AQA A-Level Physics Particles and Radiation Complete Guide — AQA A-Level 物理：粒子与辐射完全指南

在 AQA A-Level 物理课程中，第一单元的核心主题是”粒子与辐射”（Particles and Radiation）。这一部分把物理学的视角缩小到原子内部，介绍构成物质的基本粒子、原子核的衰变、光子的能量，以及量子世界中最令人惊讶的现象之一：光电效应。对于 A-Level 学生来说，这个单元不仅是考试的必考内容，也是理解整个现代物理学（从核电站到半导体器件）的起点。本文将以中英对照的方式，系统讲解这一单元的全部关键知识点，帮助你建立完整的知识框架。

In the AQA A-Level Physics course, the first unit centres on “Particles and Radiation”. This topic zooms physics down to the inside of the atom, introducing the fundamental particles that make up matter, the decay of atomic nuclei, the energy of photons, and one of the most surprising phenomena in the quantum world: the photoelectric effect. For A-Level students, this unit is not only required exam content, but also the starting point for understanding all of modern physics, from nuclear power stations to semiconductor devices. This article explains every key point of the unit in a side-by-side Chinese and English format, helping you build a complete knowledge framework.

一、原子结构：质子、中子与电子如何构成原子 | Atomic Structure: How Protons, Neutrons and Electrons Build an Atom

原子由三种基本粒子组成：质子（proton）、中子（neutron）和电子（electron）。质子和中子集中在原子中心一个极小的区域，称为原子核（nucleus）；电子则在原子核外以壳层（shell）的形式分布。质子带一个正电荷，电子带一个负电荷，中子则不带电荷。一个中性原子中，质子数与电子数相等，因此正负电荷相互抵消。

An atom is made of three kinds of fundamental particles: protons, neutrons and electrons. Protons and neutrons are concentrated in a tiny region at the centre of the atom, called the nucleus, while electrons are arranged in shells around it. The proton carries one positive charge, the electron carries one negative charge, and the neutron carries no charge. In a neutral atom the number of protons equals the number of electrons, so the positive and negative charges cancel out.

这三种粒子的质量相差很大。质子和中子的质量几乎相等，约为 1.67 × 10⁻²⁷ kg，而电子的质量只有质子的大约 1/1836，因此在计算原子质量时通常可以忽略电子。理解这一点很重要：原子几乎所有的质量都集中在体积极小的原子核中，这说明原子核的密度极其巨大。一个直观的类比是，如果把一个原子放大到足球场那么大，原子核只有一颗豌豆大小，但它几乎承载了全部质量。

The three particles differ greatly in mass. The proton and neutron have almost equal masses of about 1.67 × 10⁻²⁷ kg, whereas the electron is only about 1/1836 as heavy as a proton, so its mass is usually ignored when calculating atomic mass. This point matters: almost all of an atom’s mass is packed into its tiny nucleus, which means the nuclear density is enormous. As an analogy, if an atom were enlarged to the size of a football stadium, the nucleus would be only the size of a pea, yet it would carry almost all of the mass.

在 A-Level 考试中，你常常会被要求识别原子的组成部分，或者根据给定的原子序数和质量数判断质子、中子、电子的数目。请记住三条简单规则：质子数 = 原子序数 Z；电子数 = 质子数（中性原子）；中子数 = 质量数 A 减去原子序数 Z。这些规则是后续所有核物理计算的基础。

In A-Level exams you are frequently asked to identify the constituents of an atom, or to work out the number of protons, neutrons and electrons from a given atomic number and mass number. Remember three simple rules: number of protons = atomic number Z; number of electrons = number of protons (for a neutral atom); number of neutrons = mass number A minus atomic number Z. These rules are the foundation of every later nuclear physics calculation.

二、同位素与核符号：质量数与原子序数的含义 | Isotopes and Nuclide Notation: Mass Number and Atomic Number

同一种元素的原子拥有相同的质子数，但中子数可能不同，这样的原子称为同位素（isotope）。例如碳的三种同位素碳-12、碳-13 和碳-14 都含有 6 个质子，但分别含有 6、7 和 8 个中子。它们的化学性质几乎完全相同，因为化学性质由电子结构决定，而电子数没有变化；但它们的物理性质（特别是质量）有所不同。

Atoms of the same element have the same number of protons but can differ in the number of neutrons; such atoms are called isotopes. For example, the three isotopes of carbon, carbon-12, carbon-13 and carbon-14, all contain 6 protons but contain 6, 7 and 8 neutrons respectively. Their chemical properties are almost identical, because chemical behaviour is determined by the electron arrangement, which does not change; however, their physical properties, especially mass, differ.

