁺ + νₑ. Occurs in proton‑rich nuclei.

β⁺ 衰变：p → n + e⁺ + νₑ，发生在富质子核。

Beta particles have a continuous spectrum of kinetic energies because the available energy is shared with the neutrino.

β 粒子动能谱连续，因为衰变能由电子和中微子共享。

6. Gamma Radiation | γ 辐射

Gamma radiation is an electromagnetic wave emitted when an excited nucleus moves to a lower energy state. Unlike α and β, gamma emission does not change A or Z; it simply releases excess energy.

γ 辐射是受激核跃迁至低能态时放出的电磁波。与 α、β 不同，γ 辐射不改变 A 或 Z，仅释放多余能量。

Gamma photons typically have energies in the MeV range and are highly penetrating, requiring lead or thick concrete for shielding.

γ 光子能量通常在 MeV 量级，穿透力强，需铅板或厚混凝土屏蔽。

Often follows an α or β decay, leaving the daughter nucleus in an excited state.

常伴随 α 或 β 衰变，子核处于激发态后放出 γ 退激。

7. The Decay Law and Half‑life | 衰变定律与半衰期

Radioactive decay is a random process described by the exponential decay law N = N₀ e^(−λt) and activity A = λN = A₀ e^(−λt), where λ is the decay constant (probability of decay per unit time).

放射性衰变是随机过程，遵循指数规律 N = N₀ e^(−λt)，活度 A = λN = A₀ e^(−λt)，λ 为衰变常量（单位时间衰变概率）。

N = N₀ e^(−λt) A = λN

Half‑life T₁/₂ is the time for half the original nuclei to decay: T₁/₂ = ln 2 / λ ≈ 0.693 / λ.

半衰期 T₁/₂ 为一半原子核衰变所需时间：T₁/₂ = ln 2 / λ ≈ 0.693 / λ。

Examiners may ask you to find λ from a graph (gradient of ln N vs t is −λ) or to calculate remaining fraction after n half‑lives as (½)ⁿ.

考试中可能要求依据图像求 λ（ln N ‑ t 图斜率为 −λ），或计算 n 个半衰期后剩余分数为 (½)ⁿ。

8. Mass–Energy Equivalence | 质能等价

Einstein’s relation E = mc² links mass and energy. In nuclear processes, mass is not conserved, but the total mass–energy is conserved. A small change in mass Δm corresponds to a huge energy release or absorption: ΔE = Δm c².

爱因斯坦质能方程 E = mc² 建立了质量与能量联系。核过程中质量不守恒，但总质能守恒。微小的质量变化 Δm 对应巨大的能量释放或吸收：ΔE = Δm c²。

1 u of mass is equivalent to 931.5 MeV. Use this conversion in all mass‑defect calculations.

1 u 质量相当 931.5 MeV 能量。在所有质量亏损计算中需用此换算。

9. Nuclear Binding Energy | 核结合能

The binding energy of a nucleus is the energy required to separate it into its individual nucleons. It is equal to the mass defect Δm = (Zmₚ + Nmₙ) – M_nucleus, converted to energy using E = Δm c².

核结合能是将原子核拆散为独立核子所需能量，等于质量亏损 Δm = (Zmₚ + Nmₙ) – M核，再通过 E = Δm c² 换算。

Binding energy per nucleon = total BE / A. This graph peaks at iron‑56, indicating the most stable nucleus.

平均结合能 = 总结合能 / A。该曲线在铁‑56 处最大，表明铁核最稳定。

Fusion (light nuclei) and fission (heavy nuclei) both move products towards higher binding energy per nucleon, releasing energy.

轻核聚变和重核裂变都使产物移向更高平均结合能，从而释放能量。

ΔE = Δm c²

10. Nuclear Fission | 核裂变

Fission is the splitting of a heavy nucleus into two lighter fragments, accompanied by the release of neutrons and a large amount of energy. Uranium‑235 and plutonium‑239 are common fission fuels.

裂变是重核分裂为两个较轻碎片，伴随释放中子和巨大能量。铀‑235 和钚‑239 是常用裂变燃料。

Typical reaction: ²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3 ¹₀n + energy.

典型反应：²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3 ¹₀n + 能量。

Chain reaction is sustained if at least one neutron per fission triggers another fission; a controlled chain reaction underpins nuclear reactors.

若每次裂变至少有一个中子引发下一次裂变，可实现链式反应；受控链式反应是核反应堆的基础。

11. Nuclear Fusion | 核聚变

Fusion combines light nuclei, such as isotopes of hydrogen, into a heavier nucleus, releasing energy because the product has a greater binding energy per nucleon. Fusion requires extremely high temperatures to overcome Coulomb repulsion.

聚变将轻核（如氢同位素）结合成较重核，因产物平均结合能更高而释放能量。聚变需要极高温度以克服库仑斥力。

Example: ²₁H + ³₁H → ⁴₂He + ¹₀n + 17.6 MeV.

例：²₁H + ³₁H → ⁴₂He + ¹₀n + 17.6 MeV。

Fusion is the process powering the Sun and is being developed for commercial power on Earth, but plasma confinement remains challenging.

聚变是太阳的能源机制，正进行地面商用研发，但等离子体约束仍具挑战性。

12. Applications and Safety | 应用与安全

Nuclear physics has wide applications: medical imaging (PET scans, gamma cameras), radiotherapy, carbon‑14 dating, smoke detectors (α sources), and nuclear power. Safe use involves controlling radiation dose, shielding, and safe disposal of radioactive waste.

核物理应用广泛：医学成像（PET、γ 相机）、放射治疗、碳‑14 测年、烟雾探测器（α 源）及核电。安全措施包括剂量控制、屏蔽和放射性废物安全处置。

Absorbed dose (Gy) and equivalent dose (Sv) account for biological effect. Effective dose considers tissue sensitivity.

吸收剂量（Gy）和当量剂量（Sv）考虑生物效应。有效剂量还纳入组织敏感性。

Half‑lives and activity are used to determine safe storage times for nuclear waste.

利用半衰期和活度确定核废料的安全贮存时限。

Master these concepts and practise rearranging decay equations, interpreting binding‑energy graphs, and applying E = mc². You’ll be well prepared for both IB and AQA exams.

掌握以上概念，勤练衰变方程、结合能图线解读及 E = mc² 应用，即可从容应对 IB 和 AQA 考试。

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Nuclear Physics Revision for IB & AQA | IB与AQA物理核物理考点精讲