IB Physics: Nuclear Fission | IB物理：核裂变

📚 IB Physics: Nuclear Fission | IB物理：核裂变

Nuclear fission is one of the most consequential topics in IB Physics, connecting the microscopic world of the nucleus to macroscopic energy production on a national scale. This article will guide you through the core concepts, key equations, and exam-relevant details of nuclear fission, following the IB Physics syllabus.

核裂变是IB物理中最具影响力的课题之一，它将微观的原子核世界与宏观的国家级能源生产紧密相连。本文将按照IB物理教学大纲，带你系统掌握核裂变的核心概念、关键方程和考试相关细节。

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1. What is Nuclear Fission? | 什么是核裂变？

Nuclear fission is a nuclear reaction in which a heavy nucleus (such as uranium-235 or plutonium-239) splits into two or more smaller nuclei, known as fission fragments, along with the release of neutrons and a large amount of energy. The process is typically initiated by the absorption of a slow-moving neutron.

核裂变是一种核反应，其中重原子核（如铀-235或钚-239）分裂成两个或更多较小的原子核，称为裂变碎片，同时释放出中子和大量能量。该过程通常由吸收一个慢中子引发。

For IB Physics, the definition you must remember is: fission is the splitting of a large unstable nucleus into two smaller nuclei, with the release of energy. The energy originates from the difference in binding energy per nucleon between the parent nucleus and the daughter nuclei.

对于IB物理，你必须记住的定义是：裂变是一个大的不稳定原子核分裂成两个较小原子核的过程，并释放能量。能量来源于母核与子核之间每个核子结合能的差异。

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2. The Fission Process | 裂变过程

When a uranium-235 nucleus absorbs a neutron, it becomes uranium-236 in an excited state. This excited nucleus is highly unstable and undergoes deformation, elongating into a dumbbell shape. When the electrostatic repulsion between the two lobes overcomes the short-range strong nuclear force, the nucleus splits apart.

当铀-235原子核吸收一个中子时，它变成处于激发态的铀-236。这个激发态的原子核极不稳定，会发生形变，拉长成哑铃形状。当两叶之间的静电排斥力超过短程强核力时，原子核就会分裂开来。

A typical fission reaction of uranium-235 can be written as:

²³⁵U + ¹n → ¹⁴¹Ba + ⁹²Kr + 3¹n + Energy (~200 MeV)

Note that the mass number is conserved (235 + 1 = 141 + 92 + 3 = 236), and charge is conserved (92 = 56 + 36). The exact fission products vary; over 200 different isotopes have been observed as fission fragments. This variability is an important point that examiners love to test.

注意质量数是守恒的（235 + 1 = 141 + 92 + 3 = 236），电荷也是守恒的（92 = 56 + 36）。具体的裂变产物并不唯一；目前已观察到200多种不同的同位素作为裂变碎片。这种多样性是考官喜欢考查的重要考点。

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3. Energy Released in Fission | 裂变释放的能量

The enormous energy released in fission can be understood through the binding energy per nucleon curve. For nuclei with mass numbers around 240 (such as uranium), the binding energy per nucleon is approximately 7.6 MeV. For nuclei around mass number 100 (such as krypton or barium), it is approximately 8.5 MeV.

裂变释放的巨大能量可以通过每个核子的结合能曲线来理解。对于质量数约为240的原子核（如铀），每个核子的结合能约为7.6 MeV。对于质量数约为100的原子核（如氪或钡），每个核子的结合能约为8.5 MeV。

The energy released per fission event can be calculated from the mass defect:

E = Δm × c²

where Δm is the difference between the mass of the reactants and the mass of the products. For a typical uranium-235 fission, Δm ≈ 0.22 u (atomic mass units). Since 1 u = 931.5 MeV/c², the energy released is approximately 200 MeV per fission event.

其中Δm是反应物质量与产物质量之差。对于典型的铀-235裂变，Δm ≈ 0.22 u（原子质量单位）。由于1 u = 931.5 MeV/c²，每次裂变释放的能量约为200 MeV。

Let’s verify this with a concrete calculation using the masses: the mass of ²³⁵U is 235.0439 u, a neutron has mass 1.0087 u, ¹⁴¹Ba has mass 140.9144 u, and ⁹²Kr has mass 91.9262 u.

