A-Level AQA Physics: Nuclear Physics Key Points Explained | A-Level AQA 物理：核物理考点精讲

📚 A-Level AQA Physics: Nuclear Physics Key Points Explained | A-Level AQA 物理：核物理考点精讲

This comprehensive guide for AQA A-Level Physics covers all the essential nuclear physics concepts: from the structure of the nucleus and the nature of the strong force to the mathematics of radioactive decay, mass–energy equivalence, and the energetics of fission and fusion. Every section pairs clear English explanations with equivalent Chinese text, ensuring both language and content mastery.

这份AQA A-Level物理综合指南覆盖了所有关键的核物理概念：从原子核结构、强相互作用本质，到放射性衰变的数学、质能等效以及裂变与聚变的能量学。每个章节都提供清晰的英文讲解及对应的中文文本，帮助你同时掌握语言和学科内容。

1. The Composition of the Nucleus | 原子核的组成

A nucleus is characterised by its proton number (atomic number) Z and its nucleon number (mass number) A. The number of neutrons N is therefore A – Z. Nuclei of the same element with different neutron numbers are called isotopes.

原子核由质子数（原子序数）Z 和核子数（质量数）A 描述。中子数 N 就是 A – Z。同一种元素具有不同中子数的核称为同位素。

The approximate radius R of a nucleus depends on its mass number according to the relation R = r₀ A¹ˡ³, where r₀ ≈ 1.2 fm. This shows that the density of nuclear matter is roughly constant across all nuclei.

原子核的半径 R 依据质量数近似满足 R = r₀ A¹ˡ³，其中 r₀ ≈ 1.2 fm。这表明所有原子核的核物质密度大致恒定。

Evidence for this small, dense nucleus came from Rutherford’s alpha-scattering experiment, which revealed that most of the atom’s mass and all of its positive charge are concentrated in a very small central region.

关于这个微小致密核的证据来源于卢瑟福 α 散射实验，该实验表明原子绝大部分质量和所有正电荷都集中在一个极小的中心区域。

2. The Strong Nuclear Force and Stability | 强核力与稳定性

The strong nuclear force binds nucleons together. It is attractive at separations of about 1–3 fm, much stronger than the electrostatic repulsion between protons. At separations smaller than ~0.5 fm, however, it becomes repulsive, preventing nucleons from overlapping.

强核力将核子束缚在一起。它在约1–3 fm的距离上是吸引的，远强于质子间的静电斥力。但在小于约0.5 fm时变为排斥，阻止核子相互重叠。

This force acts equally between proton–proton, neutron–neutron and proton–neutron pairs, and it is charge-independent. It is a short-range force, falling rapidly to zero beyond a few femtometres.

这个力在质子－质子、中子－中子以及质子－中子对之间作用相同，与电荷无关。它是一种短程力，在几个飞米之外迅速降为零。

The stability of a nucleus can be understood through the N–Z graph. Light stable nuclei lie close to the line N = Z. For heavier nuclei, extra neutrons are needed to dilute the Coulomb repulsion, so the stability line curves upwards, giving N > Z.

通过中子－质子（N–Z）图可以理解核的稳定性。轻的稳定核靠近 N = Z 直线。对于较重的核，需要额外的中子来稀释库仑斥力，因此稳定线向上弯曲，使得 N > Z。

3. Mass Defect and Binding Energy | 质量亏损与结合能

The mass of a nucleus is always less than the sum of the masses of its individual nucleons. This difference is called the mass defect, Δm. Using Einstein’s mass–energy equation, the binding energy of the nucleus is given by E_b = Δm c².

原子核的质量总是小于其组成核子的质量总和，这个差值称为质量亏损 Δm。利用爱因斯坦质能方程，原子核的结合能由 E_b = Δm c² 给出。

Binding energy per nucleon, E_b/A, is a measure of the stability of a nucleus. The curve of E_b/A against A peaks around iron-56, indicating that iron-group nuclei are the most stable.

每核子结合能 E_b/A 是衡量核稳定性的指标。E_b/A 对 A 的曲线在铁-56 附近达到峰值，表明铁族核最为稳定。

Binding energy = (Z m_p + N m_n – m_nucleus) × 931.5 MeV/u

结合能 = (Z m_p + N m_n – m_nucleus) × 931.5 MeV/u

In calculations, atomic masses are often used, and the electron binding energy is usually negligible. One unified atomic mass unit, u, is equivalent to 1.661×10⁻²⁷ kg and 931.5 MeV.

在计算中，常使用原子质量，电子结合能通常可以忽略。一个统一原子质量单位 u 等于 1.661×10⁻²⁷ kg 和 931.5 MeV。

4. Types of Radioactive Decay | 放射性衰变类型

Radioactive decay is a spontaneous process in which an unstable nucleus emits radiation to become more stable. The three main types are alpha (α), beta-minus (β⁻), beta-plus (β⁺) and gamma (γ) emissions.