核符号（nuclide notation）用统一的格式表示一种核素：元素符号左上角写质量数 A（质子数 + 中子数），左下角写原子序数 Z（质子数）。例如氦-4 写成 ⁴₂He，表示 2 个质子和 2 个中子。在书写核反应方程时，必须保证两边的质量数之和相等，电荷数（原子序数）之和也相等，这是守恒定律的体现。

Nuclide notation expresses a nuclide in a standard format: the mass number A (protons plus neutrons) is written at the upper left of the element symbol, and the atomic number Z (protons) is written at the lower left. For example, helium-4 is written ⁴₂He, showing 2 protons and 2 neutrons. When writing nuclear equations you must make sure the total mass number and the total charge (atomic number) are the same on both sides; this is a direct expression of the conservation laws.

比结合能（specific charge）是这个单元的一个高频考点。某种粒子的比结合能等于它的电荷量除以它的质量，单位是 C kg⁻¹。例如一个质子带有 1.60 × 10⁻¹⁹ C 的电荷、质量为 1.67 × 10⁻²⁷ kg，因此其比结合能约为 9.58 × 10⁷ C kg⁻¹。考试中经常要求比较质子、电子和各种原子核的比结合能，注意电子质量最小，因此电子的比结合能数值最大。

Specific charge is a high-frequency exam topic in this unit. The specific charge of a particle equals its charge divided by its mass, with units of C kg⁻¹. For example a proton carries a charge of 1.60 × 10⁻¹⁹ C and has a mass of 1.67 × 10⁻²⁷ kg, so its specific charge is about 9.58 × 10⁷ C kg⁻¹. Exams often ask you to compare the specific charge of protons, electrons and various nuclei; note that because the electron has the smallest mass, the electron has the largest specific charge.

三、稳定与不稳定原子核：α、β、γ三种衰变 | Stable and Unstable Nuclei: Alpha, Beta and Gamma Decay

原子核并非全都稳定。当中子与质子的比例不合适，或者原子核过大时，它就会通过发射辐射来变得更稳定，这个过程称为放射性衰变（radioactive decay）。A-Level 课程要求掌握三种衰变：α 衰变（发射一个氦核）、β⁻ 衰变（发射一个电子）、以及伴随衰变释放的 γ 辐射（高能电磁波）。

Not all nuclei are stable. When the ratio of neutrons to protons is unsuitable, or the nucleus is simply too large, it becomes more stable by emitting radiation, a process called radioactive decay. The A-Level course requires you to know three kinds of decay: alpha decay (emission of a helium nucleus), beta-minus decay (emission of an electron), and gamma radiation (high-energy electromagnetic waves) released alongside the decay.

在 α 衰变中，原子核发射一个由 2 个质子和 2 个中子组成的 α 粒子，即一个氦核 ⁴₂He。结果是质量数减少 4、原子序数减少 2，元素在周期表中向前移动两位。例如铀-238 衰变为钍-234：²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He。α 粒子电离能力强，但穿透能力弱，一张纸就能挡住它。

In alpha decay the nucleus emits an alpha particle made of 2 protons and 2 neutrons, that is, a helium nucleus ⁴₂He. The result is that the mass number falls by 4 and the atomic number falls by 2, so the element moves two places back in the periodic table. For example, uranium-238 decays into thorium-234: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He. Alpha particles are strongly ionising but weakly penetrating; a sheet of paper stops them.

在 β⁻ 衰变中，原子核内的一个中子转变成一个质子，同时发射一个电子（β⁻ 粒子）和一个反中微子（antineutrino）。原子序数增加 1 而质量数不变，因此元素在周期表中向后移动一位。例如碳-14 衰变为氮-14：¹⁴₆C → ¹⁴₇N + ⁰₋₁e + 反中微子。理解 β⁻ 衰变的关键在于记住它发生在原子核内部，是”中子变质子”的过程，而不是电子从壳层中掉出来。γ 辐射则通常伴随 α 或 β 衰变出现，用于释放原子核的剩余能量，它不改变质量数或原子序数。

In beta-minus decay a neutron inside the nucleus turns into a proton, emitting an electron (a beta-minus particle) and an antineutrino at the same time. The atomic number increases by 1 while the mass number stays the same, so the element moves one place forward in the periodic table. For example, carbon-14 decays into nitrogen-14: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e + antineutrino. The key to understanding beta-minus decay is to remember that it happens inside the nucleus, a “neutron becomes a proton” process, rather than an electron falling out of a shell. Gamma radiation usually accompanies alpha or beta decay and carries away the nucleus’s leftover energy without changing either the mass number or the atomic number.

