Edexcel A-Level Physics: Nuclear Physics and Radioactivity (Combined 031) | 核物理与放射性（综合031）

📚 Edexcel A-Level Physics: Nuclear Physics and Radioactivity (Combined 031) | 核物理与放射性（综合031）

This comprehensive revision guide covers the essential concepts of nuclear physics and radioactivity from the Edexcel A-Level Physics specification. It brings together the structure of the nucleus, the different types of radioactive decay, nuclear equations, activity and half-life, mass–energy equivalence, binding energy, fission and fusion. Designed as a combined resource, it helps you consolidate theory, practise key calculations and prepare effectively for examination questions.

这本综合复习指南涵盖了 Edexcel A-Level 物理考纲中核物理与放射性的核心概念。它整合了原子核结构、不同放射性衰变类型、核反应方程、活度与半衰期、质能等价、结合能、裂变与聚变等内容。作为一份组合式学习资料，它帮助你巩固理论、练习关键计算，并有针对性地备考。

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1. The Nucleus and Nuclides | 原子核与核素

The nucleus of an atom contains protons and neutrons, collectively called nucleons. The atomic number Z is the number of protons, defining the element. The mass number A is the total number of nucleons. A nuclide is a distinct nuclear species denoted by the symbol ^A_ZX, such as ¹²₆C. Isotopes are nuclides of the same element (same Z) with different neutron numbers.

原子核由质子和中子组成，合称核子。原子序数 Z 是质子数，决定了元素种类。质量数 A 是核子总数。核素用符号 ^A_ZX 表示，例如 ¹²₆C。同位素是同一种元素（Z 相同）但中子数不同的核素。

r very short distances (≈ 1 × 10⁻¹⁵ m). It is attractive at nucleon separations of about 1– ns. Beyond this range it falls rapidly to zero, ensuring the nucleus is compact and stable – as long as the neutron-to-proton ratio lies within the band of stability.

强核力在极短距离（约 1 × 10⁻¹⁵ m）内将核子结合在一起。当核子间距约为 1–3 fm 时该力表现为吸引，能克服质子间的静电斥力。超出此范围力迅速降为零，使原子核保持致密并稳定——只要中子–质子比位于稳定带内。

In Edexcel problems you may be asked to identify the number of neutrons (A – Z) or to explain why certain combinations are unstable. Remember that too many protons lead to increased Coulomb repulsion, while too many neutrons can push the nucleus towards beta decay.

在 Edexcel 试题中，你可能需要计算中子数（A – Z）或解释某些组合为何不稳定。记住质子过多会导致库仑斥力增大，而中子过多可能使原子核趋向 β 衰变。

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2. Radioactive Decay: Alpha, Beta and Gamma | 放射性衰变：α、β 与 γ 衰变

Radioactive decay is a spontaneous process in which an unstable nucleus emits radiation to become more stable. The three main types are alpha (α), beta (β) and gamma (γ) radiation.

放射性衰变是不稳定原子核自发发射辐射、变得更稳定的过程。三种主要类型是 α 辐射、β 辐射和 γ 辐射。

• Alpha decay: the nucleus emits an α-particle, which is a helium nucleus ⁴₂He. The mass number decreases by 4 and the atomic number by 2. Example: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂α.
• Alpha 衰变：核发射一个 α 粒子，即氦核 ⁴₂He。质量数减少 4，原子序数减少 2。例如：²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂α。
• Beta-minus (β⁻) decay: a neutron in the nucleus converts into a proton, emitting an electron (β⁻) and an antineutrino (ν_e). The atomic number increases by 1, mass number stays the same. Example: ¹⁴₆C → ¹⁴₇N + ⁰_-1e + ν_e.
• β⁻ 衰变：核内一个中子转变为质子，放出一个电子（β⁻）和一个反中微子（ν_e）。原子序数增加 1，质量数不变。例如：¹⁴₆C → ¹⁴₇N + ⁰_-1e + ν_e。
• Beta-plus (β⁺) decay: a proton converts into a neutron, emitting a positron (β⁺) and a neutrino (ν_e). Atomic number decreases by 1. Example: ³⁰₁₅P → ³⁰₁₄Si + ⁰₊₁e + ν_e.
• β⁺ 衰变：一个质子转变为中子，放出一个正电子（β⁺）和一个中微子（ν_e）。原子序数减少 1。例如：³⁰₁₅P → ³⁰₁₄Si + ⁰₊₁e + ν_e。
• Gamma decay: an excited nucleus releases energy as a high-energy photon (γ-ray). No change in A or Z; often accompanies alpha or beta decay.
• γ 衰变：激发态原子核以高能光子（γ 射线）形式释放能量。A 和 Z 均不变；常伴随 α 或 β 衰变发生。

Penetrating power increases from α (stopped by paper or a few cm of air) to β (stopped by a few mm of aluminium) to γ (reduced significantly by several cm of lead or very thick concrete). Ionising ability follows the reverse order.

