📚 AS Physics: Nuclear Physics Key Points | AS 物理：核物理 考点精讲
Nuclear physics is a core topic in AS Physics that explores the structure of the atom, the forces holding the nucleus together, and the processes by which unstable nuclei transform. A solid understanding of atomic notation, the properties of alpha, beta, and gamma radiation, half‑life calculations, and mass–energy equivalence is essential for both examinations and practical applications. This guide walks you through every key concept, from the strong nuclear force to binding energy, with clear bilingual explanations and worked examples.
核物理是 AS 物理的核心主题，探讨原子结构、维系原子核的力以及不稳定核衰变的过程。牢固掌握核素符号、α、β、γ 辐射的性质、半衰期计算以及质能等价等重要考点，对考试和实际应用都至关重要。本篇精讲以清晰的中英双语逐一梳理强核力、结合能等每一个关键概念，并配有实例说明。
1. Atomic Structure and the Nucleus | 原子结构与原子核
Every atom consists of a tiny, dense nucleus surrounded by electrons in energy levels. The nucleus contains positively charged protons and neutral neutrons, collectively called nucleons. Almost all the mass of the atom is concentrated in the nucleus, yet its volume is extremely small compared with the overall size of the atom.
每个原子都由一个微小致密的原子核和绕核分层排布的电子组成。原子核含有带正电的质子和不带电的中子，统称为核子。原子的几乎全部质量都集中在原子核中，但原子核的体积相对于整个原子却极小。
The atomic number Z is the number of protons in the nucleus, which determines the element. The mass number A is the total number of protons plus neutrons. In a neutral atom, the number of electrons equals Z, balancing the positive nuclear charge.
原子序数 Z 是原子核中的质子数，决定了元素的种类。质量数 A 是质子数与中子数之和。在中性原子中，电子数等于 Z，与原子核的正电荷平衡。
2. Nuclear Notation and Isotopes | 核素符号与同位素
A nuclide is represented by the notation ⁴₂X, where X is the chemical symbol, A is the mass number and Z is the atomic number. For example, the most common isotope of carbon is written as ¹²₆C. The number of neutrons N can be found from N = A – Z.
核素用符号 ⁴₂X 表示，其中 X 是元素符号，A 是质量数，Z 是原子序数。例如最常见的碳同位素写作 ¹²₆C。中子数 N 可由 N = A – Z 得出。
Isotopes are atoms of the same element (same Z) that have different numbers of neutrons, and therefore different mass numbers A. They exhibit identical chemical properties because the electron arrangement is unchanged, but their nuclear stability can vary significantly.
同位素是同一元素（Z 相同）而中子数不同、因而质量数 A 不同的原子。它们因电子排布相同而具有完全相同的化学性质，但核稳定性可能存在很大差异。
3. The Strong Nuclear Force | 强核力
The nucleus contains protons that repel each other through the electrostatic force. To hold the nucleus together, a powerful attractive force called the strong nuclear force acts between all nucleons (protons and neutrons). This force is very strong at extremely short ranges (about 1–3 fm), but drops to zero beyond a few femtometres.
原子核内的质子通过静电力相互排斥。为了将原子核维系在一起，所有核子（质子和中子）之间存在着一种强大的吸引力，称为强核力。这种力在极短距离（约 1–3 fm）内非常强，但超过几飞米便迅速降为零。
The strong nuclear force is charge‑independent, meaning it acts equally between proton–proton, neutron–neutron and proton–neutron pairs. It overcomes the electrostatic repulsion between protons at typical nuclear separations, but at very small distances it becomes repulsive, preventing the nucleons from collapsing into each other.
强核力与电荷无关，即它在质子‑质子、中子‑中子和质子‑中子之间作用相同。在典型的核间距下，它能克服质子间的静电排斥；但在极近距离下它变为排斥力，从而阻止核子互相坍缩。
4. Radioactive Decay | 放射性衰变
Some nuclei are unstable because they have an imbalance of protons and neutrons, or simply contain too many nucleons. Such nuclei undergo radioactive decay – a spontaneous and random process in which they emit radiation to become more stable. The decay rate is unaffected by temperature, pressure or chemical environment.
某些原子核因质子与中子比例失衡或核子总数过多而不稳定。这类原子核会发生放射性衰变——一种自发的、随机的过程，通过释放辐射变得更稳定。衰变速率不受温度、压力或化学环境影响。
Radioactive decay is a truly random process: it is impossible to predict when a particular nucleus will decay. However, for a large number of nuclei, the overall decay rate follows a predictable statistical pattern characterised by the decay constant λ and half‑life T₁/₂.
