📚 Nuclear Physics for IB and OCR | IB OCR 核物理考点精讲
Nuclear physics is a cornerstone of both the IB Diploma and OCR A-Level Physics syllabi, offering a deep dive into the structure of the atomic nucleus, the forces that hold it together, and the energetic processes that can tear it apart. From the properties of alpha, beta and gamma radiation to the principles of nuclear fission and fusion, this topic blends theoretical insight with real-world applications such as power generation, medical imaging and carbon dating. Mastering these concepts demands a clear grasp of mass–energy equivalence, binding energy per nucleon, radioactive decay laws and the conservation rules governing nuclear reactions. This revision guide walks you through every key idea, pairing clear explanations in English with their precise Chinese counterparts, and is designed to help you tackle multiple‑choice, structured and data‑analysis questions with confidence.
核物理是 IB 文凭课程和 OCR A-Level 物理大纲的核心内容之一，深入探讨了原子核的结构、将其束缚在一起的力以及能够使其分裂的能量过程。从 α、β 和 γ 辐射的性质到核裂变与核聚变原理，这一主题将理论洞察与发电、医学成像和碳定年等实际应用融为一体。要掌握这些概念，必须清晰理解质能等价、每核子结合能、放射性衰变定律以及支配核反应的守恒规则。本复习指南带你逐一梳理所有关键知识点，英文与中文讲解精准对应，旨在帮助你自信应对选择题、结构化题目和数据分析题。
1. Structure of the Nucleus | 原子核的结构
The nucleus consists of protons and neutrons, collectively called nucleons. The number of protons Z is the atomic number, which defines the chemical element. The total number of nucleons A = Z + N (where N is the neutron number) is the mass number. A nuclide is denoted as ᴬ ZX, for example ²³⁸ ₉₂U represents uranium‑238 with 92 protons and 146 neutrons. Isotopes are nuclei with the same Z but different N, meaning they have identical chemical properties but differing nuclear stabilities. The radius of a nucleus is approximately R = r₀A^(1/3), with r₀ ≈ 1.2 × 10⁻¹⁵ m, indicating that nuclear volume is proportional to the mass number.
原子核由质子和中子（统称核子）组成。质子数 Z 即原子序数，决定了化学元素的种类。核子的总数 A = Z + N（N 为中子数）为质量数。核素用符号 ᴬ ZX 表示，例如 ²³⁸ ₉₂U 代表铀‑238，含有 92 个质子和 146 个中子。同位素是指 Z 相同但 N 不同的核素，它们化学性质相同，但核稳定性各异。原子核的半径近似为 R = r₀A^(1/3)，其中 r₀ ≈ 1.2 × 10⁻¹⁵ m，这表明核体积与质量数成正比。
2. Nuclear Forces and Binding Energy | 核力与结合能
The strong nuclear force binds nucleons together, acting over very short ranges (~10⁻¹⁵ m). It is attractive at nucleon separations of about 1–3 fm and repulsive at even shorter distances, preventing collapse. The mass of a nucleus is always less than the sum of the masses of its individual nucleons; this mass defect Δm corresponds to the binding energy via E = Δmc². The binding energy per nucleon is obtained by dividing the total binding energy by A. A graph of binding energy per nucleon against mass number peaks around iron‑56, meaning that energy can be released both by fusing light nuclei (fusion) and by splitting heavy nuclei (fission).
强核力将核子束缚在一起，其作用范围极短（约 10⁻¹⁵ m）。在核子间距约为 1–3 fm 时表现为吸引力，在更短距离上表现为排斥力，从而防止核坍缩。原子核的质量总是小于其各个核子质量之和；这一质量亏损 Δm 通过 E = Δmc² 与结合能对应。将总结合能除以 A 即可得到每核子结合能。每核子结合能随质量数变化的曲线在铁‑56 附近达到峰值，这意味着无论是轻核的融合（聚变）还是重核的分裂（裂变）都能释放能量。
3. Types of Radioactive Decay | 放射性衰变类型
Unstable nuclei spontaneously transform into more stable configurations through radioactive decay. Alpha (α) decay involves the emission of a helium‑4 nucleus (⁴₂He), reducing A by 4 and Z by 2. Beta‑minus (β⁻) decay occurs when a neutron converts into a proton, emitting an electron and an antineutrino: n → p + e⁻ + ν̄ₑ. This increases Z by 1 while A remains unchanged. Beta‑plus (β⁺) decay occurs when a proton converts into a neutron, emitting a positron and a neutrino: p → n + e⁺ + νₑ. Gamma (γ) emission is the release of high‑energy photons from an excited nucleus, leaving A and Z unchanged. Each decay mode is governed by conservation of charge, nucleon number, energy and momentum.
