📚 Atomic and Nuclear Physics | 原子与核物理
Atomic and nuclear physics explores the smallest building blocks of matter and the forces that govern their interactions. From the photoelectric effect and quantised energy levels in atoms to radioactivity, nuclear reactions and the constituents of the nucleus, this field underpins modern technology, energy generation and our understanding of the universe. In this IB Physics revision guide, we cover the essential concepts, equations and data analysis techniques required for the IB Diploma.
原子与核物理研究物质的最小组成单元以及支配它们相互作用的力。从光电效应和原子的量子化能级到放射性、核反应以及原子核的构成，这一领域是现代技术、能源生产和宇宙认知的基础。在这份IB物理复习指南中，我们将涵盖IB文凭课程所需的基本概念、方程和数据分析方法。
1. The Photoelectric Effect | 光电效应
When electromagnetic radiation of sufficiently high frequency strikes a metal surface, electrons are emitted. This photoelectric effect cannot be explained by classical wave theory, which would predict that emission depends on intensity rather than frequency. Einstein proposed that light consists of photons, each carrying energy E = hf, where h is the Planck constant and f is the frequency.
当频率足够高的电磁辐射照射金属表面时，会发射电子。这一光电效应无法用经典波动理论解释，因为波动理论预测发射应取决于光强而不是频率。爱因斯坦提出光由光子组成，每个光子携带能量 E = hf，其中 h 是普朗克常量，f 是频率。
A photon can eject an electron only if its energy exceeds the work function Φ of the metal. The maximum kinetic energy of the emitted photoelectron is given by Ek max = hf – Φ. The stopping voltage Vs in a photoelectric circuit satisfies eVs = Ek max, where e is the elementary charge.
只有当光子能量超过金属的逸出功 Φ 时，光子才能击出一个电子。发射的光电子的最大动能由 Ek max = hf – Φ 给出。光电回路中的遏止电压 Vs 满足 eVs = Ek max，其中 e 是元电荷。
Experimentally, the graph of kinetic energy against frequency yields a straight line with slope h, and the x-intercept gives the threshold frequency f₀ = Φ/h. This confirmed the particle nature of light.
实验中，动能对频率的图线是一条斜率为 h 的直线，其横截距给出阈值频率 f₀ = Φ/h。这证实了光的粒子性。
2. Matter Waves and De Broglie Wavelength | 物质波与德布罗意波长
Louis de Broglie proposed that particles of momentum p have an associated wavelength λ = h/p. This wave–particle duality was later verified by electron diffraction experiments, where electrons passing through a graphite film produced an interference pattern.
路易·德布罗意提出动量为 p 的粒子具有与之对应的波长 λ = h/p。这一波粒二象性后来被电子衍射实验证实，电子穿过石墨薄膜产生了干涉图样。
For an electron accelerated through a potential difference V, its kinetic energy is eV = p²/(2m), so the de Broglie wavelength is λ = h / √(2meV). This wavelength is of the order of interatomic spacings in crystals, making electron diffraction a powerful tool for studying crystal structures.
对于被电势差 V 加速的电子，其动能为 eV = p²/(2m)，因此德布罗意波长为 λ = h / √(2meV)。该波长与晶体中原子的间距在同一数量级，使得电子衍射成为研究晶体结构的有力工具。
3. Atomic Spectra and Energy Levels | 原子光谱与能级
Atoms emit and absorb light only at specific wavelengths, producing line spectra. Bohr’s model for hydrogen postulates that electrons occupy discrete circular orbits without radiating, and that photons are emitted or absorbed when an electron transitions between energy levels. The energy of a photon equals the difference between two levels: ΔE = Ei – Ef.
原子只在特定波长发射和吸收光，产生线状光谱。玻尔的氢原子模型假设电子处于分立的圆形轨道上而不辐射，当电子在能级之间跃迁时会发射或吸收光子。光子能量等于两个能级的差：ΔE = Ei – Ef。
For hydrogen, the allowed energies are En = –13.6 eV / n², where n is the principal quantum number. The Lyman series corresponds to transitions down to n = 1, the Balmer series to n = 2. The ionisation energy is 13.6 eV, which is the energy required to remove the electron from the ground state.
