📚 IB CIE Physics: Nuclear Physics Essentials | IB CIE 物理：核物理考点精讲
Nuclear physics is a cornerstone of both the IB and CIE A‑Level syllabuses, blending fundamental concepts with real‑world applications. Mastering this topic means understanding everything from the stability of the nucleus to the equations that power the stars. This guide walks you through all the essential learning points, reinforced with paired English‑Chinese explanations to build exam confidence.
核物理是 IB 与 CIE A‑Level 课程大纲的核心支柱，它将基本概念与现实应用紧密结合。掌握本专题意味着你需要深入理解从原子核稳定性到驱动恒星能量的那些方程。这篇考点精讲将带你走过每一个核心知识点，并以中英对照的形式强化理解，助你建立考试信心。
1. Nuclear Structure & Notations | 原子核的结构与表示法
Every atom consists of a tiny, dense nucleus surrounded by electrons. The nucleus contains protons and neutrons, collectively called nucleons. The number of protons Z determines the element, while the total nucleon number A equals the sum of protons and neutrons. The number of neutrons N is therefore A − Z.
每个原子都由一个微小致密的原子核和绕核的电子组成。原子核内含有质子和中子，统称为核子。质子数 Z 决定了元素种类，而总核子数 A 等于质子数与中子数之和。因此中子数 N = A − Z。
Nuclides are represented using the standard notation AZX, where X is the chemical symbol. For example, carbon‑12 is written as 126C, indicating 6 protons and 6 neutrons. Isotopes of an element share the same Z but have different N and thus different A.
核素用标准符号 AZX 表示，其中 X 为化学符号。例如碳‑12 写作 126C，表示 6 个质子和 6 个中子。一种元素的同位素具有相同的 Z 但不同的 N，因此质量数 A 不同。
2. Nuclear Stability & the Strong Force | 原子核的稳定性与强相互作用力
Why don’t positively charged protons fly apart? The strong nuclear force binds nucleons together over a very short range (≈1–3 fm). It is the same for all nucleon pairs (p‑p, n‑n, p‑n) and overwhelms the electrostatic repulsion at nuclear distances. Beyond a few femtometres, the strong force becomes negligible.
为什么带正电的质子不会相互排斥飞开？强核力在极短距离（约 1–3 fm）内将核子束缚在一起。它对所有核子对（p‑p、n‑n、p‑n）作用相同，并在核尺度上压倒静电斥力。一旦超出几个飞米，强核力便可忽略不计。
Stability depends on the balance between the strong force and Coulomb repulsion. A plot of neutron number N against proton number Z reveals a ‘stability belt’. Light nuclei are most stable when N ≈ Z, whereas heavier nuclei need an excess of neutrons (N > Z) to dilute the growing Coulomb repulsion.
原子核的稳定性取决于强核力与库仑斥力之间的平衡。将中子数 N 对质子数 Z 作图可得到一条“稳定带”。轻核在 N ≈ Z 时最稳定，而重核需要中子过剩（N > Z）来稀释不断增长的库仑斥力。
3. Radioactive Decay: Types & Properties | 放射性衰变：类型与性质
Unstable nuclei release energy by emitting particles or electromagnetic radiation. Three common decay modes are alpha (α), beta‑minus (β⁻), and gamma (γ) decay.
不稳定的原子核通过发射粒子或电磁辐射来释放能量。三种常见的衰变模式是 α 衰变、β⁻ 衰变和 γ 衰变。
Alpha decay: a heavy nucleus ejects a helium‑4 nucleus (42He). The parent nucleus loses 2 protons and 2 neutrons, so A decreases by 4 and Z by 2. Alpha particles have a short range in air, are highly ionising, and can be stopped by a sheet of paper.
α 衰变：重核射出一个氦‑4 核（42He）。母核失去 2 个质子和 2 个中子，因此 A 减少 4，Z 减少 2。α 粒子在空气中的射程短，电离能力强，可被一张纸阻挡。
Beta‑minus (β⁻) decay: a neutron transforms into a proton, emitting an electron and an antineutrino: n → p + e⁻ + ν̅e. The symbol is 0−1e. The daughter nucleus has Z increased by 1 and A unchanged. β⁻ particles are moderately ionising and can be stopped by a few mm of aluminium.