穿透能力由 α（纸张或几厘米空气即可阻挡）到 β（几毫米铝板阻挡）再到 γ（几厘米铅或厚混凝土显著减弱）依次增强。电离能力则相反。

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3. Nuclear Equations and Conservation Laws | 核反应方程与守恒定律

All nuclear processes obey conservation of mass number, atomic number and charge. When writing nuclear equations, the sum of A on the left must equal the sum of A on the right; the same applies for Z. Energy and momentum are also conserved, though we usually concentrate on the particle count.

所有核过程遵循质量数守恒、原子序数守恒和电荷守恒。书写核反应方程时，左边 A 的总和必须等于右边 A 的总和；Z 同理。能量和动量也守恒，但我们通常关注粒子数目。

For decay chains, you may need to identify the product after several successive decays. Work step by step: for each alpha, reduce A by 4 and Z by 2; for each beta-minus, Z increases by 1 with no change in A. Always check that the neutron number (A – Z) makes physical sense.

对于衰变链，你可能需要确定多次连续衰变后的产物。逐步推算：每发生一次 α 衰变，A 减 4、Z 减 2；每发生一次 β⁻ 衰变，Z 加 1、A 不变。始终检查中子数（A – Z）是否合理。

Example: ²³²₉₀Th → ²²⁸₈₈Ra + ⁴₂α

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4. Activity and the Decay Constant | 活度与衰变常量

y s⁻¹. Activity is proportional to the number of undecayed nuclei N present in the sample:

放射性样品的活度 A 是单位时间内的衰变次数，单位为贝克勒尔（Bq），1 Bq = 1 次衰变/秒。活度与样品中尚未衰变的核子数 N 成正比：

A = λN

where λ is the decay constant (s⁻¹), the probability per unit time that a given nucleus will decay. A large λ indicates rapid decay.

其中 λ 为衰变常量（s⁻¹），表示单位时间内某个核发生衰变的概率。λ 大意味着衰变快。

The relation is fundamental: as N decreases exponentially, so does activity. The decay constant is related to the half-life t_½ by λ = ln 2 / t_½. This equation is crucial for calculations linking half-life to measurable decay rates.

此关系是基础：随着 N 呈指数衰减，活度也指数衰减。衰变常量与半衰期 t_½ 关系为 λ = ln 2 / t_½。该方程是将半衰期与可测量的衰变率联系起来的关键。

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5. Half-Life Calculations | 半衰期计算

Half-life is the time taken for the number of radioactive nuclei (or the activity) to fall to half its initial value. It is a constant for a given isotope, unaffected by temperature, pressure or chemical state. Typical half-lives range from microseconds to billions of years.

半衰期是放射性核数目（或活度）降至初始值一半所需的时间。对给定同位素，半衰期是常数，不受温度、压力或化学状态影响。典型的半衰期从微秒到数十亿年不等。

To find the number of nuclei remaining after n half-lives, use:

求经过 n 个半衰期后剩余的核数目，用：

N = N₀ × (½)ⁿ

If you know the total time elapsed t, n = t / t_½. Direct substitution gives N = N₀ × (½)^{t / t_½}.

若已知总时间 t，则 n = t / t_½。代入得 N = N₀ × (½)^{t / t_½}。

For non-integer numbers of half-lives, it is safer to use the exponential form: N = N₀ e^–λt. The Edexcel exam expects you to apply both the fraction method and the exponential equation, particularly when analysing graphs of ln N against t.

当半衰期数不是整数时，最好使用指数形式：N = N₀ e^–λt。Edexcel 考试希望你既能用分数法，也能用指数方程，尤其是在分析 ln N 对 t 的图像时。

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6. Exponential Decay and Graphs | 指数衰减与图像

s: the rate of decay is proportional to N. This gives an exponential decrease: N(t) = N₀ e^–λt. Similarly, activity A = A₀ e^–λt.

