📚 IB Physics: Atoms and Nuclear Physics Knowledge Points Summary | IB物理：原子和核物理知识点汇总
Atomic and nuclear physics forms a core component of the IB Physics syllabus, connecting the microscopic world of subatomic particles to macroscopic phenomena such as energy generation and medical imaging. This article consolidates the essential knowledge points from this topic, providing a structured revision guide that aligns closely with IB assessment requirements.
原子和核物理是IB物理课程的核心组成部分，它将亚原子粒子的微观世界与能量产生、医学成像等宏观现象联系起来。本文系统梳理了该主题的关键知识点，提供一份与IB考试要求紧密对齐的结构化复习指南。
1. Atomic Structure and the Rutherford Model | 原子结构与卢瑟福模型
The modern understanding of atomic structure begins with Rutherford’s gold foil experiment in 1911. A beam of alpha particles was directed at a thin gold foil, and the scattering patterns revealed that most particles passed straight through, while a very small fraction were deflected at large angles — some even reflected back. This evidence led to the conclusion that the atom consists of a tiny, dense, positively charged nucleus surrounded by mostly empty space, with electrons orbiting at relatively large distances.
对原子结构的现代认识始于1911年的卢瑟福金箔实验。一束α粒子射向薄金箔，散射图样显示大多数粒子径直穿过，而极少数粒子发生大角度偏转——甚至有的被反弹回来。这一证据表明，原子由微小、致密、带正电的原子核构成，核外大部分是空的空间，电子在较远距离上绕核运动。
Key properties of the atomic nucleus to remember:
需要牢记的原子核关键性质如下：
- The nucleus contains protons (positive) and neutrons (neutral), collectively called nucleons.
- 原子核包含质子（带正电）和中子（电中性），统称为核子。
- The atomic number Z equals the number of protons; the mass number A equals the total number of nucleons.
- 原子序数Z等于质子数；质量数A等于核子总数。
- The nucleus has a radius on the order of 10⁻¹⁵ m, while the atom itself has a radius of about 10⁻¹⁰ m — meaning the nucleus is roughly 100,000 times smaller than the atom.
- 原子核的半径约为10⁻¹⁵ m，而原子本身半径约为10⁻¹⁰ m——这意味着原子核比整个原子小约10万倍。
- Almost all of the atom’s mass is concentrated in the nucleus due to the relatively large mass of nucleons.
- 由于核子质量较大，原子几乎全部质量都集中在原子核中。
2. Atomic Energy Levels and Spectra | 原子能级与光谱
Electrons within an atom can only occupy specific discrete energy levels, a concept central to the Bohr model. When an electron transitions from a higher energy level to a lower one, it emits a photon of energy equal to the difference between the two levels. Conversely, the absorption of a photon with exactly the right energy can excite an electron to a higher level.
原子中的电子只能占据特定的离散能级，这是玻尔模型的核心概念。当电子从高能级跃迁到低能级时，会发射一个光子，其能量等于两个能级之差。反之，吸收恰好具有相应能量的光子能使电子激发到更高能级。
ΔE = Eₕᵢᵍₕ − Eₗₒʷ = hf = hc/λ
where h is Planck’s constant (6.63 × 10⁻³⁴ J·s), f is the photon frequency, c is the speed of light, and λ is the photon wavelength. The discrete nature of these energy levels explains why atomic emission and absorption spectra consist of sharp spectral lines rather than continuous bands — each line corresponds to a specific electronic transition.
其中h是普朗克常数（6.63 × 10⁻³⁴ J·s），f是光子频率，c是光速，λ是光子波长。能级的离散性解释了为什么原子发射光谱和吸收光谱由尖锐的谱线而非连续谱带构成——每条谱线对应一次特定的电子跃迁。
For hydrogen, the energy of level n is given by:
对于氢原子，第n能级的能量由下式给出：
Eₙ = −13.6 eV / n² (n = 1, 2, 3, …)
The ground state (n = 1) has energy −13.6 eV; the negative sign indicates that the electron is bound to the nucleus. The ionization energy of hydrogen from its ground state is therefore +13.6 eV.