β⁻ 衰变：一个中子转变为质子，放出一个电子和一个反中微子：n → p + e⁻ + ν̅e。符号为 0−1e。子核的 Z 增加 1，A 不变。β⁻ 粒子电离能力中等，可被几毫米铝板阻挡。
Gamma (γ) decay: an excited nucleus drops to a lower energy state by emitting a high‑energy photon. No change in A or Z occurs. Gamma rays are weakly ionising but highly penetrating; thick lead or concrete is needed to absorb them.
γ 衰变：激发态原子核跃迁到较低能态并发射高能光子。A 和 Z 均不改变。γ 射线电离能力弱但穿透力极强，需要用厚铅板或混凝土来吸收。
| Property | Alpha (α) | Beta‑minus (β⁻) | Gamma (γ) |
|---|---|---|---|
| Nature | 42He nucleus | Fast electron | EM photon |
| Ionising power | Very high | Medium | Low |
| Penetration | Paper | ~3 mm Al | Several cm Pb |
4. The Radioactive Decay Law & Half‑Life | 放射性衰变定律与半衰期
Radioactive decay is a random, spontaneous process. For a large number of identical nuclei, the activity A (decays per second) follows an exponential law: A = λN, where N is the number of undecayed nuclei and λ is the decay constant. The decay constant is the probability per unit time that a given nucleus will decay.
放射性衰变是一种随机、自发的过程。对于大量相同的原子核，活度 A（每秒衰变次数）遵循指数规律：A = λN，其中 N 为尚未衰变的原子核数，λ 为衰变常数。衰变常数是单位时间内一个原子核发生衰变的概率。
The number of undecayed nuclei decreases with time t: N = N₀ e−λt. Activity decays similarly: A = A₀ e−λt. Half‑life T½ is the time taken for half the nuclei to decay, and it is related to the decay constant by T½ = ln 2 / λ.
未衰变原子核数目随时间 t 变化：N = N₀ e−λt。活度的衰减规律类似：A = A₀ e−λt。半衰期 T½ 是半数原子核发生衰变所需的时间，它与衰变常数的关系为 T½ = ln 2 / λ。
The becquerel (Bq) is the SI unit of activity: 1 Bq = 1 decay per second. Exam questions often require using the exponential equations or determining half‑life from graphs of N versus t or A versus t.
贝克勒尔（Bq）是活度的 SI 单位：1 Bq = 1 次衰变/秒。考题常要求运用指数方程，或从 N‑t 图或 A‑t 图中确定半衰期。
5. Nuclear Reactions & Conservation Laws | 核反应与守恒定律
Nuclear reactions include radioactive decays, fission, fusion, and artificial transmutations. All nuclear reactions obey strict conservation laws: total nucleon number, total charge (proton number), energy, and momentum must all be conserved. Mass‑energy is conserved in the relativistic sense (Section 6).
核反应包括放射性衰变、裂变、聚变和人工嬗变。所有核反应都遵循严格的守恒定律：总核子数、总电荷（质子数）、能量和动量都必须守恒。在相对论意义上质能也守恒（见第 6 节）。
When writing a nuclear reaction equation, ensure the sum of A values on both sides is equal, and the sum of Z values is equal. For example, in the α‑decay of uranium‑238: 23892U → 23490Th + 42He. Check: 238 = 234 + 4 and 92 = 90 + 2.
书写核反应方程时，必须确保两侧的 A 值之和相等，Z 值之和相等。例如铀‑238 的 α 衰变：23892U → 23490Th + 42He。验证：238 = 234 + 4，92 = 90 + 2。
The Q‑value of a reaction is the net energy released. It equals the difference between the total rest mass of reactants and products multiplied by c². A positive Q means the reaction is exothermic (releasing energy); a negative Q means it is endothermic.