四、光子与电磁波谱：光如何携带能量 | Photons and the Electromagnetic Spectrum: How Light Carries Energy

在经典物理学中，电磁辐射被看作连续的波；但量子理论告诉我们，电磁辐射以一份一份的能量包传播，每一份称为一个光子（photon）。一个光子的能量由公式 E = hf 给出，其中 h 是普朗克常数（6.63 × 10⁻³⁴ J s），f 是辐射的频率。这个公式是整个量子物理的基石之一。

In classical physics, electromagnetic radiation is treated as a continuous wave; but quantum theory tells us that electromagnetic radiation travels in discrete packets of energy, each packet called a photon. The energy of one photon is given by E = hf, where h is Planck’s constant (6.63 × 10⁻³⁴ J s) and f is the frequency of the radiation. This formula is one of the cornerstones of quantum physics.

由于波速 c = fλ，光子的能量也可以用波长表示：E = hc/λ。这揭示了一个重要关系：波长越短，频率越高，单个光子的能量就越大。电磁波谱从低能量到高能量依次为无线电波、微波、红外线、可见光、紫外线、X 射线和伽马射线。可见光只是电磁波谱中极窄的一段，而紫外线和 X 射线由于光子能量高，具有足够的能量使原子电离。

Because the wave speed satisfies c = fλ, the photon energy can also be written as E = hc/λ. This reveals an important relationship: the shorter the wavelength, the higher the frequency and the greater the energy of each photon. The electromagnetic spectrum runs from radio waves, microwaves and infrared, through visible light, to ultraviolet, X-rays and gamma rays in order of increasing energy. Visible light is only a very narrow band of the spectrum, while ultraviolet and X-rays have photons energetic enough to ionise atoms.

考试中一个常见的题型是计算某种辐射的光子能量，或者根据光子能量反推频率与波长。你需要熟练地在 E = hf 和 E = hc/λ 之间切换，并牢记普朗克常数和光速（3.0 × 10⁸ m s⁻¹）的数值。当题目给出的波长以纳米（nm）为单位时，务必先换算成米再进行计算。

A common exam question asks you to calculate the photon energy of a given radiation, or to work backwards from photon energy to frequency and wavelength. You need to move fluently between E = hf and E = hc/λ, and remember the values of Planck’s constant and the speed of light (3.0 × 10⁸ m s⁻¹). When a question gives a wavelength in nanometres (nm), always convert it to metres before calculating.

五、粒子分类：强子、重子、介子与轻子 | Classifying Particles: Hadrons, Baryons, Mesons and Leptons

随着实验物理的发展，物理学家发现了大量亚原子粒子，于是需要一套分类系统。最基本的划分依据是粒子是否参与强相互作用（strong nuclear force）。参与强相互作用的粒子称为强子（hadron），不参与的称为轻子（lepton）。强子又分为重子（baryon）和介子（meson）两类。

As experimental physics advanced, physicists discovered a large number of subatomic particles, which required a classification system. The most basic division is based on whether a particle takes part in the strong nuclear force. Particles that do take part are called hadrons, and those that do not are called leptons. Hadrons are further divided into baryons and mesons.

重子由三个夸克组成，代表粒子是质子和中子；反重子由三个反夸克组成，例如反质子。介子由一个夸克和一个反夸克组成，代表粒子是 π 介子（pion）和 K 介子（kaon）。轻子的代表是电子、μ 子（muon）以及它们对应的中微子（neutrino）。轻子被认为是基本粒子，即它们不再由更小的粒子组成。

Baryons are made of three quarks, the representative particles being the proton and the neutron; antibaryons are made of three antiquarks, such as the antiproton. Mesons are made of one quark and one antiquark, the representative particles being the pion and the kaon. The representative leptons are the electron, the muon and their associated neutrinos. Leptons are regarded as fundamental particles, meaning they are not made of anything smaller.

考试中常要求你判断某个粒子属于哪一类。判断方法如下：先看它是否参与强相互作用（质子、中子、π 介子等是强子；电子、中微子是轻子），再看它是重子还是介子（由三个夸克组成的是重子，由一个夸克和一个反夸克组成的是介子）。此外还要能识别粒子的反粒子，即质量相同、电荷相反（或不带电荷）的对应粒子。

Exams often ask you to decide which class a particle belongs to. The method is: first check whether it takes part in the strong force (protons, neutrons and pions are hadrons; electrons and neutrinos are leptons), then check whether it is a baryon or a meson (made of three quarks means baryon, made of one quark and one antiquark means meson). You should also recognise antiparticles, the counterparts with the same mass but opposite charge (or no charge).