基态（n = 1）的能量为−13.6 eV；负号表示电子被束缚在原子核周围。因此，氢原子从基态电离所需的电离能为+13.6 eV。
3. Wave–Particle Duality and de Broglie Wavelength | 波粒二象性与德布罗意波长
Matter exhibits wave-like properties, as proposed by Louis de Broglie in 1924. Every particle with momentum p has an associated wavelength. This concept is essential for understanding why electron energies in atoms are quantized: the electron behaves as a standing wave around the nucleus, and only certain orbital circumferences can accommodate a whole number of wavelengths.
1924年，路易·德布罗意提出物质具有波动性。每个具有动量p的粒子都伴随一个特征波长。这一概念对于理解原子中电子能量为何量子化至关重要：电子表现为围绕原子核的驻波，只有某些满足整数倍波长的轨道周长才被允许。
λ = h/p = h/(mv)
where m is the particle mass and v is its velocity. Electrons accelerated through a potential difference V acquire kinetic energy eV; their de Broglie wavelength is then given by λ = h/√(2meV). Electron diffraction experiments confirm this wave-like behaviour. The IB syllabus often asks students to calculate the de Broglie wavelength of electrons or protons and to relate it to the scale of atomic spacing.
其中m为粒子质量，v为其速度。电子经电势差V加速后获得的动能为eV；其德布罗意波长为λ = h/√(2meV)。电子衍射实验证实了这种波动行为。IB大纲常要求学生计算电子或质子的德布罗意波长，并将其与原子间距的尺度联系起来。
4. Radioactive Decay: Types and Properties | 放射性衰变：类型与性质
Radioactive decay is a random, spontaneous process in which an unstable nucleus transforms into a more stable configuration. The three primary types of decay are alpha (α), beta (β), and gamma (γ), each with distinct characteristics.
放射性衰变是原子核自发、随机地转变为更稳定状态的过程。三种主要衰变类型为α衰变、β衰变和γ衰变，各自具有不同的特征。
| Property / 性质 | Alpha (α) / α粒子 | Beta (β) / β粒子 | Gamma (γ) / γ射线 |
|---|---|---|---|
| Nature / 本质 | Helium-4 nucleus (²He⁴) / 氦-4原子核 | Fast electron (e⁻) or positron (e⁺) / 高速电子或正电子 | Electromagnetic radiation (photon) / 电磁辐射（光子） |
| Charge / 电荷 | +2e | −e (β⁻) or +e (β⁺) | 0 |
| Rest mass / 静质量 | 4 u | Approximately 1/1836 u / 约1/1836 u | 0 |
| Ionizing power / 电离能力 | Highest / 最强 | Moderate / 中等 | Lowest / 最弱 |
| Penetrating power / 穿透能力 | Stopped by paper or a few cm of air / 被纸或几厘米空气阻挡 | Stopped by a few mm of aluminium / 被几毫米铝阻挡 | Reduced by several cm of lead / 被数厘米铅减弱 |
The alpha particle has the largest mass and charge, causing intense ionization along a short path. Beta particles are lighter and penetrate farther. Gamma rays are the most penetrating but ionize least effectively.
α粒子质量和电荷最大，在短路径上产生强烈电离。β粒子较轻，穿透更深。γ射线穿透力最强，但电离效率最低。
5. Nuclear Decay Equations | 核衰变方程
Writing balanced nuclear equations is a fundamental skill tested in IB Physics. In any decay equation, both the total mass number A and the total atomic number Z must be conserved.
书写配平的核衰变方程是IB物理考查的基本技能。在任何衰变方程中，总质量数A和总原子序数Z都必须守恒。
Alpha decay: The parent nucleus loses 2 protons and 2 neutrons.
α衰变：母核失去2个质子和2个中子。
ᵤᵃX → ᵤ₋₂ᵃ⁻⁴Y + ₂⁴He
Example: Uranium-238 undergoes alpha decay to thorium-234:
示例：铀-238发生α衰变生成钍-234：
₉₂²³⁸U → ₉₀²³⁴Th + ₂⁴He
Beta-minus decay: A neutron converts into a proton, emitting an electron and an antineutrino.
β⁻衰变：一个中子转化为质子，同时发射一个电子和一个反中微子。
ₙ⁰ → ₚ⁺ + e⁻ + ν̄ₑ
Beta-plus decay: A proton converts into a neutron, emitting a positron and a neutrino.
β⁺衰变：一个质子转化为中子，同时发射一个正电子和一个中微子。
ₚ⁺ → ₙ⁰ + e⁺ + νₑ
Gamma emission usually accompanies other decay modes, releasing excess energy from the daughter nucleus without changing A or Z.