反应的 Q 值就是净释放的能量。它等于反应物总静止质量与生成物总静止质量之差乘以 c²。Q 值为正表示放热反应（释放能量）；Q 为负表示吸热反应。
6. Mass Defect & 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 constituent protons and neutrons. This difference Δm is called the mass defect. According to Einstein’s mass‑energy equivalence, the energy equivalent of the mass defect is the binding energy EB of the nucleus: EB = Δm c².
原子核的质量总是小于其组成质子和中子的质量之和。这个差值 Δm 叫做质量亏损。根据爱因斯坦的质能方程，与质量亏损对应的能量就是原子核的结合能 EB：EB = Δm c²。
Binding energy per nucleon = EB / A. This is a key measure of nuclear stability. A graph of binding energy per nucleon against mass number A rises steeply to a broad maximum around iron‑56 (≈8.8 MeV/nucleon) and then slowly decreases for heavier nuclei. This curve explains why energy can be released in both fission (heavy nuclei splitting) and fusion (light nuclei merging).
比结合能 = EB / A。这是衡量核稳定性的关键指标。比结合能随质量数 A 变化的曲线先是急剧上升到铁‑56 附近（≈8.8 MeV/核子）的一个宽峰，然后对于更重的核缓慢下降。这条曲线解释了为什么裂变（重核分裂）和聚变（轻核合并）都能释放能量。
In calculations, rest masses are often given in atomic mass units u; 1 u = 931.5 MeV/c². Use this conversion to find binding energy in MeV.
在计算中，静止质量通常以原子质量单位 u 给出；1 u = 931.5 MeV/c²。利用这个换算即可求出以 MeV 为单位的结合能。
7. Fission, Fusion & Energy Production | 裂变、聚变与能量生产
Nuclear fission occurs when a heavy nucleus (e.g. 23592U) absorbs a slow (thermal) neutron, becomes unstable, and splits into two lighter daughter nuclei plus several neutrons and a large amount of energy. A typical fission reaction is: 23592U + 10n → 14156Ba + 9236Kr + 3 10n.
核裂变是指重核（如 23592U）吸收一个慢（热）中子后变得不稳定，分裂成两个较轻的子核，同时放出几个中子和大量能量。一个典型的裂变反应是：23592U + 10n → 14156Ba + 9236Kr + 3 10n。
The released neutrons can induce further fissions, leading to a chain reaction. In a nuclear reactor, control rods (e.g. boron or cadmium) absorb excess neutrons to keep the chain reaction steady. The moderator (e.g. water, graphite) slows neutrons down to thermal speeds, increasing the probability of further fission.
释放出的中子可以引发更多的裂变，形成链式反应。在核反应堆中，控制棒（如硼或镉）吸收多余中子，使链式反应保持平稳。慢化剂（如水、石墨）将中子减速至热速度，从而提高继续引发裂变的概率。
Nuclear fusion is the joining of two light nuclei to form a heavier nucleus, releasing energy because the products have a higher binding energy per nucleon. The Sun fuses hydrogen into helium via the proton‑proton chain. Achieving controlled fusion on Earth requires extremely high temperatures (≈10⁸ K) to overcome Coulomb repulsion, a condition found in tokamaks and stellarators.
核聚变是两个轻核结合成一个较重的核，由于产物具有更高的比结合能，因而释放能量。太阳通过质子‑质子链将氢聚变成氦。在地球上实现可控聚变需要极高的温度（≈10⁸ K）来克服库仑斥力，这种条件存在于托卡马克和仿星器装置中。
8. Background Radiation & Detection | 背景辐射与探测
We are constantly exposed to natural background radiation from cosmic rays, terrestrial rocks (e.g. uranium, thorium), radon gas, and even our own bodies. The level of background radiation must be subtracted from experimental measurements when determining the activity of a sample.
我们持续暴露在自然背景辐射中，它来自宇宙射线、地球岩石（如铀、钍）、氡气，甚至我们自身的身体。在测定样品活度时，必须从实验测量结果中扣除背景辐射的水平。
Common detectors include the Geiger‑Müller (GM) tube, which produces an electrical pulse each time ionising radiation enters the tube. The GM tube can register alpha, beta, and gamma radiation with different efficiencies. Cloud chambers and spark counters can also reveal particle tracks.