放射性衰变是真正随机的过程：无法预言某个特定核何时衰变。但对大量核子而言，整体衰变速率符合可预测的统计规律，由衰变常量 λ 和半衰期 T₁/₂ 表征。
5. Alpha (α) Particles | α 粒子
An alpha particle is identical to a helium nucleus, consisting of two protons and two neutrons, with a charge of +2e. It is emitted by very heavy nuclei such as uranium‑238 and radium‑226. The general alpha decay equation is:
α 粒子等同于一个氦原子核，由两个质子和两个中子组成，带 +2e 电荷。它由铀‑238、镭‑226 等非常重的核发射。一般 α 衰变方程为：
ᴬ₂X → ᴬ⁻⁴₂₋₂Y + ⁴₂He
Alpha particles have a very high ionising power because their large mass and double charge enable them to pull electrons from many atoms along a short track. However, they have low penetrating power – they can be stopped by a sheet of paper or a few centimetres of air.
α 粒子具有极高的电离能力，因其质量大且带双倍电荷，能在短距离内从大量原子中击出电子。但它们贯穿本领很弱，一张纸或几厘米厚的空气即可阻挡。
Because of their low penetration, alpha sources are particularly hazardous if ingested or inhaled, as they can cause intense localised ionisation inside living tissue.
由于穿透力弱，如果 α 源被摄入或吸入体内，会在活组织内引起极强的局部电离，危害极大。
6. Beta (β) Particles and Gamma (γ) Rays | β 粒子与 γ 射线
Beta decay comes in two forms: β⁻ and β⁺. In β⁻ decay, a neutron in the nucleus transforms into a proton, emitting an electron (β⁻ particle) and an antineutrino. In β⁺ decay, a proton converts into a neutron, emitting a positron and a neutrino.
β 衰变有两种形式：β⁻ 和 β⁺。在 β⁻ 衰变中，核内一个中子转变为质子，放出一个电子（β⁻ 粒子）和一个反中微子。在 β⁺ 衰变中，一个质子转变为中子，放出一个正电子和一个中微子。
Beta particles are much less ionising than alpha particles but can penetrate further: a few millimetres of aluminium will stop most β⁻ particles. Their deflected paths in electric and magnetic fields are opposite to alpha particles because of their negative charge.
β 粒子的电离能力远弱于 α 粒子，但穿透性更强：几毫米厚的铝板就能阻挡绝大多数 β⁻ 粒子。由于带负电，它们在电场和磁场中的偏转方向与 α 粒子相反。
Gamma rays are electromagnetic waves of very high frequency and energy, emitted when a nucleus moves from an excited state to a lower energy state. Gamma emission often accompanies alpha or beta decay. Gamma rays have extremely high penetrating power – thick lead or concrete is required to reduce their intensity significantly – but they have low ionising ability.
γ 射线是原子核从激发态跃迁到较低能态时发射的极高频率、高能量电磁波。γ 辐射常伴随 α 或 β 衰变发生。γ 射线贯穿力极强，需要厚铅板或混凝土才能显著减弱其强度，但电离能力较低。
A common example of gamma emission is cobalt‑60, which emits beta particles followed by two gamma photons of energies 1.17 MeV and 1.33 MeV as the daughter nucleus de‑excites.
一个常见的 γ 辐射例子是钴‑60：它先发射 β 粒子，随后子核退激释放出能量为 1.17 MeV 和 1.33 MeV 的两个 γ 光子。
7. Decay Equations and Conservation Laws | 衰变方程与守恒定律
In all nuclear processes, certain quantities are conserved: nucleon number A, proton number Z (hence charge), mass–energy, and momentum. Balancing decay equations means ensuring that the total A and total Z are the same on both sides. For β⁻ decay, the electron emitted has Z = –1, A = 0; the antineutrino has zero mass and zero charge.
所有核过程中，某些量是守恒的：核子数 A、质子数 Z（即电荷）、质‑能量和动量。配平衰变方程意味着确保两边总 A 和总 Z 相等。对于 β⁻ 衰变，释放的电子具有 Z = –1, A = 0；反中微子质量和电荷均为零。
Example of β⁻ decay: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̅ₑ. Here the mass number stays 14, while the atomic number increases by 1. The energy released in the decay is shared between the beta particle and the antineutrino.
β⁻ 衰变实例：¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̅ₑ。质量数保持为 14，原子序数增加 1。衰变释放的能量由 β 粒子和反中微子共享。
For alpha decay, the daughter nucleus has its mass number reduced by 4 and atomic number reduced by 2. Kinetic energy of the alpha particle and the recoiling daughter nucleus are in inverse proportion to their masses to conserve momentum.