让我们用具体质量来验证这一计算：²³⁵U的质量为235.0439 u，中子的质量为1.0087 u，¹⁴¹Ba的质量为140.9144 u，⁹²Kr的质量为91.9262 u。

Mass of reactants = 235.0439 + 1.0087 = 236.0526 u. Mass of products = 140.9144 + 91.9262 + 3 × 1.0087 = 235.8667 u. Mass defect Δm = 236.0526 − 235.8667 = 0.1859 u. Converting to energy: E = 0.1859 × 931.5 ≈ 173 MeV. (The difference from 200 MeV is due to the specific fission channel; some energy also appears in gamma rays and neutrinos.)

反应物质量 = 235.0439 + 1.0087 = 236.0526 u。产物质量 = 140.9144 + 91.9262 + 3 × 1.0087 = 235.8667 u。质量亏损Δm = 236.0526 − 235.8667 = 0.1859 u。转换为能量：E = 0.1859 × 931.5 ≈ 173 MeV。（与200 MeV的差异源于具体的裂变通道不同；部分能量还以伽马射线和中微子的形式释放。）

A key exam point: the energy released is mostly carried by the kinetic energy of the fission fragments (about 85%), with the rest shared between neutrons, gamma radiation, and neutrinos.

一个关键考点：释放的能量大部分由裂变碎片的动能携带（约占85%），其余部分由中子、伽马辐射和中微子共享。

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4. Binding Energy and Fission | 结合能与裂变

The binding energy per nucleon curve is essential for understanding why fission releases energy. The curve peaks around iron-56 (binding energy ≈ 8.8 MeV/nucleon). Nuclei heavier than iron are less tightly bound; when they split into lighter nuclei closer to the iron peak, the products are more stable, and the difference in binding energy is released.

每个核子的结合能曲线对于理解裂变为何释放能量至关重要。该曲线在铁-56附近达到峰值（每个核子结合能≈8.8 MeV）。比铁更重的原子核结合得较松散；当它们分裂成更接近铁峰的较轻原子核时，产物更加稳定，结合能的差值便以能量的形式释放。

For fission to be energetically favourable, the binding energy per nucleon of the fragments must exceed that of the parent nucleus. The energy released equals the binding energy of the products minus the binding energy of the reactant.

要使裂变在能量上有利，裂变碎片的每个核子结合能必须大于母核的结合能。释放的能量等于产物的总结合能减去反应物的总结合能。

E_released = BE_products − BE_reactant

This relationship is the physical origin of the “energy output” of nuclear power. An exam question may ask you to calculate this using a binding energy per nucleon graph, where you read off values for U-235 (≈7.6 MeV/nucleon) and the fragments (≈8.4–8.6 MeV/nucleon). The difference of approximately 0.8–1.0 MeV per nucleon, multiplied by 240 nucleons, gives roughly 200 MeV.

这一关系是核能”能量输出”的物理根源。考试题目可能会要求你使用每个核子结合能图来计算，从图中读取U-235（约7.6 MeV/核子）和碎片（约8.4–8.6 MeV/核子）的数值。每个核子约0.8–1.0 MeV的差值，乘以240个核子，得到约200 MeV。

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5. Chain Reactions | 链式反应

A fission chain reaction occurs when the neutrons released from one fission event go on to trigger further fission events. For uranium-235, an average of 2–3 neutrons are released per fission. If at least one of these neutrons causes another fission, a self-sustaining chain reaction is established.

当一次裂变事件释放的中子继续触发更多裂变事件时，就会发生裂变链式反应。对于铀-235，每次裂变平均释放2–3个中子。如果这些中子中至少有一个引发另一次裂变，就建立了自持的链式反应。

The multiplication factor k is a crucial parameter:

• k < 1: Subcritical — the reaction dies out.
• k = 1: Critical — a steady controlled reaction.
• k > 1: Supercritical — the reaction grows rapidly.

增殖因子k是一个关键参数：

• k < 1：次临界——反应逐渐停止。
• k = 1：临界——稳定受控的反应。
• k > 1：超临界——反应迅速增长。

For a chain reaction to occur, a critical mass of fissile material is required. The critical mass is the minimum amount of material needed to sustain a chain reaction. For a bare sphere of uranium-235, the critical mass is approximately 52 kg; with a neutron reflector, it can be reduced to about 15 kg.

链式反应的发生需要一定质量的易裂变材料，即临界质量。临界质量是维持链式反应所需的最小材料量。对于裸铀-235球体，临界质量约为52 kg；若使用中子反射层，可降至约15 kg。

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6. Nuclear Reactors | 核反应堆

In a nuclear reactor, a controlled chain reaction is maintained to produce energy at a steady rate. The key components of a reactor include:

在核反应堆中，维持受控链式反应以稳定的速率产生能量。反应堆的关键组成部分包括：

• Fuel: Typically uranium dioxide (UO₂) enriched to 3–5% ²³⁵U.
• Moderator: A material (water, heavy water, or graphite) that slows down fast neutrons to thermal energies, increasing the probability of inducing fission.
• Control rods: Made of boron or cadmium, which absorb neutrons to control the reaction rate.
• Coolant: Water, liquid sodium, or gas that transfers heat away from the core.
• Shielding: Concrete and lead barriers to absorb radiation.