对于氢原子，允许的能量为 En = –13.6 eV / n²，其中 n 是主量子数。莱曼系对应于跃迁至 n = 1 能级，巴尔末系对应于 n = 2 能级。电离能是 13.6 eV，即将电子从基态移走所需的能量。
Emission spectra are produced when excited electrons fall to lower energy levels, whereas absorption spectra show dark lines where continuous light has been absorbed at specific wavelengths. These spectral fingerprints allow the identification of elements in stars and laboratory plasmas.
当受激电子落到较低能级时产生发射光谱；而吸收光谱则显示连续光在特定波长被吸收后形成的暗线。这些光谱指纹可以识别恒星和实验室等离子体中的元素。
4. Nuclear Structure and Isotopes | 核结构与同位素
The nucleus consists of protons and neutrons, collectively called nucleons. The atomic number Z is the number of protons, which determines the element, and the mass number A is the total number of nucleons. Isotopes are nuclei with the same Z but different A, meaning they have different numbers of neutrons.
原子核由质子和中子组成，统称为核子。原子序数 Z 是质子数，它决定了元素种类；质量数 A 是核子总数。同位素是 Z 相同而 A 不同的原子核，即它们的中子数不同。
The strong nuclear force binds nucleons together within the tiny nucleus, overcoming the electrostatic repulsion between protons. This force is very short-range (about 1–2 fm) and acts between all nucleons. Nuclear radii R can be estimated by R = R₀A¹/³, with R₀ ≈ 1.2 × 10⁻¹⁵ m, demonstrating that nuclear density is approximately constant for all nuclei.
强核力将核子束缚在微小的原子核内，克服了质子之间的静电排斥力。这种力作用距离极短（约 1–2 fm），且作用于所有核子。核半径 R 可用公式 R = R₀A¹/³ 估算，其中 R₀ ≈ 1.2 × 10⁻¹⁵ m，这表明所有原子核的核密度大致恒定。
5. Radioactive Decay | 放射性衰变
Unstable nuclei decay spontaneously, emitting radiation to become more stable. The three common types are alpha (α) particles (helium-4 nuclei), beta-minus (β–) particles (electrons) and gamma (γ) rays (high-energy photons). In β– decay, a neutron transforms into a proton, an electron and an antineutrino: n → p + e– + ν̄e.
不稳定的原子核会自发衰变，发射辐射从而变得更稳定。常见的三种衰变是α粒子（氦-4核）、β–粒子（电子）和γ射线（高能光子）。在β–衰变中，一个中子转变为质子、电子和反中微子：n → p + e– + ν̄e。
The activity A of a sample is the number of decays per second, measured in becquerels (Bq). The decay law states that activity decreases exponentially: A = A₀e–λt, where λ is the decay constant. The half-life T½ is the time for half the nuclei to decay, related to λ by T½ = ln2 / λ.
样品的活度 A 是每秒衰变次数，单位是贝克勒尔 (Bq)。衰变定律指出活度按指数规律减小：A = A₀e–λt，其中 λ 是衰变常量。半衰期 T½ 是半数原子核衰变所需的时间，它与 λ 的关系为 T½ = ln2 / λ。
6. Half-life and Carbon Dating | 半衰期与碳定年法
Half-life is independent of the initial number of nuclei and external conditions like temperature and pressure. Since it is a statistical quantity, it applies reliably only to large numbers of nuclei. The fraction of undecayed nuclei after n half-lives is (1/2)ⁿ.
半衰期与初始核的数量以及温度、压强等外部条件无关。由于它是一个统计量，仅在大数量核的情况下才可靠。经过 n 个半衰期后，未衰变的核所占比例为 (1/2)ⁿ。
Carbon-14 dating relies on the radioactive decay of ¹⁴C, which is constantly produced in the atmosphere and absorbed by living organisms. After death, the ¹⁴C decays with T½ ≈ 5730 years, and measuring the remaining activity allows the determination of the sample’s age.