α 衰变中，子核的质量数减少 4，原子序数减少 2。为满足动量守恒，α 粒子和反冲子核的动能与其质量成反比。
8. Half‑Life | 半衰期
The half‑life T₁/₂ of a radioactive isotope is the average time taken for half the nuclei in a given sample to decay, or equivalently for the activity of the sample to fall to half its initial value. Half‑life is a constant property of the isotope and ranges from fractions of a second to billions of years.
放射性同位素的半衰期 T₁/₂ 是指给定样品中一半原子核发生衰变——或等效地，样品的活度降为初始值一半——所需的平均时间。半衰期是同位素的不变性质，从不到一秒到数十亿年不等。
The decay law can be expressed as N = N₀ e⁻λt or as A = A₀ e⁻λt, where λ is the decay constant. The relationship λ T₁/₂ = ln 2 ≈ 0.693 links λ and the half‑life. Students are often asked to determine the half‑life from a graph of activity versus time or from a table of count rate data.
衰变规律可表示为 N = N₀ e⁻λt 或 A = A₀ e⁻λt，其中 λ 为衰变常量。关系式 λ T₁/₂ = ln 2 ≈ 0.693 将 λ 与半衰期联系起来。考题常要求学生从活度‑时间图或计数率数据表中求出半衰期。
For example, if a sample initially has an activity of 800 Bq and after 6 hours it drops to 100 Bq, the number of half‑lives that have passed is 3 (800 → 400 → 200 → 100), so T₁/₂ = 6 h ÷ 3 = 2 h.
例如，某样品初始活度为 800 Bq，6 小时后降至 100 Bq，则已经过 3 个半衰期（800 → 400 → 200 → 100），因此 T₁/₂ = 6 h ÷ 3 = 2 h。
9. Mass Defect and Binding Energy (E = mc²) | 质量亏损与结合能 (E = mc²)
The mass of a nucleus is always slightly less than the sum of the masses of its individual protons and neutrons. This difference is called the mass defect Δm. Einstein’s equation E = mc² tells us that the mass defect corresponds to the binding energy Eb that holds the nucleus together.
原子核的质量总是略小于其各个自由质子与中子质量之和。这一差值称为质量亏损 Δm。爱因斯坦方程 E = mc² 告诉我们，质量亏损对应于将核子结合在一起的结合能 Eb。
Binding energy is defined as the energy required to separate a nucleus into its individual nucleons. The average binding energy per nucleon is a measure of nuclear stability: it peaks around iron‑56, making iron one of the most stable elements.
结合能被定义为将一个原子核拆散为单个核子所需的能量。每个核子的平均结合能是核稳定性的量度：它在铁‑56 附近达到最大值，使得铁成为最稳定的元素之一。
In nuclear reactions, the energy released can be calculated from the change in total mass of the system: Q = Δm c². For example, in an alpha decay, the kinetic energy of the products equals the decrease in total rest mass. This explains why nuclear processes can release millions of times more energy than chemical reactions.
核反应释放的能量可以通过系统总质量的变化计算：Q = Δm c²。例如在 α 衰变中，产物的动能等于总静止质量的减少。这解释了为什么核过程释放的能量可比化学反应高出百万倍。
10. Background Radiation and Practical Applications | 背景辐射与实际应用
Background radiation is always present, originating from cosmic rays, naturally occurring radioactive minerals in rocks and soil, radon gas, and even from building materials and food. The average effective dose is about 2–3 mSv per year, but it varies with location.
背景辐射无处不在，来源包括宇宙射线、岩石和土壤中天然存在的放射性矿物、氡气，甚至建筑材料和食物。人均年有效剂量约为 2–3 mSv，但因地而异。
When measuring the count rate from a radioactive source in the laboratory, the background count must be subtracted to obtain the corrected count rate. A Geiger–Müller tube connected to a counter is commonly used for such measurements.
在实验室测量放射性源的计数率时，必须扣除背景计数才能得到修正计数率。盖革‑弥勒计数管连接计数器是常用的测量设备。
Radioisotopes have numerous practical applications: americium‑241 is used in smoke detectors as an alpha source; carbon‑14 dating determines the age of archaeological specimens; iodine‑131 serves in medical treatment of thyroid conditions; and technetium‑99m is used as a gamma tracer in diagnostic imaging.
放射性同位素有众多实际应用：镅‑241 用作烟雾探测器的 α 源；碳‑14 定年用于测定考古样品的年代；碘‑131 用于治疗甲状腺疾病；锝‑99m 则用作诊断成像中的 γ 示踪剂。
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