📚 E.4 Fission | E.4 裂变
Nuclear fission is a nuclear reaction in which a heavy nucleus splits into two or more smaller nuclei, accompanied by the release of a large amount of energy. In IB Physics topic E.4, we explore the physical mechanism, the energy calculations based on mass–energy equivalence, the conditions for chain reactions, and the engineering principles behind nuclear reactors.
核裂变是一种核反应，重原子核分裂成两个或多个较轻的原子核，同时释放出巨大能量。在IB物理E.4中，我们将探讨其物理机理、基于质能等价的能量计算、链式反应的条件以及核反应堆背后的工程原理。
1. Introduction to Nuclear Fission | 核裂变简介
Fission was discovered in 1938 by Otto Hahn and Fritz Strassmann, and interpreted by Lise Meitner and Otto Frisch. The process typically involves a heavy, neutron-rich nucleus such as uranium-235 absorbing a slow neutron. The resulting compound nucleus is highly unstable and deforms, overcoming the strong nuclear force, and splits into two medium-mass fission fragments.
裂变于1938年由奥托·哈恩和弗里茨·斯特拉斯曼发现，并由莉泽·迈特纳和奥托·弗里施解释。这个过程通常涉及一个富含中子的重核（如铀-235）吸收一个慢中子。生成的复合核极不稳定，发生形变，克服强核力，分裂成两个中等质量的裂变碎片。
The fragments are neutron-rich and radioactive. They release prompt neutrons and gamma rays within about 10⁻¹⁴ seconds, followed by delayed neutrons and beta decays. The total energy released per fission event is about 200 MeV, predominantly as kinetic energy of the fragments.
碎片富含中子，具有放射性。它们在约10⁻¹⁴秒内释放瞬发中子和伽马射线，随后释放缓发中子和进行β衰变。每次裂变释放的总能量约为200 MeV，主要是碎片的动能。
2. The Fission Process and Products | 裂变过程与产物
A typical fission reaction initiated by a thermal neutron on uranium-235 is:
n + ²³⁵U → ¹⁴¹Ba + ⁹²Kr + 3n + energy
一个由热中子引发铀-235的典型裂变反应为：
n + ²³⁵U → ¹⁴¹Ba + ⁹²Kr + 3n + 能量
utrons, energetic prompt gamma rays are emitted. The fission products are themselves radioactive and undergo a sequence of beta decays until they become stable isotopes.
裂变碎片并不是唯一的；质量数分布分别在A ≈ 95和A ≈ 140附近出现峰值。除中子外，还会发射高能瞬发伽马射线。裂变产物本身具有放射性，会经历一系列β衰变直到变成稳定同位素。
3. Binding Energy and Energy Release | 结合能与能量释放
f typical fission fragments (e.g. around A = 140 and A = 95) is about 8.5 MeV per nucleon.
裂变释放的能量来源于重母核与中等质量碎片之间每个核子结合能的差异。²³⁵U的比结合能约为7.6 MeV/核子，而典型裂变碎片（如A ≈ 140和A ≈ 95）的比结合能约为8.5 MeV/核子。
After fission, the total binding energy of the system has increased; the decrease in total mass appears as kinetic energy of the products. The shape of the binding energy per nucleon curve explains why both fission of heavy nuclei and fusion of light nuclei are exothermic.
裂变后，系统的总结合能增加；总质量的减少体现为产物的动能。比结合能曲线的形状解释了为什么重核裂变和轻核聚变都是放能的。
4. Mass-Energy Equivalence in Fission | 裂变中的质能等价
The energy released, ΔE, is calculated from the mass defect Δm using Einstein's mass–energy relation:
ΔE = Δm c²
释放的能量ΔE由质量亏损Δm通过爱因斯坦质能关系计算：
ΔE = Δm c²
erage fission of ²³⁵U, the mass defect is around 0.2 u, yielding about 186 MeV per fission. Comparing this to chemical reactions (a few eV per atom) illustrates the enormous energy density of nuclear fuels.
当质量以原子质量单位(u)表示时，能量当量为1 u = 931.5 MeV/c²。对于²³⁵U的平均裂变，质量亏损约为0.2 u，每次裂变产生约186 MeV。对比化学反应（每原子数eV），可见核燃料的能量密度之巨大。
5. Chain Reactions and Critical Mass | 链式反应与临界质量
1, the reaction dies out (subcritical); if k > 1, it grows exponentially (supercritical).
一次裂变产生的中子可以引发更多裂变，形成自持链式反应。由一个裂变产生并引起下一次裂变的中子平均数目称为倍增因子k。对于稳态反应堆，k=1（临界）。若k<1，反应逐渐停止（次临界）；若k>1，链式反应指数增长（超临界）。
Critical mass is the minimum amount of fissile material needed to sustain a chain reaction for a given configuration and neutron economy. For a bare sphere of ²³⁵U, the critical mass is about 50 kg. The presence of a neutron reflector, moderator, or enrichment reduces the required mass.
临界质量是在给定几何布置和中子经济条件下，维持链式反应所需的可裂变材料的最小质量。对于裸球体²³⁵U，临界质量约为50 kg。有中子反射层、慢化剂或提高浓缩度会降低所需质量。
6. Nuclear Reactors: Components | 核反应堆：组件
A nuclear reactor is designed to extract useful heat from a controlled fission chain reaction. The main components and their functions are summarised in the table below.
核反应堆旨在从受控裂变链式反应中提取有用的热量。下表总结了主要组件及其功能。
| Component | Function | Example Materials |
| Fuel | Provide fissile nuclei | Enriched UO₂ (²³⁵U), PuO₂ (²³⁹Pu) |
| Moderator | Slow fast neutrons to thermal energies | Light water, heavy water, graphite |
| Control rods | Absorb neutrons to adjust k | Boron, cadmium, hafnium |
| Coolant | Remove heat from the core | Water, heavy water, CO₂, liquid sodium |
7. Control Rods and Moderators | 控制棒与慢化剂
Control rods contain materials with high neutron capture cross-sections, such as boron or cadmium. Inserting the rods increases neutron absorption, reducing k and power output. Rapid full insertion (SCRAM) shuts down the chain reaction in seconds. Fine movement allows precise control of reactor power.
控制棒含有高中子俘获截面的材料，如硼或镉。插入控制棒会增加中子吸收，降低k和功率输出。
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