📚 Nuclear Energy | 核能
This article provides a complete revision guide for the OxfordAQA International A-level Physics topic on nuclear energy. It covers core definitions, equations, worked examples and common exam traps to help you score full marks in topic tests.
本文为牛津AQA国际A-level物理核能主题提供完整复习指南，涵盖核心定义、方程、例题和常见陷阱，帮助你在专题测试中获得满分。
1. Nuclear Structure and the Strong Force | 原子核结构与核力
The nucleus contains protons and neutrons, collectively called nucleons. The number of protons is the atomic number Z, and the total number of nucleons is the mass number A.
原子核包含质子和中子，统称为核子。质子数称为原子序数 Z，总核子数称为质量数 A。
The strong nuclear force acts between nucleons at a very short range (around 1-3 fm). It overcomes the electrostatic repulsion between protons, binding the nucleus together. This force is charge-independent: it acts equally on protons and neutrons.
强核力在极短距离（约1-3费米）内作用于核子之间，克服质子间的静电斥力，将原子核束缚在一起。该力与电荷无关，对质子和中子作用相同。
At very small separations (less than about 0.5 fm) the strong force becomes repulsive, preventing nucleons from collapsing into each other. Beyond about 3 fm it falls rapidly to zero, which limits the size of stable nuclei.
在极短距离（小于约0.5费米）内，强核力表现为斥力，防止核子相互重叠；超过约3费米后快速降至零，这限制了稳定原子核的尺寸。
For heavy nuclei, the neutron-to-proton ratio is greater than 1, providing extra strong-force attraction without extra Coulomb repulsion, which helps stabilise the nucleus.
对于重核，中子与质子比大于1，提供额外的强核力吸引力而不增加静电斥力，从而有助于稳定原子核。
2. Mass Defect and Mass-Energy Equivalence | 质量亏损与质能等价
Albert Einstein’s mass-energy equivalence is given by the equation:
阿尔伯特·爱因斯坦的质能等价方程如下：
E = mc²
Here, E is energy in joules, m is mass in kilograms and c is the speed of light in a vacuum (3.00 × 10⁸ m s⁻¹). Even tiny mass changes correspond to enormous energy changes because c² is huge.
其中 E 为能量（单位焦耳），m 为质量（单位千克），c 为真空中的光速（3.00 × 10⁸ m s⁻¹）。由于 c² 数值巨大，极小的质量变化也对应巨大的能量变化。
The mass defect Δm of a nucleus is the difference between the total mass of its separated nucleons and the mass of the nucleus itself:
原子核的质量亏损 Δm 是指组成它的所有独立核子总质量与原子核实际质量的差值：
Δm = (Zmₚ + Nmₙ) − Mₙᵤcₗₑᵤₛ
The atomic mass unit u is defined as one-twelfth of the mass of a neutral carbon-12 atom: 1 u = 1.66 × 10⁻²⁷ kg. Using E = mc², this corresponds to 931.5 MeV/c², or 931.5 MeV of energy per u.
原子质量单位 u 定义为碳-12中性原子质量的十二分之一：1 u = 1.66 × 10⁻²⁷ kg。由 E = mc² 可知，这对应约 931.5 MeV/c²，即每 u 相当于 931.5 MeV 的能量。
In any nuclear reaction, the change in mass is given by Δm = (total mass of reactants) − (total mass of products). The energy released is then ΔE = Δmc². If Δm is positive, mass is lost and energy is released.
在任何核反应中，质量变化 Δm 等于反应物总质量减去产物总质量。释放的能量为 ΔE = Δmc²。如果 Δm 为正值，则质量减少，能量释放。
3. Binding Energy and Nuclear Stability | 结合能与核稳定性
The binding energy of a nucleus is the minimum energy required to separate it into its individual protons and neutrons. It is equal to the energy equivalent of the mass defect: E_b = Δmc².
原子核的结合能是将它拆分为独立质子和中子所需的最小能量，等于质量亏损对应的能量：E_b = Δmc²。
The binding energy per nucleon is obtained by dividing the total binding energy by the mass number A. It is a measure of how tightly nucleons are bound together.
每个核子的平均结合能等于总结合能除以质量数 A，它衡量核子结合的紧密程度。
The graph of binding energy per nucleon against mass number rises steeply for light nuclei, reaches a maximum at iron-56 (about 8.75 MeV per nucleon), then slowly falls for heavier nuclei.
每个核子平均结合能随质量数的曲线在轻核区域急剧上升，在铁-56处达到峰值（约8.75 MeV/核子），然后随质量数增加缓慢下降。
Nuclei near the peak are most stable. Heavy nuclei can release energy by splitting into smaller fragments (fission), while very light nuclei can release energy by fusing together (fusion), because both move toward higher binding energy per nucleon.
处于峰附近的原子核最稳定。重核可通过分裂成较小碎片释放能量（裂变），而很轻的核可通过聚合释放能量（聚变），因为两者都向更高平均结合能方向移动。
4. Nuclear Fission | 核裂变
Nuclear fission is the splitting of a heavy nucleus (such as uranium-235) after absorbing a neutron. The nucleus becomes unstable and splits into two smaller nuclei, releasing energy, gamma radiation and usually two or three neutrons.