放射性衰变是一个自发过程，不稳定核通过发射辐射变得更加稳定。主要类型有 α 衰变、β⁻ 衰变、β⁺ 衰变和 γ 辐射。

Alpha particle is a helium nucleus, ⁴₂He. It has high ionising power but very low penetration (stopped by paper or a few cm of air).	α 粒子是氦核 ⁴₂He。电离能力强但穿透力极弱（可被纸张或几厘米空气阻挡）。
Beta-minus (β⁻) decay occurs when a neutron transforms into a proton, emitting an electron and an antineutrino: n → p + e⁻ + ν̅_e.	β⁻ 衰变是一个中子变为一个质子，并放出一个电子和一个反电子中微子：n → p + e⁻ + ν̅_e。
Beta-plus (β⁺) decay involves a proton converting into a neutron, emitting a positron and a neutrino: p → n + e⁺ + ν_e.	β⁺ 衰变是质子转变为中子，放出一个正电子和一个中微子：p → n + e⁺ + ν_e。
Gamma radiation consists of high-energy photons (electromagnetic waves) emitted when an excited nucleus loses energy. It has low ionising power but very high penetration (several cm of lead).	γ 辐射由高能光子（电磁波）组成，在激发核失去能量时放出。电离能力弱但穿透力极强（可穿透数厘米铅）。

In all decays, certain conservation laws must hold: conservation of nucleon number, proton number (charge), energy, and momentum.

在所有衰变中，必须遵守守恒定律：核子数守恒、质子数（电荷）守恒、能量守恒和动量守恒。

5. Decay Equations and Transmutation | 衰变方程与核嬗变

For alpha decay, the parent nucleus loses two protons and two neutrons. The general equation is ᴬ_ZX → ᴬ⁻⁴_Z⁻₂Y + ⁴₂He. An example is ²³⁸_₉₂U → ²³⁴_₉₀Th + ⁴₂He.

对于 α 衰变，母核失去两个质子和两个中子。一般方程为 ᴬ_ZX → ᴬ⁻⁴_Z⁻₂Y + ⁴₂He。例如 ²³⁸_₉₂U → ²³⁴_₉₀Th + ⁴₂He。

In beta-minus decay, a neutron in the nucleus changes into a proton, so the atomic number increases by 1 while the mass number remains the same: ¹⁴_₆C → ¹⁴_₇N + e⁻ + ν̅_e.

在 β⁻ 衰变中，核内的一个中子变为质子，所以原子序数增加1，而质量数不变：¹⁴_₆C → ¹⁴_₇N + e⁻ + ν̅_e。

Gamma decay is often emitted alongside alpha or beta decay when the daughter nucleus is left in an excited state. It does not change the nucleon or proton number of the nucleus.

γ 衰变常伴随 α 或 β 衰变发生，当子核处于激发态时发射出来。它不改变核的核子数或质子数。

6. The Exponential Decay Law | 指数衰变规律

Radioactive decay is a random process, and for a large number of nuclei it follows the exponential law N = N₀ e^{−λt}, where N is the number of undecayed nuclei at time t, N₀ is the initial number, and λ is the decay constant (s⁻¹).

放射性衰变是随机过程，对于大量原子核遵循指数规律 N = N₀ e^{−λt}，其中 N 是 t 时刻尚未衰变的核数，N₀ 是初始核数，λ 是衰变常数（单位 s⁻¹）。

The probability per unit time that a given nucleus will decay is λ. The decay constant is unique for each radioactive species.

每个核在单位时间内衰变的概率为 λ。每种放射性核素有其特定的衰变常数。

N = N₀ e^{−λt}

The half-life T_½ is the time taken for the number of undecayed nuclei (or the activity) to halve. It is linked to λ by T_½ = ln 2 / λ.

半衰期 T_½ 是待衰变核数（或活度）减半所需的时间。它与 λ 的关系为 T_½ = ln 2 / λ。

7. Activity and the Decay Constant | 活度与衰变常数

The activity A of a sample is the rate at which nuclei decay, measured in becquerels (Bq), where 1 Bq = 1 decay per second. It is given by A = λN.

样品的活度 A 是原子核衰变的速率，以贝克勒尔（Bq）为单位，1 Bq = 1次衰变/秒。它由 A = λN 给出。

Since N decreases exponentially, activity also follows an exponential decrease: A = A₀ e^{−λt}. This means a graph of ln A versus t yields a straight line of gradient –λ.

由于 N 呈指数减少，活度也遵循指数衰减：A = A₀ e^{−λt}。这意味着 ln A 对 t 作图得到一条斜率为 –λ 的直线。

Radioactive dating exploits this law. For example, carbon-14 dating compares the current activity of ¹⁴C in a dead sample to that in living tissue, using the known half-life of 5730 years to estimate the time since death.

放射性测年利用了这一规律。例如，碳-14 测年是将死组织样品中 ¹⁴C 当前的活度与活体组织中的活度进行比较，利用已知的半衰期 5730 年来推算死亡时间。

8. Nuclear Fission | 核裂变

Nuclear fission occurs when a heavy, unstable nucleus splits into two smaller fragments of comparable mass, along with the release of several neutrons and a large amount of energy. It can be induced by the absorption of a thermal neutron.