γ发射通常伴随其他衰变模式，释放子核的多余能量，但不改变A或Z。
6. Half-Life and Radioactive Decay Law | 半衰期与放射性衰变定律
Radioactive decay follows first-order kinetics. The number of undecayed nuclei N at time t is related to the initial number N₀ by an exponential decay law. The half-life T₁/₂ is the time required for half of the original nuclei to decay, and it is a characteristic constant for each radioactive isotope, independent of external conditions such as temperature or pressure.
放射性衰变遵循一级动力学规律。t时刻未衰变的原子核数N与初始核数N₀之间满足指数衰变定律。半衰期T₁/₂是原始原子核衰变一半所需的时间，它是每种放射性同位素的特征常数，与温度、压强等外部条件无关。
N = N₀ (1/2)^(t/T₁/₂)
Equivalent forms using the decay constant λ:
使用衰变常数λ的等价形式：
N = N₀e^(−λt) and T₁/₂ = ln 2 / λ
The rate of decay, or activity A, is defined as A = λN and is measured in becquerels (Bq), where 1 Bq = 1 decay per second. Students should be comfortable using these equations to determine the age of archaeological samples (carbon dating) or to calculate remaining activity after a given time.
衰变速率，即活度A，定义为A = λN，单位为贝可勒尔（Bq），1 Bq = 每秒1次衰变。学生应熟练掌握利用这些方程确定考古样品的年龄（碳定年法）或计算经过给定时间后剩余的活度。
7. Nuclear Binding Energy and Mass Defect | 核结合能与质量亏损
The mass of a nucleus is always less than the sum of the masses of its individual nucleons. This difference, called the mass defect Δm, is converted into the binding energy that holds the nucleus together. Einstein’s mass–energy equivalence relates the two quantities.
原子核的质量总是小于其组成核子各自的的质量之和。这个差值称为质量亏损Δm，它转化为将原子核束缚在一起的结合能。爱因斯坦的质能等价关系将两者联系起来。
ΔE = Δmc²
where c = 3.00 × 10⁸ m/s. In nuclear physics, masses are often expressed in atomic mass units (u), where 1 u = 1.66 × 10⁻²⁷ kg ≈ 931.5 MeV/c².
其中c = 3.00 × 10⁸ m/s。在核物理中，质量常用原子质量单位（u）表示，1 u = 1.66 × 10⁻²⁷ kg ≈ 931.5 MeV/c²。
For a nucleus ᵤᵃX with Z protons and (A − Z) neutrons:
对于具有Z个质子和(A − Z)个中子的原子核ᵤᵃX：
Δm = Z·mₚ + (A − Z)·mₙ − mₙᵤcₗₑᵤₛ
The binding energy per nucleon, ΔE/A, is a measure of nuclear stability. The binding energy per nucleon curve peaks around iron-56 (approximately 8.8 MeV per nucleon), indicating that iron is the most stable nucleus. This curve explains why energy is released in both nuclear fission (splitting heavy nuclei) and nuclear fusion (combining light nuclei): both processes move the products toward the region of maximum binding energy per nucleon.
每个核子的结合能ΔE/A是衡量原子核稳定性的指标。每个核子的结合能曲线在铁-56附近达到峰值（约8.8 MeV/核子），表明铁是最稳定的原子核。这条曲线解释了为什么核裂变（重核分裂）和核聚变（轻核聚合）都能释放能量：两种过程都将产物推向每核子结合能最大的区域。
8. Nuclear Fission and Fusion | 核裂变与核聚变
Nuclear fission occurs when a heavy nucleus (such as uranium-235 or plutonium-239) absorbs a slow neutron and splits into two smaller nuclei, emitting two or three additional neutrons and releasing a large amount of energy. A typical fission reaction of uranium-235 is:
核裂变发生在重原子核（如铀-235或钚-239）吸收一个慢中子后分裂成两个较小的核，同时发射两到三个额外中子并释放大量能量。铀-235的典型裂变反应为：
₉₂²³⁵U + ₀¹n → ₅₆¹⁴⁴Ba + ₃₆⁸⁹Kr + 3₀¹n + Energy
The emitted neutrons can trigger further fission events, producing a chain reaction. In a nuclear reactor, control rods absorb excess neutrons to maintain a steady rate of fission; the energy released heats a coolant, which drives turbines to generate electricity.
