📚 IB Physics: Nuclear & Particle Physics Special Topic | IB物理：原子核与粒子物理专题
The study of nuclear and particle physics takes us from the heart of the atom to the fundamental building blocks of the universe. This special topic consolidates the core knowledge required for IB Physics Paper 1 and Paper 2, covering atomic structure, radioactive decay, binding energy, fission and fusion, as well as the Standard Model of particle physics.
原子核与粒子物理专题带领我们从原子核心走向宇宙的基本构成单元。本文围绕IB物理Paper 1和Paper 2的核心考点，系统梳理原子结构、放射性衰变、结合能、核裂变与聚变，以及粒子物理标准模型等重点内容。
1. Atomic Structure & Nuclear Notation | 原子结构与核素符号
Every atom consists of a dense central nucleus surrounded by orbiting electrons. The nucleus contains protons and neutrons, collectively called nucleons. The atomic number Z equals the number of protons, while the mass number A equals the total number of protons plus neutrons.
每个原子由致密的原子核和绕核运动的电子组成。原子核包含质子和中子，统称核子。原子序数Z等于质子数，质量数A等于质子数加中子数之和。
The standard nuclear notation is written as:
ᴀᴢX
where X is the chemical symbol, A is the mass number (nucleon number) and Z is the atomic number (proton number). For example, ²³⁸₉₂U represents a uranium nucleus with 238 nucleons and 92 protons, which therefore contains 238 − 92 = 146 neutrons.
核素符号写作：
ᴀᴢX
其中X为化学元素符号，A为质量数（核子数），Z为原子序数（质子数）。例如，²³⁸₉₂U表示一个含有238个核子、92个质子的铀核，因此其中子数为238 − 92 = 146。
Isotopes are nuclides of the same element that share the same number of protons but differ in their number of neutrons. Since electrons determine chemical behaviour, isotopes display identical chemical properties but may differ in nuclear stability.
同位素是同一元素中质子数相同而中子数不同的核素。由于化学性质由电子决定，同位素具有相同的化学性质，但核稳定性可能存在差异。
- Proton number Z defines the element | 质子数Z决定元素种类
- Nucleon number A = Z + N, where N is neutron number | 核子数A = Z + N，N为中子数
- Neutron number N = A − Z | 中子数N = A − Z
2. Fundamental Forces Inside the Nucleus | 原子核内部的基本相互作用
Two competing forces govern nuclear stability. The electrostatic (Coulomb) repulsion between positively charged protons pushes the nucleus apart, while the strong nuclear force, which acts between all nucleons at very short range (about 1–3 fm), holds the nucleus together.
两种相互竞争的力决定了原子核的稳定性。质子间带正电的库仑斥力倾向于使原子核瓦解，而强核力则在极短距离（约1–3飞米）内作用于所有核子之间，将原子核束缚在一起。
The strong nuclear force is approximately 100 times stronger than the electromagnetic force at nuclear distances, but it has a very limited range. Beyond about 3 fm, the attractive strong force rapidly drops to zero, which is why large unstable nuclei are prone to decay.
在原子核尺度内，强核力约为电磁力的100倍，但其作用距离极短。超过约3飞米，吸引力迅速衰减至零，这就是大质量不稳定核容易发生衰变的原因。
The relationship between nucleon number and stability follows a general trend: light nuclei tend to be stable when Z ≈ N, but heavier stable nuclei require a greater proportion of neutrons to dilute the proton–proton repulsion while contributing additional strong-force attraction.
核子数与稳定性之间的关系存在一般规律：轻核在Z ≈ N时较为稳定，而重核则需要更高比例的中子来稀释质子间的斥力，同时增加额外的强核力吸引力。
3. Radioactive Decay: α, β⁻, β⁺ and γ | 放射性衰变：α、β⁻、β⁺与γ
Unstable nuclei spontaneously transform into more stable configurations through radioactive decay. There are four primary decay modes that IB students must be able to describe with full nuclear equations.