不稳定核素通过放射性衰变自发转变为更稳定的结构。α 衰变释放一个氦‑4 核（⁴₂He），使 A 减少 4、Z 减少 2。β⁻ 衰变中，一个中子转变为一个质子，释放一个电子和一个反中微子：n → p + e⁻ + ν̄ₑ，Z 增加 1，A 不变。β⁺ 衰变是一个质子转变为中子，释放一个正电子和一个中微子：p → n + e⁺ + νₑ。γ 辐射是激发态原子核释放高能光子，A 和 Z 均保持不变。所有衰变模式都必须遵守电荷、核子数、能量和动量守恒。
4. Decay Law and Half‑life | 衰变规律与半衰期
Radioactive decay is a random and spontaneous process. The number of undecayed nuclei N at time t obeys the exponential law N = N₀e^(−λt), where λ is the decay constant. The activity A = λN, measured in becquerels (Bq), where 1 Bq equals one decay per second. The half‑life T₁/₂ is the time taken for half the nuclei in a sample to decay, related to λ by T₁/₂ = ln 2 / λ. On an N–t graph, the half‑life is constant regardless of starting point. Practical determinations of half‑life often involve background subtraction and logarithmic plots to find λ from the gradient of ln A vs t.
放射性衰变是一种随机且自发的过程。未衰变核数 N 随时间 t 遵从指数规律 N = N₀e^(−λt)，其中 λ 是衰变常量。活度 A = λN，单位是贝克勒尔（Bq），1 Bq 表示每秒一次衰变。半衰期 T₁/₂ 是样品中一半核发生衰变所需的时间，与 λ 的关系为 T₁/₂ = ln 2 / λ。在 N–t 图上，无论从何处开始计时，半衰期都是恒定的。实验测定半衰期常需要扣除本底，并利用 ln A–t 图的斜率来求 λ。
5. Nuclear Reactions and Q‑value | 核反应与 Q 值
A nuclear reaction is written as a + X → Y + b, where a is the projectile and X the target nucleus. Reactions must conserve total charge, total nucleon number, energy and momentum. The reaction energy Q is the difference between the total rest masses of the reactants and products multiplied by c²: Q = (mᵢₙᵢₜᵢₐₗ − m_final)c². If Q is positive, the reaction is exothermic and releases kinetic energy; if negative, the reaction is endothermic and requires a threshold kinetic energy of the incident particle. Common examples include (α, p) and (n, γ) reactions.
核反应通常写作 a + X → Y + b，其中 a 是入射粒子，X 是靶核。反应必须遵守总电荷、总核子数、能量和动量守恒。反应能 Q 是反应物与生成物的总静止质量之差再乘以 c²：Q = (m_initial − m_final)c²。若 Q 为正，反应放热并释放动能；若 Q 为负，反应吸热，要求入射粒子具有阈动能。常见的核反应有 (α, p) 反应和 (n, γ) 反应等。
6. Mass–Energy Equivalence | 质能等价
Einstein’s relation E = mc² is the bedrock of nuclear energy calculations. It states that mass and energy are interchangeable: a system’s rest energy is its rest mass multiplied by the square of the speed of light in vacuum. In nuclear processes, the tiny mass defect is multiplied by a huge factor (9 × 10¹⁶ J/kg) to produce significant energy changes. The standard atomic mass unit u is defined as 1/12 the mass of a carbon‑12 atom, so 1 u = 1.661 × 10⁻²⁷ kg, and its energy equivalent is 931.5 MeV. This conversion factor is essential when computing binding energies and Q‑values from tabulated nuclear masses.