发射的中子可以触发进一步的裂变事件，产生链式反应。在核反应堆中，控制棒吸收多余中子以维持稳定的裂变速率；释放的能量加热冷却剂，驱动涡轮机发电。
Nuclear fusion is the process in which two light nuclei combine to form a heavier nucleus. Fusion of hydrogen isotopes — deuterium (²H) and tritium (³H) — is the most promising for energy production:
核聚变是两个轻原子核结合形成一个较重原子核的过程。氢同位素——氘（²H）和氚（³H）的聚变是能量生产中最有前景的反应：
₁²H + ₁³H → ₂⁴He + ₀¹n + 17.6 MeV
Fusion requires extremely high temperatures (about 10⁸ K) to overcome the electrostatic repulsion between positively charged nuclei. Unlike fission, fusion produces no long-lived radioactive waste, making it an attractive — though technically challenging — energy source. In the Sun, gravitational pressure and high temperatures sustain the fusion of hydrogen into helium.
聚变需要极高的温度（约10⁸ K）以克服带正电原子核之间的静电排斥力。与裂变不同，聚变不产生长寿命放射性废物，因此是一种很有吸引力——尽管在技术上极具挑战性——的能源。在太阳内部，引力压强和高温维持着氢聚变为氦的过程。
9. Applications and Risks of Nuclear Radiation | 核辐射的应用与风险
Radioactive isotopes are widely used across medicine, industry, and research. The same radiation that provides these benefits also poses health risks, making a thorough understanding of both aspects essential for the IB candidate.
放射性同位素广泛应用于医学、工业和研究领域。带来这些益处的辐射也同时构成健康风险，因此全面理解利弊两方面对IB考生至关重要。
Common applications:
常见应用：
- Medical imaging: Technetium-99m emits gamma rays and is used as a tracer in organ imaging (e.g., bone scans).
- 医学成像：锝-99m发射γ射线，用作器官成像（如骨扫描）中的示踪剂。
- Cancer treatment: Cobalt-60 produces gamma radiation that damages and destroys tumour tissue.
- 癌症治疗：钴-60产生γ辐射，破坏和杀死肿瘤组织。
- Carbon dating: The ratio of carbon-14 to carbon-12 in organic material indicates its age up to about 50,000 years.
- 碳定年法：有机材料中碳-14与碳-12的比例可指示其年龄，最长约5万年。
- Industrial gauging: Beta sources measure the thickness of paper, plastic, or metal sheets during production.
- 工业测量：β源在生产过程中测量纸张、塑料或金属薄板的厚度。
Health risks and protection: Ionizing radiation can remove electrons from atoms in living tissue, causing DNA damage that may lead to cancer or cell death. The three fundamental principles of radiation protection are time (minimize exposure duration), distance (maximize distance from the source), and shielding (use appropriate absorbing materials between the source and the body).
健康风险与防护：电离辐射可以从活体组织中的原子中移除电子，造成DNA损伤，可能导致癌症或细胞死亡。辐射防护的三条基本原则是：时间（尽量缩短照射时间）、距离（尽量远离辐射源）和屏蔽（在辐射源与人体之间使用合适的吸收材料）。
The absorbed dose is measured in grays (Gy), where 1 Gy = 1 J/kg. The equivalent dose accounts for the biological effect of different radiation types, with the weighting factor being 1 for gamma and beta radiation and up to 20 for alpha particles due to their high ionizing power.
吸收剂量以戈瑞（Gy）为单位，1 Gy = 1 J/kg。当量剂量则考虑了不同类型辐射的生物效应，其中γ和β辐射的权重因子为1，而α粒子因其强电离能力权重因子可达20。
This comprehensive overview of atomic and nuclear physics covers the core concepts and equations required for IB Physics Paper 1 and Paper 2. Practice writing balanced nuclear equations, interpreting binding energy curves, and applying the exponential decay law to quantitative problems — these are the most frequently tested skills in this topic. A confident grasp of these fundamentals will serve you well in the examination and in understanding the physics that shapes modern technology.
本综述覆盖了IB物理试卷1和试卷2所需的原子和核物理核心概念与方程。练习书写配平的核方程、解读结合能曲线以及应用指数衰变定律解决定量问题——这些是本主题中最常考查的技能。扎实掌握这些基础知识，将在考试中以及理解塑造现代技术的物理原理时为你提供有力支持。
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