燃料：通常是铀二氧化物（UO₂），富集至3–5%的²³⁵U。

慢化剂：一种材料（水、重水或石墨），用于将快中子减速至热能范围，增加引发裂变的概率。

控制棒：由硼或镉制成，吸收中子以控制反应速率。

冷却剂：水、液态钠或气体，将热量从堆芯带走。

屏蔽层：混凝土和铅屏障，用于吸收辐射。

The moderator works by elastic collision: fast neutrons (with kinetic energy around 2 MeV) collide with light nuclei in the moderator, losing energy until they reach thermal energies (around 0.025 eV). Light water (H₂O) is an effective moderator, but it also absorbs neutrons; heavy water (D₂O) absorbs fewer neutrons and allows natural uranium to be used as fuel.

慢化剂通过弹性碰撞起作用：快中子（动能约2 MeV）与慢化剂中的轻原子核碰撞，损失能量直至达到热能范围（约0.025 eV）。轻水（H₂O）是有效的慢化剂，但它也会吸收中子；重水（D₂O）吸收的中子较少，因此允许使用天然铀作为燃料。

A common IB exam question asks: why must neutrons be slowed down in a thermal reactor? The answer is that the probability of fission in ²³⁵U is much higher for thermal (slow) neutrons than for fast neutrons. The fission cross-section of ²³⁵U for thermal neutrons is about 580 barns, compared to about 1 barn for fast neutrons.

一个常见的IB考试问题是：为什么热中子反应堆中必须将中子减慢？答案是²³⁵U对热（慢）中子的裂变截面远大于快中子。²³⁵U对热中子的裂变截面约为580靶恩，而对快中子仅约1靶恩。

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7. Energy Output and Power | 能量输出与功率

To calculate the energy output of a reactor, you need to know the number of fission events per second. If a reactor operates at a thermal power of 3 GW (3 × 10⁹ J/s) and each fission releases 200 MeV = 3.2 × 10⁻¹¹ J, then the number of fissions per second is:

要计算反应堆的能量输出，你需要知道每秒钟发生的裂变事件数。如果一个反应堆以3 GW（3 × 10⁹ J/s）的热功率运行，每次裂变释放200 MeV = 3.2 × 10⁻¹¹ J，那么每秒的裂变次数为：

N = P / E_fission = (3 × 10⁹) / (3.2 × 10⁻¹¹) ≈ 9.4 × 10¹⁹ fissions per second

To find the mass of fuel consumed per day, we use the fact that 235 g of uranium contains 6.02 × 10²³ atoms (Avogadro’s number). If 9.4 × 10¹⁹ atoms fission per second, then per day: 9.4 × 10¹⁹ × 86400 ≈ 8.1 × 10²⁴ atoms. The mass consumed per day = (8.1 × 10²⁴ / 6.02 × 10²³) × 0.235 ≈ 3.2 kg. This remarkably small mass — roughly the size of a brick — powers an entire city-scale reactor for a day.

要计算每天消耗的燃料质量，我们利用235 g铀含有6.02 × 10²³个原子（阿伏伽德罗常数）这一事实。如果每秒有9.4 × 10¹⁹个原子裂变，那么每天：9.4 × 10¹⁹ × 86400 ≈ 8.1 × 10²⁴个原子。每天消耗的质量 = (8.1 × 10²⁴ / 6.02 × 10²³) × 0.235 ≈ 3.2 kg。这个惊人的小质量——大约一块砖的大小——足以让一个城市规模的反应堆运行一整天。

The “burning” of 1 kg of uranium-235 releases roughly 8 × 10¹³ J, equivalent to burning about 2,700 tonnes of coal. This staggering energy density is why nuclear power is so effective despite the associated risks.

燃烧1 kg铀-235大约释放8 × 10¹³ J，相当于燃烧约2700吨煤。这种令人惊叹的能量密度是核能尽管存在相关风险却依然高效的原因。

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8. Fission vs Fusion | 裂变与聚变对比

IB Physics requires you to compare and contrast fission and fusion. Both processes release energy because they move nuclei toward the peak of the binding energy curve, but in opposite directions on the periodic table.