不稳定的原子核通过放射性衰变自发转变为更稳定的形态。IB学生必须掌握四种基本衰变方式及其完整的核反应方程。
Alpha (α) decay involves the emission of a helium nucleus ⁴₂He. This reduces both Z and A:
²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He
α衰变放出一个氦核⁴₂He，原子序数与质量数同时减小：
²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He
Beta-minus (β⁻) decay occurs in neutron-rich nuclei. A neutron converts into a proton, emitting an electron and an antineutrino:
¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̄ₑ
β⁻衰变发生在中子过多的原子核中。一个中子转化为质子，同时放出一个电子和一个反中微子：
¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̄ₑ
Beta-plus (β⁺) decay occurs in proton-rich nuclei. A proton converts into a neutron, emitting a positron and an electron neutrino:
²²₁₁Na → ²²₁₀Ne + ⁰₊₁e + νₑ
β⁺衰变发生在质子过多的原子核中。一个质子转化为中子，同时放出一个正电子和一个电子中微子：
²²₁₁Na → ²²₁₀Ne + ⁰₊₁e + νₑ
Gamma (γ) decay releases excess energy from a nucleus in an excited state, without changing Z or A. It usually accompanies α or β decay when the daughter nucleus is left in an excited energy state:
⁶⁰₂₇Co* → ⁶⁰₂₇Co + γ
γ衰变从激发态的原子核中释放多余能量，不改变Z或A。当子核处于激发态时，γ衰变常伴随α或β衰变发生：
⁶⁰₂₇Co* → ⁶⁰₂₇Co + γ
4. Half-Life and the Exponential Decay Law | 半衰期与指数衰变定律
The half-life T₁.₂ of a radioactive nuclide is defined as the time required for half of the original number of nuclei in a sample to decay. It is a statistical quantity: it applies to large populations of nuclei, not to a single nucleus.
放射性核素的半衰期T₁.₂定义为样品中一半数量的原子核发生衰变所需的时间。这是一个统计量：适用于大量原子核的集合，而不适用于单个原子核。
The number of undecayed nuclei N(t) as a function of time follows an exponential law:
N(t) = N₀(½)^(t/T₁.₂) = N₀e^(−λt)
where N₀ is the initial number of nuclei, t is the elapsed time, and λ is the decay constant, related to the half-life by λ = ln2 / T₁.₂ ≈ 0.693 / T₁.₂.
未衰变核的数量N(t)随时间服从指数规律：
N(t) = N₀(½)^(t/T₁.₂) = N₀e^(−λt)
其中N₀为初始核数，t为经过的时间，λ为衰变常数，与半衰期的关系为λ = ln2 / T₁.₂ ≈ 0.693 / T₁.₂。
The activity A of a sample, measured in becquerels (Bq), is the rate of decay A = λN. Activity also decays exponentially according to A(t) = A₀e^(−λt).
样品的活度A以贝克勒尔（Bq）为单位，定义为衰变率A = λN。活度同样遵从指数衰变规律A(t) = A₀e^(−λt)。
| Quantity | 物理量 | Symbol | 符号 | Unit | 单位 |
| Decay constant | 衰变常数 | λ | s⁻¹ |
| Half-life | 半衰期 | T₁.₂ | s |
| Activity | 活度 | A | Bq |
| Number of nuclei | 核数 | N | (dimensionless) | 无量纲 |
5. Mass Defect and Nuclear Binding Energy | 质量亏损与核结合能
The mass of a nucleus is always less than the sum of the masses of its individual constituent nucleons. This difference, known as the mass defect Δm, is converted into the binding energy that holds the nucleus together.
原子核的质量总是小于其各个组成核子的质量之和。这一差值称为质量亏损Δm，它转化为将原子核束缚在一起的结合能。
According to Einstein’s mass–energy equivalence, the binding energy is calculated using:
E_b = Δm × c²
where c = 3.00 × 10⁸ m s⁻¹. In nuclear physics, masses are often expressed in atomic mass units (u), where 1 u = 1.661 × 10⁻²⁷ kg ≈ 931.5 MeV/c².
根据爱因斯坦的质能等价关系，结合能通过以下公式计算：
E_b = Δm × c²
其中c = 3.00 × 10⁸ m s⁻¹。在核物理中，质量通常以原子质量单位（u）表示，1 u = 1.661 × 10⁻²⁷ kg ≈ 931.5 MeV/c²。
For a nucleus ᴀᴢX, the mass defect is:
Δm = [Z × mₚ + (A − Z) × mₙ] − m_nucleus
where mₚ and mₙ are the masses of a free proton and neutron respectively.
对于核素ᴀᴢX，质量亏损为：
Δm = [Z × mₚ + (A − Z) × mₙ] − m_nucleus
其中mₚ和mₙ分别为自由质子和自由中子的质量。
6. The Binding Energy Per Nucleon Curve | 比结合能曲线
A graph of binding energy per nucleon against nucleon number A is one of the most important diagrams in nuclear physics. It reveals which nuclear transformations release energy.
比结合能随核子数A变化的曲线是核物理中最重要的图像之一。它揭示了哪些核转变可以释放能量。
- At low A, the binding energy per nucleon increases sharply, reaching a maximum of about 8.8 MeV per nucleon around A ≈ 56 (iron-56) | 在低A区，比结合能迅速增加，在A ≈ 56（铁-56）附近达到约8.8 MeV/核子的最大值
- For A > 56, the binding energy per nucleon gradually decreases | 当A > 56时，比结合能逐渐下降
- Nuclei near iron are the most stable | 铁附近的核素最为稳定
Energy is released in nuclear transformations when nucleons move from a region of lower binding energy per nucleon to a region of higher binding energy per nucleon. This is why both fission (splitting heavy nuclei) and fusion (joining light nuclei) release energy.