核裂变是指重核（如铀-235）吸收中子后发生分裂的过程。该原子核变得不稳定，分裂为两个较小的核，释放能量、γ辐射以及通常两到三个中子。
A typical fission reaction is:
一个典型裂变反应式为：
²³⁵U + n → ¹⁴¹Ba + ⁹²Kr + 3n + energy
Mass number and charge are conserved in this equation: 235 + 1 = 141 + 92 + 3, and 92 = 56 + 36.
这个方程满足质量数和电荷守恒：235 + 1 = 141 + 92 + 3，且 92 = 56 + 36。
Each fission event releases about 200 MeV of energy, mainly as kinetic energy of the fragments. The fragments are often radioactive and decay further via beta and gamma emission.
每次裂变事件释放约200 MeV能量，主要体现为碎片动能。碎片通常具有放射性，并会进一步发生β和γ衰变。
The emitted neutrons can trigger further fission reactions, leading to a chain reaction if a critical mass of fuel is present.
释放出的中子可引发更多裂变反应，若存在临界质量的燃料，就会导致链式反应。
5. Nuclear Fusion | 核聚变
Nuclear fusion is the process in which two light nuclei combine to form a heavier nucleus. This process releases an enormous amount of energy because the product is more tightly bound.
核聚变是两个轻核结合形成一个较重核的过程。由于产物结合得更紧密，这一过程释放巨大能量。
The most important fusion reaction on Earth and in the Sun is between deuterium and tritium (isotopes of hydrogen):
在地球和太阳中最重要聚变反应是氘和氚（氢的同位素）之间的反应：
²H + ³H → ⁴He + n + 17.6 MeV
Here, 17.6 MeV is the energy released per reaction. The mass of the product (helium-4 plus a neutron) is less than the mass of the two hydrogen isotopes; the missing mass is converted into energy.
这里每次反应释放 17.6 MeV 能量。产物（氦-4加一个中子）的总质量小于两个氢同位素的总质量，损失的质量转化为能量。
Fusion requires extremely high temperatures (about 100 million kelvin) to overcome electrostatic repulsion between positively charged nuclei, so controlled fusion is very difficult to achieve on Earth.
聚变需要极高温度（约1亿开尔文）以克服带正电核之间的静电排斥，因此在地球上实现受控聚变非常困难。
Fusion has a higher energy output per unit mass of fuel than fission and produces less long-lived radioactive waste, making it an attractive future energy source.
聚变每单位质量燃料的能量输出高于裂变，且产生的长寿命放射性废物更少，因此被认为是有吸引力的未来能源。
6. Chain Reactions and Critical Mass | 链式反应与临界质量
In fission, each neutron absorbed by U-235 produces on average 2-3 neutrons. If at least one of these goes on to cause another fission, the reaction becomes self-sustaining — this is called a chain reaction.
在裂变中，每个被铀-235吸收的中子平均产生2-3个中子。如果其中至少有一个继续引发新的裂变，反应就能自我维持——这称为链式反应。
The critical mass is the minimum amount of fissile material needed to maintain a steady chain reaction. If the mass is below critical, the reaction dies out; above critical, the reaction grows rapidly.
临界质量是指维持稳定链式反应所需的最小裂变材料质量。如果质量低于临界值，反应逐渐终止；高于临界值，反应迅速增长。
Natural uranium contains only 0.7% of the fissile isotope U-235; for most reactors the fuel must be enriched to around 3-5% U-235. In weapons-grade material, enrichment is over 90%.
天然铀中仅含0.7%的易裂变同位素铀-235；大多数反应堆需将燃料浓缩至3-5%铀-235。武器级铀浓缩程度超过90%。
In a controlled reactor, the chain reaction is sustained at a constant rate by using control rods that absorb excess neutrons and a moderator that slows down fast neutrons to increase the probability of fission.
在受控反应堆中，通过使用吸收多余中子的控制棒以及使快中子减速以增加裂变概率的慢化剂，链式反应以恒定速率持续进行。
7. How a Nuclear Reactor Works | 核反应堆的工作原理
A nuclear reactor contains five main components: fuel, moderator, control rods, coolant and shielding. The fuel is usually uranium dioxide pellets encased in metal tubes called fuel rods.
核反应堆包含五个主要部分：燃料、慢化剂、控制棒、冷却剂和屏蔽层。燃料通常是封装在金属管内的二氧化铀芯块，这些金属管称为燃料棒。
The moderator, often graphite or water, slows down fast neutrons produced by fission to thermal energies (about 0.025 eV). Thermal neutrons have a much higher probability of causing fission in U-235.
慢化剂（常用石墨或水）将裂变产生的快中子减速到热能区（约0.025 eV）。热中子引发铀-235裂变的概率高得多。
Control rods, made of boron or cadmium, absorb neutrons without undergoing fission. They are inserted more deeply to reduce the reaction rate or withdrawn to increase it, allowing precise control of the reactor power.
控制棒由硼或镉制成，吸收中子但不发生裂变。插入较深可降低反应速率，抽出则可提高速率，从而精确控制反应堆功率。
The coolant (water, heavy water or carbon dioxide) removes heat from the core and transfers it to a heat exchanger to produce steam. The steam drives a turbine connected to a generator, producing electricity. Shielding, usually thick concrete, protects workers from radiation.
冷却剂（水、重水或二氧化碳）将
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