碳-14 定年法依赖于放射性同位素 ¹⁴C 的衰变。¹⁴C 在大气中不断产生并被生物体吸收。死亡后，¹⁴C 以约 5730 年的半衰期衰变，测量剩余的活度即可确定样品的年代。
7. Mass–Energy Equivalence | 质能等价
Einstein’s mass–energy relation E = mc² implies that mass and energy are interchangeable. In nuclear reactions, the total mass of the products is often slightly less than that of the reactants. This mass difference Δm appears as released energy: ΔE = Δm c².
爱因斯坦的质能关系 E = mc² 表明质量与能量可以相互转化。在核反应中，产物的总质量往往略小于反应物的总质量。这一质量差 Δm 以释放能量的形式出现：ΔE = Δm c²。
Energy can be expressed in joules, but in nuclear physics the electronvolt (eV) and the unified atomic mass unit (u) are more convenient. One u is equivalent to 931.5 MeV/c². Thus a mass defect of 1 u corresponds to 931.5 MeV of binding energy.
能量可以用焦耳表示，但在核物理中，电子伏特 (eV) 和统一原子质量单位 (u) 更为便捷。1 u 相当于 931.5 MeV/c²。因此 1 u 的质量亏损对应于 931.5 MeV 的结合能。
8. Binding Energy and Nuclear Stability | 结合能与核稳定性
The binding energy of a nucleus is the energy required to separate it into its individual nucleons. It is the energy equivalent of the mass defect: Eb = Δm c², where Δm = Zmp + Nmn – mnucleus. The average binding energy per nucleon is a key indicator of stability; nuclei with binding energy per nucleon around 8.8 MeV are the most stable, such as iron-56.
原子核的结合能是将其分解为单个核子所需的能量。它等价于质量亏损的能量：Eb = Δm c²，其中 Δm = Zmp + Nmn – m原子核。平均每个核子的结合能是稳定性的关键指标；每个核子结合能约为 8.8 MeV 的原子核最稳定，例如铁-56。
The binding energy per nucleon curve rises steeply for light nuclei, peaks around iron, and then gradually decreases for heavier nuclei. This shape explains why energy can be released both by fusion of light nuclei and by fission of heavy nuclei.
每个核子结合能的曲线在轻核区域陡升，在铁附近达到峰值，然后对更重的核逐渐下降。这种形状解释了为什么轻核的聚变和重核的裂变都能释放能量。
9. Nuclear Fission | 核裂变
Nuclear fission occurs when a heavy nucleus, such as uranium-235, absorbs a slow neutron and splits into two smaller nuclei (fission fragments), along with two or three neutrons and a large amount of energy. The reaction can be sustained as a chain reaction if at least one neutron from each fission induces further fissions.
当一个重核（如铀-235）吸收一个慢中子并分裂成两个较小的核（裂变碎片），同时释放两到三个中子和大量能量时，就会发生核裂变。如果每次裂变中至少有一个中子能引起进一步的裂变，该反应就能以链式反应的方式自持进行。
The critical mass is the minimum mass of fissile material required for a self-sustaining chain reaction. Control rods made of neutron-absorbing materials (e.g., cadmium or boron) are used to regulate the reaction in nuclear reactors. The moderator (often water or graphite) slows down neutrons to increase the probability of causing fission in ²³⁵U.
临界质量是指自持链式反应所需的可裂变材料的最小质量。由吸收中子的材料（如镉或硼）制成的控制棒用于调节核反应堆中的反应。慢化剂（通常是水或石墨）减慢中子速度，以提高它们引发 ²³⁵U 裂变的概率。
10. Nuclear Fusion | 核聚变
Nuclear fusion is the joining of light nuclei to form a heavier nucleus, releasing energy because the binding energy per nucleon increases dramatically for light elements. The Sun’s energy comes from the fusion of hydrogen into helium via the proton–proton chain, in which four protons ultimately produce one helium-4 nucleus, two positrons and two neutrinos, with a total energy release of about 26.7 MeV.