当核子从比结合能较低的区域向比结合能较高的区域转移时，核转变就会释放能量。这就是重核裂变和轻核聚变都能释放能量的原因。
7. Nuclear Fission and Nuclear Fusion | 核裂变与核聚变
Nuclear fission is the splitting of a heavy nucleus into two lighter nuclei, accompanied by the release of neutrons and a large amount of energy. A typical fission reaction of uranium-235 induced by a neutron is:
²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n + Energy
核裂变是指一个重原子核分裂成两个较轻原子核的过程，伴随中子释放和大量能量产生。一个典型的中子诱发的铀-235裂变反应为：
²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n + Energy
The fission fragments are typically radioactive, and the emitted neutrons can trigger a chain reaction if the sample exceeds a critical mass. Fission power plants control this chain reaction using control rods that absorb neutrons and a moderator that slows neutrons down to increase the probability of further fission.
裂变碎片通常具有放射性，释放的中子若样品超过临界质量则可引发链式反应。裂变电站通过吸收中子的控制棒和使中子减速的慢化剂来控制链式反应，以提高后续裂变的概率。
Nuclear fusion is the process in which two light nuclei combine to form a heavier nucleus. A key fusion reaction in the Sun and in experimental reactors such as ITER is:
²₁H + ³₁H → ⁴₂He + ¹₀n + 17.6 MeV
核聚变是两个轻原子核结合形成一个较重原子核的过程。太阳内部及ITER等实验反应堆中的一个关键聚变反应为：
²₁H + ³₁H → ⁴₂He + ¹₀n + 17.6 MeV
Fusion requires extremely high temperatures (around 10⁸ K) to overcome the Coulomb barrier between positively charged nuclei. It produces far more energy per nucleon than fission and generates less long-lived radioactive waste.
聚变需要极高的温度（约10⁸ K）以克服带正电原子核之间的库仑势垒。聚变每核子产出的能量远高于裂变，且产生的长寿命放射性废物更少。
8. The Standard Model of Particle Physics | 粒子物理标准模型
The Standard Model classifies all known elementary particles into fermions (matter particles with half-integer spin) and bosons (force-carrying particles with integer spin). There are three generations of fermions and four fundamental forces in the model.
标准模型将所有已知基本粒子分为费米子（半整数自旋的物质粒子）和玻色子（整数自旋的传递力的粒子）。该模型包含三代费米子和四种基本相互作用。
| Category | 类别 | Particles | 粒子 | Charge | 电荷 |
| Up-type quarks | 上型夸克 | u, c, t | +2/3 e |
| Down-type quarks | 下型夸克 | d, s, b | −1/3 e |
| Charged leptons | 带电轻子 | e, μ, τ | −1 e |
| Neutrinos | 中微子 | νₑ, νμ, ντ | 0 |
| Gauge bosons | 规范玻色子 | γ, W±, Z⁰, g | 0, ±1, 0, 0 |
| Scalar boson | 标量玻色子 | H (Higgs) | 0 |
Hadrons, such as protons and neutrons, are composite particles made of quarks held together by gluons. Baryons consist of three quarks (e.g., proton = uud), mesons consist of a quark–antiquark pair (e.g., pion = ud̄).
强子（如质子和中子）是由夸克通过胶子束缚在一起构成的复合粒子。重子由三个夸克组成（如质子 = uud），介子由一对夸克-反夸克组成（如π介子 = ud̄）。
Leptons, in contrast, are fundamental particles that do not experience the strong nuclear force. The electron, muon, tau and their associated neutrinos are all leptons.
轻子则是不参与强相互作用的基元粒子。电子、μ子、τ粒子及其对应的中微子都属于轻子。
9. Fundamental Interactions & Exchange Particles | 基本相互作用与交换粒子
According to quantum field theory, forces are mediated by the exchange of virtual particles. Each fundamental force corresponds to a specific exchange boson:
根据量子场论，力通过虚粒子的交换传递。每种基本相互作用对应特定的交换玻色子：
- Strong nuclear force → gluons (g) | 强核力 → 胶子（g）
- Electromagnetic force → photons (γ) | 电磁力 → 光子（γ）
- Weak nuclear force → W⁺, W⁻, Z⁰ bosons | 弱核力 → W⁺、W⁻、Z⁰玻色子
- Gravitational force → gravitons (hypothesised) | 引力 → 引力子（假说）
The weak interaction is responsible for β decay and changes quark flavour, e.g., a down quark in a neutron decays to an up quark, emitting a W⁻ boson that subsequently decays into an electron and an antineutrino. This is the underlying mechanism of β⁻ decay.