六、夸克与反夸克：质子和中子的内部结构 | Quarks and Antiquarks: The Inner Structure of Protons and Neutrons

强子并不是基本粒子，它们由更小的粒子，即夸克（quark），组成。A-Level 课程要求掌握六种夸克：上夸克（up）、下夸克（down）、奇夸克（strange）、粲夸克（charm）、顶夸克（top）和底夸克（bottom），但实际计算中主要用到前三种。每种夸克都有对应的反夸克，具有相反的电荷。

Hadrons are not fundamental particles; they are made of even smaller particles called quarks. The A-Level course requires you to know six quarks: up, down, strange, charm, top and bottom, although in practice the first three are the ones used in calculations. Every quark has a corresponding antiquark with the opposite charge.

夸克的电荷是分数电荷：上夸克带 +2/3 e，下夸克带 -1/3 e，奇夸克带 -1/3 e。质子由两个上夸克和一个下夸克（uud）组成，其电荷为 +2/3 + 2/3 – 1/3 = +1，符合质子的 +1 电荷。中子由一个上夸克和两个下夸克（udd）组成，电荷为 +2/3 – 1/3 – 1/3 = 0，符合中子的电中性。这个分数电荷的相加关系是考试中的经典计算题。

Quarks carry fractional charges: the up quark carries +2/3 e, the down quark carries -1/3 e, and the strange quark carries -1/3 e. The proton is made of two up quarks and one down quark (uud), giving a charge of +2/3 + 2/3 – 1/3 = +1, matching the proton’s +1 charge. The neutron is made of one up quark and two down quarks (udd), giving a charge of +2/3 – 1/3 – 1/3 = 0, matching the neutron’s neutrality. This addition of fractional charges is a classic exam calculation.

在 β⁻ 衰变中，原子核内一个下夸克转变为一个上夸克，这就是”中子变质子”的夸克层面的解释。β⁺ 衰变（正电子衰变）则相反，一个上夸克转变为下夸克，质子变成中子并发射一个正电子。理解夸克层面的变化，能帮助你写出任何 β 衰变方程，而不只是死记硬背。

In beta-minus decay, a down quark inside the nucleus changes into an up quark, which is the quark-level explanation of “a neutron becoming a proton”. Beta-plus decay (positron emission) is the opposite: an up quark changes into a down quark, so a proton becomes a neutron and a positron is emitted. Understanding the quark-level change helps you write down any beta decay equation rather than simply memorising it.

七、守恒定律：重子数、轻子数与奇异数 | Conservation Laws: Baryon Number, Lepton Number and Strangeness

粒子相互作用必须遵守若干守恒定律。除了我们已经熟悉的能量守恒、动量守恒和电荷守恒之外，粒子物理还有三条特有的守恒量：重子数（baryon number）、轻子数（lepton number）和奇异数（strangeness）。它们决定了哪些粒子相互作用是可能的，哪些是不可能的。

Particle interactions must obey several conservation laws. In addition to the familiar conservation of energy, momentum and charge, particle physics has three special conserved quantities: baryon number, lepton number and strangeness. These determine which particle interactions are possible and which are impossible.

重子数的规则是：每个重子（质子、中子等）的重子数为 +1，每个反重子为 -1，而介子和轻子的重子数为 0。轻子数进一步细分为电子轻子数和 μ 子轻子数，电子和电子中微子的电子轻子数为 +1，正电子和反电子中微子为 -1。在 β⁻ 衰变中，中子（重子数 +1）变为质子（+1）加电子（轻子数 +1）加反中微子（电子轻子数 -1），两边守恒。

The baryon number rule is: every baryon (proton, neutron and so on) has baryon number +1, every antibaryon has -1, while mesons and leptons have 0. Lepton number is further split into electron lepton number and muon lepton number; the electron and electron neutrino have electron lepton number +1, while the positron and electron antineutrino have -1. In beta-minus decay, a neutron (baryon number +1) becomes a proton (+1) plus an electron (lepton number +1) plus an antineutrino (electron lepton number -1), so both sides balance.

奇异数描述含有奇夸克的粒子的性质。奇夸克的奇异数为 -1，反奇夸克为 +1。K 介子含有奇夸克，因此具有非零奇异数。重要的是，奇异数只在强相互作用中守恒，在弱相互作用中可以不守恒。这个性质常用来判断某个衰变是通过强相互作用还是弱相互作用发生的：如果奇异数改变了，那么一定是弱相互作用。

Strangeness describes particles that contain strange quarks. The strange quark has strangeness -1 and the antistrange quark has +1. Kaons contain strange quarks and therefore have non-zero strangeness. Importantly, strangeness is conserved only in strong interactions, not in weak interactions. This property is often used to decide whether a decay happens via the strong or the weak force: if strangeness changes, the interaction must be weak.