IB物理要求你比较和对比裂变与聚变。两种过程都通过将原子核推向结合能曲线的峰值来释放能量，但在元素周期表上的移动方向相反。

Aspect	Fission | 裂变	Fusion | 聚变
Process	Heavy nucleus splits into lighter nuclei	Light nuclei combine into a heavier nucleus
Process 过程	重核分裂为轻核	轻核合并为重核
Fuel	Uranium-235, Plutonium-239	Hydrogen isotopes (deuterium, tritium)
Fuel 燃料	铀-235、钚-239	氢同位素（氘、氚）
Energy per nucleon	~0.85 MeV/nucleon	~3.5 MeV/nucleon (higher)
Energy per nucleon 每核子能量	约0.85 MeV/核子	约3.5 MeV/核子（更高）
Technology status	Commercially mature	Experimental (ITER, NIF)
Technology 技术状态	商业成熟	实验阶段（ITER、NIF）
Waste products	Long-lived radioactive isotopes	Helium (non-radioactive), but activation of reactor materials
Waste 废料	长寿命放射性同位素	氦（无放射性），但反应堆材料会被活化

An important comparison point: fusion releases more energy per unit mass of fuel than fission, but requires extremely high temperatures (around 100 million K) to overcome the Coulomb barrier between nuclei. This is why fusion is called a “thermonuclear” reaction.

一个重要的比较点：聚变单位质量燃料释放的能量高于裂变，但需要极高温度（约1亿K）以克服原子核之间的库仑势垒。这就是为什么聚变被称为”热核”反应。

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9. Applications and Nuclear Power | 应用与核电

Nuclear fission has two primary applications: controlled chain reactions for electricity generation and uncontrolled chain reactions for nuclear weapons. In this article, we focus on the peaceful application. As of 2024, approximately 440 nuclear reactors operate worldwide, supplying roughly 10% of global electricity. Countries such as France derive over 70% of their electricity from nuclear power.

核裂变有两个主要应用：受控链式反应用于发电，不受控链式反应用于核武器。本文重点讨论和平利用。截至2024年，全球约有440座核反应堆运行，供应约10%的全球电力。法国等国家70%以上的电力来自核电。

In a pressurised water reactor (PWR), the nuclear fuel generates heat, which is transferred to the primary coolant loop. This heat is exchanged into a secondary loop, producing steam to drive turbines. The key principle is that the fission products remain in the fuel rods, while the energy is extracted as heat. This is a classic IB exam topic — you should be able to sketch and label a simplified reactor diagram.

在压水反应堆（PWR）中，核燃料产生热量，传递给一回路冷却剂。这些热量通过热交换器传递到二回路，产生蒸汽驱动涡轮机。关键原理是裂变产物留在燃料棒中，而能量以热量的形式被提取。这是一个经典的IB考试话题——你应该能够绘制并标注简化的反应堆示意图。

Exam tip: when describing how a nuclear reactor works, use the following sequence — fission releases heat → coolant carries heat away → heat exchanger transfers heat to secondary loop → steam drives turbine → turbine turns generator → electrical energy output.

考试提示：描述核反应堆工作原理时，使用以下顺序——裂变释放热量→冷却剂带走热量→热交换器将热量传递给二回路→蒸汽驱动涡轮机→涡轮机带动发电机→输出电能。

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10. Safety and Radioactive Waste | 安全与放射性废物

One of the main challenges of nuclear fission is the management of radioactive waste. Fission products such as ¹³⁷Cs (with a half-life of 30 years) and ⁹⁰Sr (with a half-life of 29 years) emit beta and gamma radiation and must be isolated from the environment for hundreds of years. Actinide elements such as plutonium-239 have half-lives of 24,000 years and require geological disposal.

核裂变的主要挑战之一是放射性废物管理。裂变产物如¹³⁷Cs（半衰期30年）和⁹⁰Sr（半衰期29年）发射β和γ辐射，必须与环境隔离数百年。锕系元素如钚-239的半衰期为24,000年，需要地质处置。

In the IB syllabus, you should be aware of three safety mechanisms in a reactor: the control rods that absorb excess neutrons, the negative temperature coefficient of the moderator (if the reactor overheats, water expands and reduces moderation, slowing the reaction), and the containment building that prevents radioactive release. The Chernobyl disaster occurred partly because the RBMK reactor design had a positive void coefficient — a design flaw that amplified the reaction when cooling water turned to steam.