弱相互作用负责β衰变并改变夸克味道。例如，中子中的一个下夸克衰变为上夸克时发射一个W⁻玻色子，后者随即衰变为一个电子和一个反中微子。这就是β⁻衰变的基本机制。
The Higgs boson, discovered at CERN in 2012, is associated with the Higgs field, which gives mass to fundamental particles through the Higgs mechanism.
2012年在CERN发现的希格斯玻色子与希格斯场相关联，希格斯机制赋予基本粒子以质量。
10. Quark Confinement & Elementary Charge | 夸克禁闭与基本电荷
Quarks have never been observed in isolation; they exist only in bound states. This phenomenon is known as quark confinement. The strong force between quarks increases with separation, similar to a stretched spring, making it impossible to free a single quark under normal conditions.
夸克从未被独立观测到，它们只存在于束缚态中。这一现象称为夸克禁闭。夸克之间的强相互作用力随距离增大而增强，类似于被拉伸的弹簧，因此在正常情况下不可能分离出单个夸克。
The charge of any particle is an integer multiple of the elementary charge e, except for quarks, which carry fractional charges of ±1/3 e or ±2/3 e. However, because quarks always combine into hadrons with integer total charge, the observable universe contains only integer-charge particles.
除了夸克带有±1/3 e或±2/3 e的分数电荷外，任何粒子的电荷都是基本电荷e的整数倍。然而，由于夸克总是结合成电荷为整数的强子，可观测宇宙中只存在整数电荷的粒子。
This principle is essential for balancing particle reactions and understanding why certain decays are allowed or forbidden. For example, the proton (uud) has total charge +1, and the neutron (udd) has total charge 0.
这一原则对于配平粒子反应和理解某些衰变为何允许或禁止至关重要。例如，质子（uud）总电荷为+1，中子（udd）总电荷为0。
11. Conservation Laws in Particle Reactions | 粒子反应中的守恒定律
All particle interactions must obey a set of fundamental conservation laws. Being able to apply these laws is essential for analysing and predicting particle reactions.
所有粒子相互作用都必须遵守一系列基本守恒定律。能够应用这些定律是分析和预测粒子反应的关键。
- Charge conservation: total charge before = total charge after | 电荷守恒：反应前后总电荷相等
- Baryon number conservation: total baryon number is conserved (baryons = +1, antibaryons = −1, mesons and leptons = 0) | 重子数守恒：总重子数守恒（重子为+1，反重子为−1，介子与轻子为0）
- Lepton number conservation: electron number, muon number and tau number are separately conserved | 轻子数守恒：电子数、μ子数和τ粒子数分别守恒
- Energy and momentum conservation | 能量与动量守恒
- Strangeness conservation (in strong interactions only) | 奇异数守恒（仅适用于强相互作用）
For example, in β⁻ decay, a neutron (baryon number +1) decays into a proton (baryon number +1), an electron (lepton number +1) and an antineutrino (lepton number −1). Both baryon number and lepton number are conserved.
例如，在β⁻衰变中，一个中子（重子数+1）衰变为一个质子（重子数+1）、一个电子（轻子数+1）和一个反中微子（轻子数−1）。重子数与轻子数均守恒。
12. Exam Strategies & Common Pitfalls | 应试策略与常见误区
In IB Physics examinations, nuclear and particle physics questions frequently test the ability to write balanced nuclear equations and apply conservation laws. Below are key strategies to maximise marks.
在IB物理考试中，原子核与粒子物理题目常考察核反应方程的配平能力和守恒定律的应用。以下策略有助于获得更高分数。
- Always balance A and Z in every nuclear equation — check both on both sides | 核方程中始终配平A和Z——检查左右两侧的两个量
- For binding energy problems, convert mass units to MeV using 1 u = 931.5 MeV/c² | 结合能问题中，使用1 u = 931.5 MeV/c²将质量单位换算为MeV
- Do not confuse activity A with mass number A — one is rate of decay, the other is nucleon count | 不要混淆活度A与质量数A——前者是衰变率，后者是核子数
- For half-life questions, use the exponential formula or graphical methods; pay attention to the unit of time | 半衰期问题使用指数公式或图像法，注意时间单位
- When analysing particle reactions, systematically check charge, baryon number and lepton number | 分析粒子反应时，依序检查电荷、重子数和轻子数
- When comparing fission and fusion, refer to the binding energy per nucleon curve rather than memorising facts alone | 比较裂变与聚变时，应结合比结合能曲线分析，而非仅靠机械记忆
The most common mistake in nuclear equations is forgetting to include neutrinos or antineutrinos in β decay, which leads to apparent violations of energy and momentum conservation. Always include them in your final equation.
核方程中最常见的错误是遗漏β衰变中的中微子或反中微子，这会导致能量与动量守恒表面上的不成立。务必在最终方程中包含它们。
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