核裂变是指一个重的不稳定核分裂成两个质量相近的较轻碎片，同时释放出几个中子及大量能量。裂变可由热中子的吸收诱发。

A typical reaction is the fission of uranium-235: ²³⁵_₉₂U + ¹_₀n → ¹⁴¹_₅₆Ba + ⁹²_₃₆Kr + 3¹_₀n. The products have a greater binding energy per nucleon than the original uranium, so energy is released.

一个典型反应是铀-235的裂变：²³⁵_₉₂U + ¹_₀n → ¹⁴¹_₅₆Ba + ⁹²_₃₆Kr + 3¹_₀n。产物每核子结合能比原来的铀更大，因此释放能量。

The released neutrons can trigger further fission events, leading to a chain reaction. In a nuclear reactor, control rods absorb excess neutrons to keep the multiplication factor k = 1, ensuring a steady power output.

释放的中子能够引发进一步的裂变事件，从而形成链式反应。在核反应堆中，控制棒吸收多余中子，使增殖系数 k = 1，保证稳态功率输出。

9. Nuclear Fusion | 核聚变

Fusion is the combining of two light nuclei to form a heavier nucleus, releasing energy because the products have a higher binding energy per nucleon (for nuclei lighter than iron). The Sun’s energy comes from the fusion of hydrogen into helium via the proton–proton chain.

聚变是两个轻核结合成一个较重的核，因产物每核子结合能更高（对于比铁轻的核）而释放能量。太阳的能量来源于氢通过质子－质子链聚变为氦。

For fusion to occur, the nuclei must overcome their Coulomb repulsion. This requires extremely high temperatures (of the order of 10⁷ K) and high densities, as found in stellar cores. The conditions are known as plasma confinement.

要发生聚变，核必须克服库仑斥力。这要求极高的温度（约 10⁷ K）和高密度，正如恒星核心中的条件。这些条件被称为等离子体约束。

On Earth, controlled fusion is being pursued using magnetic confinement (tokamaks) and inertial confinement. The reaction ²H + ³H → ⁴He + n + 17.6 MeV is a promising candidate for future fusion power stations.

在地球上，人们正通过磁约束（托卡马克）和惯性约束追求受控聚变。反应 ²H + ³H → ⁴He + n + 17.6 MeV 是未来聚变电站的一个有希望的候选者。

10. Energy Released in Nuclear Reactions | 核反应中的能量释放

The energy released Q in a nuclear reaction is the difference between the total rest mass of the reactants and the products: Q = (Σm_reactants − Σm_products) c². If Q is positive, the reaction is exothermic.

核反应中释放的能量 Q 是反应物与产物总静止质量的差值：Q = (Σm_reactants − Σm_products) c²。如果 Q 为正，反应放热。

In fission, Q is typically ~200 MeV per event. In the D-T fusion reaction, Q is about 17.6 MeV, but the energy per nucleon is larger than in fission. Comparison using binding energy per nucleon curves clearly shows the iron peak as the most stable region.

在裂变中，每次事件 Q 通常约 200 MeV。在 D-T 聚变反应中，Q 约为 17.6 MeV，但每核子能量比裂变大。利用每核子结合能曲线可以清晰看到铁峰是最稳定的区域。

When solving problems, always convert masses to atomic mass units or kg, calculate Δm, and then multiply by c² or the conversion factor 931.5 MeV/u. Pay attention to significant figures and units.

解题时，务必将质量转换为原子质量单位或 kg，计算 Δm，然后乘以 c² 或换算因子 931.5 MeV/u。注意有效数字和单位。

11. Radioactive Safety and Applications | 放射性安全与应用

Ionising radiation can damage living cells, so strict safety measures are followed: using shielding, minimising exposure time, maximising distance, and wearing dosimeters.

电离辐射会损伤活细胞，因此必须采取严格的安全措施：使用屏蔽、缩短暴露时间、增大距离、佩戴剂量计。

Radioactive materials are used in medicine (tracers, radiotherapy), industry (thickness gauges, smoke detectors), and archaeology (carbon dating). The choice of isotope depends on its half-life, type of radiation, and biological compatibility.

放射性材料用于医学（示踪剂、放射治疗）、工业（厚度计、烟雾探测器）和考古学（碳测年）。同位素的选择取决于其半衰期、辐射类型和生物相容性。

Managing nuclear waste, especially high-level waste from spent fuel rods, remains a major challenge. Long-term geological disposal is being developed, but the issue of long-lived radioisotopes requires careful planning over thousands of years.

管理核废料，特别是乏燃料棒产生的高放废物，仍是一大挑战。正在开发长期地质处置，但长寿命放射性同位素问题需要跨越数千年的谨慎规划。

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A-Level AQA Physics: Nuclear Physics Key Points Explained | A-Level AQA 物理：核物理 考点精讲