核聚变是轻核结合形成较重原子核的过程，由于轻元素每个核子的结合能急剧增加，因此释放出能量。太阳的能量来源于氢通过质子-质子链反应聚变成氦，在该反应中四个质子最终产生一个氦-4 核、两个正电子和两个中微子，总能量释放约为 26.7 MeV。
For fusion to occur, nuclei must overcome the electrostatic repulsion. This requires extremely high temperatures (on the order of 10⁸ K) to give particles enough kinetic energy. Achieving and confining such conditions on Earth remains a major engineering challenge, with tokamaks and laser fusion being two leading approaches.
要发生聚变，原子核必须克服静电排斥。这需要极高的温度（约 10⁸ K 量级）以使粒子具有足够的动能。在地球上实现并约束这种条件仍是一个巨大的工程挑战，托卡马克和激光聚变是两种主要的方法。
11. Fundamental Particles and Quarks | 基本粒子与夸克
The Standard Model classifies fundamental particles into quarks, leptons and gauge bosons. Protons and neutrons are not elementary; they are baryons composed of three quarks held together by the strong interaction mediated by gluons. A proton consists of two up quarks and one down quark (uud), while a neutron is udd.
标准模型将基本粒子分为夸克、轻子和规范玻色子。质子和中子不是基本粒子；它们是由三个夸克组成的重子，这些夸克通过胶子传递的强相互作用结合在一起。质子由两个上夸克和一个下夸克构成 (uud)，中子则为 udd。
Quarks have fractional electric charges: up quark +⅔ e, down quark –⅓ e. The conservation of baryon number and lepton number is upheld in all particle interactions. For example, in β– decay, a down quark changes into an up quark, conserving baryon number, and an electron and antineutrino are emitted, conserving lepton number.
夸克带有分数电荷：上夸克 +⅔ e，下夸克 –⅓ e。在所有粒子相互作用中，重子数和轻子数守恒定律均成立。例如，在 β– 衰变中，一个下夸克变为上夸克，重子数守恒；同时发射一个电子和一个反中微子，轻子数守恒。
In addition to quarks, leptons such as electrons, muons and their associated neutrinos are point-like, truly elementary particles. The Higgs boson is the quantum of the Higgs field, responsible for giving mass to W and Z bosons and fermions.
除夸克外，电子、μ子及其相应的中微子等轻子都是点状的、真正的基本粒子。希格斯玻色子是希格斯场的量子，负责赋予 W 和 Z 玻色子以及费米子质量。
12. Medical and Technological Applications | 医学与技术应用
Radioisotopes are widely used in medicine for diagnosis and therapy. Technetium-99m, a gamma emitter with a half-life of 6 hours, is used in imaging to trace blood flow and detect tumours. Iodine-131 is a β– emitter used to treat thyroid cancer, as the thyroid gland naturally accumulates iodine.
放射性同位素在医学中广泛用于诊断和治疗。锝-99m 是一种半衰期为 6 小时的 γ 发射体，用于成像以追踪血流并检测肿瘤。碘-131 是一种 β– 发射体，用于治疗甲状腺癌，因为甲状腺会天然富集碘。
Radiotherapy employs targeted ionising radiation to destroy cancerous cells while minimising damage to healthy tissue. Particle detectors such as Geiger–Müller tubes, scintillation counters and semiconductor detectors allow the measurement of radiation dosage and environmental monitoring. Smoke detectors exploit the ionisation caused by alpha particles from americium-241 to trigger an alarm.
放射治疗利用定向电离辐射破坏癌细胞，同时尽量减少对健康组织的损伤。盖革-米勒管、闪烁计数器和半导体探测器等粒子探测器可用于测量辐射剂量及环境监测。烟雾探测器利用镅-241 释放的α粒子引起的电离来触发警报。
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