📚 Modern Physics Core Exam Points | 现代物理核心考点梳理
Modern physics is a major source of exam questions in A-level and equivalent syllabuses. This article condenses the key definitions, formulas, and common traps into a clear revision guide.
现代物理是 A-level 及同类国际课程考试中的高频考点。本文将核心定义、公式和易错点浓缩为一份清晰的复习指南。
1. Atomic Structure and the Nucleus | 原子结构与原子核
An atom consists of a small, dense nucleus containing protons and neutrons, surrounded by orbiting electrons. The nucleus is about 10⁻⁵ times the size of the atom.
原子由包含质子和中子的致密原子核以及绕核运动的电子构成。原子核的尺度约为原子的 10⁻⁵ 倍。
Proton number Z is the number of protons; nucleon number A is the total number of protons and neutrons.
质子数 Z 表示质子数量；核子数 A 表示质子与中子的总数。
Isotopes are nuclei with the same Z but different A.
同位素是质子数 Z 相同、核子数 A 不同的原子核。
The strong nuclear force holds the nucleus together, overcoming electrostatic repulsion between protons.
强核力克服质子间的静电斥力，将原子核束缚在一起。
2. Radioactive Decay | 放射性衰变
Radioactive decay is a random and spontaneous process in which an unstable nucleus emits particles or radiation to become more stable.
放射性衰变是随机且自发的过程，不稳定的原子核通过释放粒子或辐射变得更稳定。
Alpha decay: the nucleus emits an α particle (²₄He), reducing A by 4 and Z by 2.
α 衰变：原子核释放 α 粒子（²₄He），A 减少 4，Z 减少 2。
Beta-minus decay: a neutron converts into a proton, emitting an electron and an antineutrino; Z increases by 1, A unchanged.
β⁻ 衰变：中子转变为质子，释放电子和反中微子；Z 增加 1，A 不变。
Beta-plus decay: a proton converts into a neutron, emitting a positron and a neutrino; Z decreases by 1.
β⁺ 衰变：质子转变为中子，释放正电子和中微子；Z 减少 1。
Gamma radiation: high-energy electromagnetic waves emitted from excited nuclei, with no change in A or Z.
γ 辐射：激发态原子核释放的高能电磁波，A 和 Z 均不变。
3. Half-Life and Decay Law | 半衰期与衰变规律
The half-life T½ is the time for half of the unstable nuclei in a sample to decay. It is independent of external conditions.
半衰期 T½ 是样品中一半不稳定原子核发生衰变所需的时间，与外部条件无关。
N = N₀ (½)t/T½
A = A₀ e−λt, λ = ln 2 / T½
N is the remaining number, A is activity in becquerels (Bq), λ is the decay constant.
N 为剩余核数，A 为活度（单位贝克勒尔 Bq），λ 为衰变常数。
The decay constant λ equals the probability of decay per unit time.
衰变常数 λ 表示单位时间内每个核发生衰变的概率。
Half-life can be found from a decay graph: read the time for activity to drop to half its initial value.
从衰变曲线求半衰期：读取活度降为初始值一半所需的时间。
4. Mass Defect and Binding Energy | 质量亏损与结合能
The mass of a nucleus is always less than the total mass of its separate nucleons. This difference is called the mass defect Δm.
原子核的质量总是小于其独立核子质量之和，这个差值称为质量亏损 Δm。
Binding energy is the energy released when a nucleus is formed from its individual nucleons.
结合能是原子核由独立核子结合时释放的能量。
Use Einstein’s equation: E = Δmc², where c = 3.0 × 10⁸ m/s.
利用爱因斯坦方程：E = Δmc²，其中 c = 3.0 × 10⁸ m/s。
Binding energy per nucleon measures nuclear stability; iron-56 has the highest value.
比结合能（每个核子的结合能）衡量原子核的稳定性；铁-56 的比结合能最大。
Δm = Z·mₚ + N·mₙ − m_nucleus
5. Nuclear Fission and Fusion | 核裂变与核聚变
Both fission and fusion release energy because the products have higher binding energy per nucleon than the reactants.
裂变和聚变都会释放能量，因为产物的比结合能高于反应物。
Fission: a heavy nucleus (e.g., ²³⁵U) splits after absorbing a neutron, releasing energy and more neutrons.
裂变：重核（如 ²³⁵U）吸收一个中子后分裂，释放能量和更多中子。
Fusion: light nuclei (e.g., hydrogen isotopes) combine to form a heavier nucleus; it powers stars.
聚变：轻核（如氢同位素）结合成更重的核；恒星的能量来源。
Controlled fission is used in reactors; fusion requires extremely high temperatures and pressure.
受控裂变用于核反应堆；聚变需要极高温度和压强。
6. The Photoelectric Effect | 光电效应
When light of sufficient frequency shines on a metal surface, electrons are emitted. This cannot be explained by wave theory alone.
当足够频率的光照射金属表面时，会发射电子。仅用波动理论无法解释该现象。
The photon energy is E = hf, where h is Planck’s constant (6.63 × 10⁻³⁴ J·s).
光子能量为 E = hf，其中 h 为普朗克常量（6.63 × 10⁻³⁴ J·s）。
The work function φ is the minimum energy needed to free an electron from the metal surface.