在IB教学大纲中，你应该了解反应堆的三种安全机制：吸收多余中子的控制棒、慢化剂的负温度系数（如果反应堆过热，水膨胀并降低慢化效果，从而减缓反应），以及防止放射性物质释放的安全壳建筑。切尔诺贝利灾难的部分原因是RBMK反应堆设计具有正的泡隙系数——当冷却水变成蒸汽时，这一设计缺陷会加剧反应。

For waste management, the IB course discusses strategies such as vitrification (incorporating waste into glass), storage in deep geological repositories, and reprocessing to extract usable isotopes. You should be able to weigh the advantages and disadvantages of nuclear power in an extended-response question, including cost, greenhouse gas emissions, and accident risk.

关于废物管理，IB课程讨论了玻璃化（将废物融入玻璃中）、深地质处置库储存以及后处理提取可用同位素等策略。你应该能够在扩展回答题中权衡核电的利弊，包括成本、温室气体排放和事故风险。

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11. Summary of Key Formulas | 关键公式总结

For your revision, the following formulas and relationships are essential for exam success:

为便于复习，以下公式和关系对考试成功至关重要：

Formula | 公式	Meaning | 含义
E = Δm × c²	Mass-energy equivalence | 质能等价
Δm = (mass of reactants) − (mass of products)	Mass defect | 质量亏损
1 u = 931.5 MeV/c²	Mass-to-energy conversion factor | 质量能量转换因子
BE = Δm × 931.5 MeV	Total binding energy | 总结合能
P = N × E_fission	Power equals fission rate × energy per fission | 功率等于裂变率×每次裂变能量

Remember that when solving numerical problems, always check units. If masses are given in atomic mass units (u), convert to energy in MeV using 1 u = 931.5 MeV/c². If masses are given in kilograms, use E = Δm × (3 × 10⁸)² in joules.

请记住，在解决数值问题时，务必检查单位。如果质量以原子质量单位（u）给出，使用1 u = 931.5 MeV/c²转换为以MeV为单位的能量。如果质量以千克给出，则使用E = Δm × (3 × 10⁸)²计算焦耳。

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12. Sample Exam Question | 典型考试题目

Let’s work through a typical IB-style question: A uranium-235 nucleus absorbs a neutron and fissions into two fragments with mass numbers 140 and 92, releasing 3 neutrons. Given that the binding energy per nucleon of U-235 is 7.6 MeV and that of the two fragments is 8.4 MeV, calculate the energy released per fission.

让我们解答一道典型的IB风格题目：一个铀-235原子核吸收一个中子，裂变成质量数分别为140和92的两个碎片，并释放3个中子。已知U-235的每个核子结合能为7.6 MeV，两个碎片的每个核子结合能为8.4 MeV，计算每次裂变释放的能量。

Solution | 解答：

Total binding energy of U-235 = 235 × 7.6 = 1786 MeV. Total binding energy of fragments = (140 + 92) × 8.4 = 232 × 8.4 = 1948.8 MeV. Energy released = 1948.8 − 1786 = 162.8 MeV.

U-235的总结合能 = 235 × 7.6 = 1786 MeV。碎片的总结合能 = (140 + 92) × 8.4 = 232 × 8.4 = 1948.8 MeV。释放的能量 = 1948.8 − 1786 = 162.8 MeV。

Note that the 3 released neutrons also carry away some energy, so the total energy budget would be slightly higher than this calculated value when accounting for neutron kinetic energy and gamma radiation. In practice, the exact value depends on the fission channel and is approximately 200 MeV.

注意释放的3个中子也带走部分能量，因此考虑中子动能和伽马辐射时，总能量预算会略高于此计算值。实际上，具体值取决于裂变通道，约为200 MeV。

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Conclusion | 结语

Nuclear fission is a rich and rewarding topic for IB Physics students. By mastering the binding energy curve, the mass defect calculation, the chain reaction mechanism, and reactor design principles, you will be well prepared for both multiple-choice and extended-response questions. Remember that the energy released in fission comes from the increase in binding energy per nucleon as heavy nuclei split into lighter, more stable fragments.

核裂变是IB物理学生一个内容丰富且有价值的课题。通过掌握结合能曲线、质量亏损计算、链式反应机制和反应堆设计原理，你将能够从容应对选择题和扩展回答题。请记住，裂变释放的能量来自于重核分裂成更轻、更稳定的碎片时每个核子结合能的增加。

For further practice, try constructing a full fission equation from memory, calculating the energy release from given masses, and drawing a labelled diagram of a reactor core. These skills will serve you well in the IB Physics examinations.

要想进一步练习，请尝试凭记忆写出完整的裂变方程、根据给定质量计算能量释放，并绘制标注齐全的反应堆堆芯图。这些技能将在IB物理考试中为你带来优势。

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