放射性衰变遵循一级动力学：衰变速率与 N 成正比。这导致指数下降：N(t) = N₀ e^–λt。同样，活度 A = A₀ e^–λt。

Taking natural logarithms: ln N = ln N₀ – λt. A plot of ln N vs t yields a straight line with gradient – nt and half-life from a set of count-rate measurements corrected for background radiation.

取自然对数：ln N = ln N₀ – λt。以 ln N 对 t 作图得到一条斜率为 –λ、截距为 ln N₀ 的直线。利用从校正背景辐射后的计数率数据中得到的直线，可以实验测定衰变常量和半衰期。

ce. The uncertainty in count rate can be estimated using the square root of the count (σ = √N).

务必从测量值中减去本底计数率，以获得放射源的真实计数率。计数率的不确定度可用计数平方根（σ = √N）来估算。

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7. Mass–Energy Equivalence (E = mc²) | 质能等价（E = mc²）

Einstein's mass– ight in a vacuum (3.00 × 10⁸ m s⁻¹). In nuclear reactions, the total mass of the products is often slightly less than the total mass of the reactants – this mass difference Δm is called the mass defect.

爱因斯坦的质能等价原理指出，质量可以转化为能量，反之亦然，遵循方程 E = mc²，其中 c 为真空中光速（3.00 × 10⁸ m s⁻¹）。在核反应中，产物的总质量往往略小于反应物的总质量——这个质量差 Δm 被称为质量亏损。

its (u) to energy: 1 u = 931.5 MeV/c². This conversion factor is provided in the Edexcel data booklet.

释放的能量称为 Q 值或衰变能，ΔE = Δm c²。计算时记得将原子质量单位（u）转换为能量：1 u = 931.5 MeV/c²。Edexcel 数据手册中会提供这一转换因子。

In beta decay, the maximum kinetic energy of the beta particle is the Q-value minus the energy carried by the (anti)neutrino, leading to a continuous energy spectrum up to an endpoint energy.

在 β 衰变中，β 粒子的最大动能是 Q 值减去（反）中微子带走的能量，因此能谱连续，直到最高能量。

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8. Binding Energy and Binding Energy per Nucleon | 结合能与比结合能

The binding energy of a nucleus is the energy required to separate it completely into its constituent protons and neutrons. It is equal to the mass defect multiplied by c². A nucleus with a larger binding energy is more stable because more energy is needed to pull it apart.

原子核的结合能是将它完全分离成组成它的质子和中子所需的能量，等于质量亏损乘以 c²。结合能越大的核越稳定，因为需要更多能量才能拆散它。

More useful for comparing stability across different nuclei is the binding energy per nucleon, obtained by dividing the total binding energy by the mass number A. Iron-56 (⁵⁶Fe) sits near the peak of the binding energy per nucleon curve (~8.8 MeV per nucleon), making it one of the most stable nuclides.

更具可比性的是比结合能，即总结合能除以质量数 A。铁-56（⁵⁶Fe）位于比结合能曲线的峰值附近（约 8.8 MeV/核子），是最稳定的核素之一。

The shape of the curve explains why energy can be released either by fusing light nuclei (fusion) or by splitting heavy nuclei (fission) – both processes move towards the maximum binding energy per nucleon around iron.

该曲线的形状解释了为何轻核聚变（聚变）或重核裂变（裂变）都能释放能量——两种过程都向着铁附近比结合能的最高点移动。

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9. Nuclear Fission | 核裂变

Nuclear fission is the splitting of a heavy nucleus into two (occasionally more) lighter fragments, accompanied by the release of several neutrons and a large amount of energy. It is most commonly induced by bombarding a fissile nucleus such as ²³⁵₉₂U with thermal (slow) neutrons.

核裂变是一个重核分裂为两个（偶尔多个）较轻碎片的过程，同时释放几个中子和大量能量。最常见的是用热（慢）中子轰击易裂变核如 ²³⁵₉₂U 来引发。

A typical fission equation: ²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3 ¹₀n + energy. The released neutrons can go on to induce further fissions, creating a chain reaction. In a nuclear reactor, control rods (e.g. boron or cadmium) absorb excess neutrons to keep the reaction rate steady.

一个典型的裂变方程：²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3 ¹₀n + 能量。释放的中子可继续引发更多裂变，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，使反应速率保持稳定。

The mass difference between reactants and products accounts for this energy via E = Δm c².