逸出功 φ 是使电子脱离金属表面所需的最小能量。
Einstein’s photoelectric equation: hf = φ + Kmax.
爱因斯坦光电效应方程：hf = φ + Kmax。
No emission occurs if f < f₀, where f₀ = φ/h is the threshold frequency.
若 f < f₀（f₀ = φ/h 为截止频率），则不发生发射。
7. Wave-Particle Duality | 波粒二象性
All matter exhibits both wave and particle properties. The wavelength of a moving particle is given by de Broglie’s relation.
所有物质都同时表现出波动性和粒子性。运动粒子的波长由德布罗意关系给出。
λ = h / p = h / (mv)
Electron diffraction through a crystal demonstrates the wave nature of electrons.
电子通过晶体的衍射实验证明了电子的波动性。
Photoelectric effect demonstrates the particle nature of light.
光电效应证明了光的粒子性。
For macroscopic objects, λ is extremely small, so wave behaviour is unobservable.
对于宏观物体，λ 极小，波动行为不可观测。
8. Energy Levels and Atomic Spectra | 能级与原子光谱
Electrons in an atom can occupy only discrete energy levels. Transitioning between levels absorbs or emits a photon of specific energy.
原子中的电子只能占据分立的能级。能级之间的跃迁会吸收或发射特定能量的光子。
Photon energy equals the energy difference: hf = E₂ − E₁.
光子能量等于能级差：hf = E₂ − E₁。
Emission spectra are produced when electrons move from higher to lower levels.
当电子从高能级跃迁到低能级时产生发射光谱。
Absorption spectra show dark lines corresponding to the wavelengths absorbed by atoms.
吸收光谱中的暗线对应原子吸收的特征波长。
9. Mass-Energy Equivalence and Applications | 质能等价与应用
The equivalence of mass and energy explains energy release in nuclear reactions. A small mass loss gives a huge energy output because c² is enormous.
质能等价解释了核反应中的能量释放。由于 c² 极大，微小的质量亏损就能产生巨大能量。
In particle accelerators, e⁺ and e⁻ annihilation converts all mass into energy.
在粒子加速器中，e⁺ 与 e⁻ 湮灭将所有质量转化为能量。
In medical PET scans, positron annihilation produces two γ photons.
在医学 PET 扫描中，正电子湮灭产生两个 γ 光子。
Sun’s energy comes from fusion of hydrogen into helium, with 0.7% of mass converted to energy.
太阳的能量来自氢聚变为氦，其中约 0.7% 的质量转化为能量。
10. Standard Model and Fundamental Particles | 标准模型与基本粒子
The Standard Model classifies elementary particles into quarks, leptons, and gauge bosons.
标准模型将基本粒子分为夸克、轻子和规范玻色子。
Hadrons (e.g., protons, neutrons) are made of quarks.
强子（如质子、中子）由夸克组成。
Leptons include electrons, muons, and neutrinos; they are fundamental and not made of smaller particles.
轻子包括电子、μ 子和中微子；它们是基本粒子，不由更小粒子构成。
Exchange particles (photons, gluons, W⁺/W⁻, Z⁰) mediate the fundamental forces.
交换粒子（光子、胶子、W⁺/W⁻、Z⁰）传递基本相互作用。
Baryons have three quarks; mesons have one quark and one antiquark.
重子由三个夸克组成；介子由一个夸克和一个反夸克组成。
11. Quark Model and Conservation Laws | 夸克模型与守恒定律
Quarks carry fractional charges: up (+⅔e), down (−⅓e). Protons are uud; neutrons are udd.
夸克带分数电荷：上夸克 (+⅔e)、下夸克 (−⅓e)。质子为 uud，中子为 udd。
In β⁻ decay, a down quark changes to an up quark, emitting W⁻, which decays to e⁻ and antineutrino.
在 β⁻ 衰变中，下夸克变为上夸克，释放 W⁻ 玻色子，W⁻ 衰变为 e⁻ 和反中微子。
In β⁺ decay, an up quark changes to a down quark, emitting W⁺, which decays to e⁺ and neutrino.
在 β⁺ 衰变中，上夸克变为下夸克，释放 W⁺ 玻色子，W⁺ 衰变为 e⁺ 和中微子。
Charge, baryon number, and lepton number are always conserved in reactions.
电荷、重子数和轻子数在反应中始终守恒。
12. Common Exam Traps and Tips | 常见易错点与提醒
Students often lose marks on definitions and sign conventions. Review these carefully.
学生常因定义不清和符号惯例而失分，请仔细复习以下内容。
Do not confuse mass number A with atomic number Z. In nuclear notation ᴬ_Z X, the top number is A.
不要混淆质量数 A 和原子序数 Z。在核素符号 ᴬ_Z X 中，上方数字是 A。
The activity of a radioactive sample is a count rate, not the number of nuclei.
放射源的活度是计数率，不是原子核个数。
Photoelectric current is proportional to intensity, not frequency; electron energy depends on frequency.
光电流与光强成正比，与频率无关；电子能量取决于频率。
Binding energy is always positive; binding energy per nucleon is largest around Fe-56.
结合能恒为正值；比结合能在铁-56 附近最大。
In calculations, convert mass from u to kg or use 1 u = 931.5 MeV/c².
计算时，将质量从 u 转换为 kg，或使用 1 u = 931.5 MeV/c²。
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