常见的探测器包括盖革‑米勒（GM）计数管，每当电离辐射进入管内就产生一个电脉冲。GM 管可以记录 α、β 和 γ 辐射，但探测效率不同。云室和火花计数器也能展示粒子的径迹。
Scintillation counters and semiconductor detectors offer energy resolution, but for syllabus purposes the GM tube and its use with a ratemeter or scaler is the primary focus. Students should be able to design experiments for half‑life determination, absorption studies, and inverse‑square law verification.
闪烁计数器和半导体探测器能提供能量分辨，但就课程大纲而言，重点在于 GM 计数管以及它与速率计或定标器的配合使用。学生应能设计测定半衰期、吸收研究和验证平方反比定律的实验。
9. Biological Effects & Uses of Radioisotopes | 生物效应与放射性同位素的应用
Ionising radiation can damage living tissue by breaking molecular bonds and creating free radicals. High doses cause radiation sickness, increase cancer risk, or induce genetic mutations. Precautions include minimising exposure time, maximising distance, and using shielding.
电离辐射能破坏分子键并产生自由基，从而损害活体组织。高剂量会引起辐射病、增加癌症风险或诱发基因突变。防护措施包括尽量缩短照射时间、增大距离以及使用屏蔽。
Radioisotopes have widespread applications. In medicine, technetium‑99m (gamma emitter, T½ ≈ 6 h) is used as a tracer in imaging; iodine‑131 (beta emitter) treats thyroid disorders. In industry, americium‑241 (alpha emitter) is used in smoke detectors, and cobalt‑60 (gamma emitter) is employed for sterilisation and radiotherapy.
放射性同位素有广泛的应用。在医学上，锝‑99m（γ 放射源，T½ ≈ 6 h）被用作成像示踪剂；碘‑131（β 放射源）用于治疗甲状腺疾病。在工业上，镅‑241（α 放射源）用于烟雾探测器，钴‑60（γ 放射源）用于灭菌和放疗。
Carbon‑14 dating determines the age of archaeological specimens up to about 50 000 years by measuring the ratio of 14C to 12C. Uranium‑lead dating is used for much older rocks. Each technique relies on the known half‑life and the predictable decay of parent nuclei.
碳‑14 定年法通过测量 14C 与 12C 的比值来确定考古样品的年代，可测范围约为 5 万年。铀‑铅定年法则用于更古老的岩石。每种技术都依赖于已知的半衰期和母核可预测的衰变规律。
10. The Standard Model & Fundamental Particles (IB Extension) | 标准模型与基本粒子（IB 扩展内容）
The Standard Model classifies all known elementary particles. Hadrons (e.g. protons, neutrons) are composed of quarks, while leptons (e.g. electrons, neutrinos) are fundamental. Beta decay is understood at the quark level: a down quark changes into an up quark, emitting a W⁻ boson that subsequently decays into an electron and an antineutrino.
标准模型对所有已知的基本粒子进行了分类。强子（如质子、中子）由夸克组成，而轻子（如电子、中微子）是基本粒子。β 衰变在夸克层面上可理解为：一个下夸克变为上夸克，放出一个 W⁻ 玻色子，该玻色子随后衰变为一个电子和一个反中微子。
The four fundamental forces are gravity, electromagnetism, the strong force, and the weak force. The weak force is responsible for beta decay and neutrino interactions. Gauge bosons mediate these forces: photons for EM, W⁺/W⁻/Z⁰ for weak, gluons for strong.
四种基本相互作用是引力、电磁力、强力和弱力。弱力导致了 β 衰变和中微子相互作用。规范玻色子传递这些力：光子传递电磁力，W⁺/W⁻/Z⁰ 传递弱力，胶子传递强力。
Students should also recognise antimatter: every particle has an antiparticle with the same mass but opposite charge and quantum numbers. For instance, the positron is the antiparticle of the electron, and pair production and annihilation illustrate mass‑energy conversion.
学生还应了解反物质：每种粒子都有对应的反粒子，它具有相同的质量，但电荷和其他量子数相反。例如正电子是电子的反粒子，电子对产生和湮灭就是质能转换的实例。
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