每次裂变释放的能量约 200 MeV，远大于化学反应。反应前后的质量差通过 E = Δm c² 解释了这部分能量。

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10. Nuclear Fusion | 核聚变

Nuclear fusion is the joining of two light nuclei to form a heavier nucleus, releasing energy because the binding energy per nucleon increases. For example, deuterium (²₁H) and tritium (³₁H) fuse to form helium-4 and a neutron:

核聚变是两个轻核结合成一个较重核的过程，由于比结合能增加而释放能量。例如氘（²₁H）和氚（³₁H）聚变生成氦-4 和一个中子：

²₁H + ³₁H → ⁴₂He + ¹₀n + 17.6 MeV

Fusion requires extremely high temperatures (≈ 10⁸ K) to give nuclei enough kinetic energy to overcome Coulomb repulsion – this is called thermonuclear fusion. At such temperatures, matter exists as a plasma. The 'Coulomb barrier' must be tunnelled through or overcome.

聚变需要极高的温度（约 10⁸ K），使原子核拥有足够的动能克服库仑斥力——这称为热核聚变。在此温度下物质呈等离子态。必须穿过或克服“库仑势垒”。

In stars, fusion proceeds through the proton–proton chain or the CNO cycle. Research into controlled fusion on Earth aims to replicate these processes for clean energy, but sustained confinement remains a major challenge.

在恒星中，聚变通过质子–质子链或 CNO 循环进行。地球上的受控聚变研究旨在复制这些过程以获取清洁能源，但持续约束仍是重大挑战。

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11. Practical Applications and Safety | 实际应用与安全

Radioisotopes are widely used in medicine, industry and research. Examples include: technetium-99m (gamma emitter) for medical imaging; iodine-131 (beta/gamma emitter) for thyroid treatment; americium-241 (alpha emitter) in smoke detectors; carbon-14 for archaeological dating; and cobalt-60 for radiotherapy and industrial radiography.

放射性同位素广泛应用于医学、工业和科研。例如：锝-99m（γ 发射体）用于医学成像；碘-131（β/γ 发射体）用于甲状腺治疗；镅-241（α 发射体）用于烟雾探测器；碳-14 用于考古断代；钴-60 用于放疗和工业射线探伤。

Safe handling of radioactive sources involves minimising exposure time, maximising distance (inverse square law applies to gamma) and using shielding appropriate to the radiation type. Always store sources in lead-lined containers and monitor dose using film badges or dosimeters.

安全处理放射源的原则包括尽量缩短暴露时间、增大距离（γ 射线遵循平方反比律）以及使用适合辐射类型的屏蔽。始终将放射源存放在衬铅容器中，并使用胶片徽章或剂量计监测剂量。

Background radiation originates from cosmic rays, terrestrial sources (rocks, radon gas), and human activities. It must be subtracted from all experimental count-rate measurements to obtain the net count from a source.

本底辐射来源于宇宙射线、地球资源（岩石、氡气）以及人类活动。所有实验计数率测定都应扣除本底辐射，以获得放射源的净计数率。

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12. Exam Tips and Key Summary | 考试技巧与要点总结

working when calculating half-life or decay constant. Quote the equations A = λN, N = N₀ e^–λt o units: convert mass to kg when using c in m s⁻¹ for energy in joules, or use u and the 931.5 MeV conversion for energy in MeV.

在 Edexcel A-Level 试题中，计算半衰期或衰变常量时务必展示完整步骤。根据需要使用公式 A = λN、N = N₀ e^–λt 和 E = Δm c²。注意单位：用 c 以 m s⁻¹ 计算焦耳时需将质量转换为 kg；或者使用原子质量单位 u 和 931.5 MeV 转换因子直接得到 MeV。

When describing radiation properties, relate penetrating range to ionising ability and safety precautions. In nuclear equation questions, balance both A and Z and clearly identify the emitted particle.

描述辐射性质时，要将穿透距离与电离能力及安全防护联系起来。在核反应方程题中，要平衡 A 和 Z，并明确指出所发射的粒子。

For binding energy graphs, be ready to explain why fusion of light elements and fission of heavy elements both release energy, referring to the peak near iron. Be precise with terminology: 'mass defect' and 'binding energy' are not the same, though they are closely linked.

对于结合能曲线图，要能解释为何轻核聚变和重核裂变都能释放能量，并引述铁附近的峰值。术语要精确：“质量亏损”和“结合能”虽然密切相关但概念不同。

Finally, practice drawing the exponential decay curve and its logarithmic linearisation; examiners often award marks for correctly labelled axes with units and for reading data from transformed graphs.

最后，练习绘制指数衰减曲线及其对数线性化；考官常会因正确标注带单位的坐标轴以及从转换图形上读取数据而给分。

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