爱因斯坦关系式 E = mc² 是核能计算的基础。它表明质量与能量可以相互转化：一个系统的静能等于其静止质量乘以真空光速的平方。在核过程中，微小的质量亏损乘以巨大的因子（9 × 10¹⁶ J/kg）就能产生显著的能量变化。标准原子质量单位 u 定义为碳‑12 原子质量的 1/12，因此 1 u = 1.661 × 10⁻²⁷ kg，其能量当量为 931.5 MeV。当从核质量表计算结合能和 Q 值时，这一换算因子至关重要。
7. Nuclear Fission | 核裂变
Fission is the splitting of a heavy nucleus, such as uranium‑235, into two lighter fragment nuclei, accompanied by the release of several neutrons and a large amount of energy. A typical reaction is n + ²³⁵₉₂U → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3n + energy. The released neutrons can induce further fissions, creating a chain reaction. The critical mass is the minimum mass of fissile material needed for a self‑sustaining chain reaction. Control rods (often containing boron or cadmium) absorb excess neutrons, while a moderator (such as water or graphite) slows down neutrons to thermal energies where they are more likely to cause fission in ²³⁵U. In an A‑level or IB exam, you may be asked to balance fission equations or explain the role of each component in a nuclear reactor.
裂变是重核（如铀‑235）分裂成两个较轻的碎片核，同时释放几个中子和大量能量的过程。一个典型反应是 n + ²³⁵₉₂U → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3n + 能量。释放的中子可以引起进一步的裂变，从而形成链式反应。临界质量是维持自持链式反应的裂变材料所需的最小质量。控制棒（通常含硼或镉）吸收多余中子，而慢化剂（如水或石墨）则将中子减速至热中子能量，使其更易引起 ²³⁵U 裂变。在 A‑level 或 IB 考试中，你可能需要配平裂变方程，或解释核反应堆各部件的作用。
8. Nuclear Fusion | 核聚变
Fusion is the joining of two light nuclei to form a heavier nucleus, again releasing energy because the binding energy per nucleon increases. The Sun’s energy comes from the proton–proton chain, which effectively converts four protons into a helium‑4 nucleus plus two positrons, two neutrinos and energy. For fusion to occur, nuclei must overcome the Coulomb repulsion between them, requiring extremely high temperatures (~10⁷–10⁸ K) to give them sufficient kinetic energy. This is called thermonuclear fusion. On Earth, magnetic confinement (tokamak) and inertial confinement are being explored as routes to controlled fusion power. In examination contexts, you should be able to calculate the energy released in simple fusion reactions, such as ²H + ³H → ⁴He + n, using the mass defect method.
聚变是两个轻核结合形成一个较重核的过程，同样因为每核子结合能增大而释放能量。太阳的能量源于质子‑质子链，它实际上将四个质子转变成一个氦‑4 核加上两个正电子、两个中微子和能量。要发生聚变，原子核必须克服彼此间的库仑排斥力，需要极高的温度（约 10⁷–10⁸ K）以提供足够的动能，这被称为热核聚变。在地球上，磁约束（托卡马克）和惯性约束正被探索作为实现可控聚变能的途径。在考试中，你应该能够利用质量亏损方法计算简单聚变反应（如 ²H + ³H → ⁴He + n）所释放的能量。
9. Radiation Detection and Measurement | 辐射的探测与测量
Ionising radiation can be detected by devices that register the ionisation it produces. A Geiger–Müller (GM) tube connected to a counter records each ionising particle that enters the tube as a ‘count’. The cloud chamber and bubble chamber make particle tracks visible through condensation or boiling along the ionisation trail. Solid‑state detectors and scintillation counters are also used for precise energy measurements. When counting, the background count must be measured separately and subtracted from the total count. Detectors are often characterised by their efficiency and resolving time (dead time). In practical activities or exam data analysis, you may need to correct for background radiation or estimate the dead time of a GM tube.
致电离辐射可由记录其产生的电离的装置进行探测。盖革‑米勒（GM）计数管连接计数器，可记录进入管内的每个电离粒子，产生一次“计数”。云室和气泡室通过将电离径迹上的凝结或沸腾显现出来，从而使粒子径迹可见。固态探测器和闪烁计数器也用于精确的能量测量。进行计数时，必须单独测量本底计数并从总计数中扣除。探测器通常用效率和分辨时间（死时间）来表征。在实验活动或考试数据分析中，你可能需要校正本底辐射，或估算 GM 计数管的死时间。
10. Biological Effects and Radiation Dose | 生物效应与辐射剂量
Ionising radiation damages living tissue by breaking chemical bonds and creating reactive ions. The absorbed dose D is the energy absorbed per unit mass of tissue, measured in grays (Gy), where 1 Gy = 1 J/kg. To account for the different biological effects of different radiation types, the absorbed dose is multiplied by a radiation weighting factor w_R to give the equivalent dose H = w_R D, measured in sieverts (Sv). For example, α particles have a much higher w_R (≈20) than β or γ radiation (w_R = 1). Effective dose further accounts for the varying sensitivity of different organs. Understanding these quantities is crucial for evaluating the risks of medical procedures and for setting safety limits in nuclear industries.
致电离辐射通过破坏化学键和产生反应性离子来损害活体组织。吸收剂量 D 是单位质量组织吸收的能量，单位为戈瑞（Gy），1 Gy = 1 J/kg。为了考虑不同类型辐射的不同生物效应，将吸收剂量乘以辐射权重因子 w_R，得出当量剂量 H = w_R D，单位为希沃特（Sv）。例如，α 粒子的 w_R（约 20）远高于 β 或 γ 辐射（w_R = 1）。有效剂量则进一步考虑了不同器官的不同敏感度。理解这些量对于评估医疗程序的风险以及设定核工业的安全限值至关重要。
11. Background Radiation and Half‑life Determinations | 背景辐射与半衰期测定
Background radiation originates from cosmic rays, terrestrial sources (e.g. radon gas), and even the building materials around us. Any measurement of radioactive sources must therefore include a background count, which is subtracted to obtain the corrected count rate. When a set of activity–time data is analysed for half‑life, the background should first be subtracted to ensure the exponential fit accurately reflects the decay constant of the source alone. Long or short half‑lives can be determined from the gradient of ln(corrected count rate) vs time. This technique is directly assessed in IB and OCR practical investigations, where students may use a GM tube and a source such as protactinium‑234 or a simulated radioactive decay.
背景辐射来源于宇宙射线、陆地源（如氡气）甚至我们周围的建筑材料。因此，任何对放射源的测量都必须包含本底计数，再从总计数中扣除以获得校正后的计数率。为了测定半衰期而分析活度‑时间数据时，应先减去本底，以确保指数拟合能准确反映放射源本身的衰变常量。利用 ln(校正后计数率) 对时间的斜率，可以确定长或短的半衰期。这种技术在 IB 和 OCR 的实验探究中直接考查，学生可能会使用 GM 计数管和类似镤‑234 的放射源或模拟的放射性衰变数据。
12. Applications of Nuclear Physics | 核物理的应用
Nuclear techniques pervade modern life. Radioactive tracers, using isotopes such as technetium‑99m (T₁/₂ = 6 hours), allow medical imaging of organs and blood flow. Carbon‑14 dating determines the age of archaeological specimens up to around 50,000 years by measuring the residual ¹⁴C activity. Industrial radiography uses gamma sources to inspect welds and metal castings for defects. In agriculture, radiation induces beneficial mutations in seeds. Nuclear power plants harness the controlled fission of uranium or plutonium to generate electricity without direct CO₂ emissions. Students should be able to discuss the benefits and risks, linking physical principles to societal and environmental contexts.
核技术深入现代生活的各个领域。放射性示踪剂，如使用锝‑99m（T₁/₂ = 6 小时）的同位素，可以实现器官和血流的医学成像。碳‑14 定年法通过测量残留的 ¹⁴C 活度来确定考古标本的年代，上限约 5 万年。工业射线照相术利用 γ 源检查焊缝和金属铸件的缺陷。在农业方面，辐射可诱导种子发生有益突变。核电站利用铀或钚的受控裂变发电，不直接排放 CO₂。学生应当能够讨论其益处与风险，将物理原理与社会和环境背景联系起来。
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