八、粒子相互作用：湮灭与对产生 | Particle Interactions: Annihilation and Pair Production

当粒子遇到它的反粒子时，两者会互相湮灭（annihilation），它们的全部质量转化为能量。根据爱因斯坦的质能方程 E = mc²，湮灭产生的能量以两个光子的形式释放（通常发射两个方向相反的光子以同时满足动量守恒）。例如电子与正电子湮灭会产生两个伽马光子。

When a particle meets its antiparticle, the two annihilate each other, and all of their mass is converted into energy. According to Einstein’s mass-energy equation E = mc², the energy released in annihilation appears as two photons (usually emitted in opposite directions so that momentum is conserved). For example, an electron and a positron annihilating produce two gamma photons.

相反的物理过程是对产生（pair production）：一个高能光子可以在原子核附近转化为一个粒子和它的反粒子。为了让这一过程发生，光子的能量必须至少等于这对粒子的静止质量能量 2mc²。因为动量守恒需要一个第三方（原子核）来带走一部分动量，所以对产生通常发生在物质内部、靠近原子核的位置。

The reverse process is pair production: a high-energy photon can convert into a particle and its antiparticle near a nucleus. For this to happen, the photon’s energy must be at least equal to the rest-mass energy of the pair, 2mc². Because momentum conservation needs a third body (the nucleus) to carry away some momentum, pair production usually happens inside matter, close to a nucleus.

计算湮灭或对产生的能量时，你需要熟练运用 E = mc² 和 E = hf。例如，一个电子与正电子湮灭时，每个粒子的静止质量能量约为 0.511 MeV，因此至少释放约 1.022 MeV 的能量，表现为两个各约 0.511 MeV 的光子。这类题目考察的是把质量、能量和光子频率联系起来的综合能力。

When calculating the energy of annihilation or pair production, you need to use E = mc² and E = hf fluently. For example, when an electron and a positron annihilate, each particle has a rest-mass energy of about 0.511 MeV, so at least about 1.022 MeV of energy is released, appearing as two photons of about 0.511 MeV each. Questions like this test your ability to link mass, energy and photon frequency together.

九、光电效应：光如何打出电子 | The Photoelectric Effect: How Light Ejects Electrons

光电效应（photoelectric effect）是指金属表面在受到电磁辐射照射时发射电子的现象。经典波动理论预测，只要照射时间足够长，任何频率的光最终都应该能积累足够的能量打出电子，而且电子逸出后应具有连续变化的动能。然而实验观测结果完全相反，这是经典物理学无法解释的重大矛盾之一。

The photoelectric effect is the emission of electrons from a metal surface when electromagnetic radiation shines on it. Classical wave theory predicts that, given enough time, light of any frequency should eventually deliver enough energy to eject electrons, and that the emitted electrons should have a continuous range of kinetic energies. Yet the experimental results are the complete opposite, making this one of the great contradictions that classical physics could not explain.

实验发现的三条规律是：第一，存在一个最低频率（阈值频率 f₀），低于该频率的光无论多强、照多久都无法打出电子；第二，光电子的最大动能只取决于光的频率，而与光的强度无关；第三，只要频率高于阈值，即使光强很弱，电子也会立即被发射，没有时间延迟。这些规律只有用光子模型才能解释。

The experiment revealed three laws: first, there is a minimum frequency (the threshold frequency f₀), below which light cannot eject electrons no matter how intense it is or how long it shines; second, the maximum kinetic energy of the photoelectrons depends only on the frequency of the light, not on its intensity; third, provided the frequency is above the threshold, electrons are emitted instantly even at very low intensity, with no time delay. Only the photon model can explain these laws.

爱因斯坦用光子模型解释了光电效应：每个电子只能吸收一个光子。如果光子能量 hf 小于从金属表面逸出所需的最小能量（逸出功 φ，work function），电子就无法逸出；如果 hf 大于 φ，多余的能量转化为电子的动能。这就是爱因斯坦光电方程：hf = φ + Ek_max，其中 Ek_max 是逸出电子的最大动能。光强增大只是增加了光子的数量（从而增加电子数量），并不改变单个光子的能量。

Einstein explained the photoelectric effect using the photon model: each electron can absorb only one photon. If the photon energy hf is less than the minimum energy needed to escape the metal surface (the work function φ), the electron cannot escape; if hf is greater than φ, the excess energy becomes the electron’s kinetic energy. This is Einstein’s photoelectric equation: hf = φ + Ek_max, where Ek_max is the maximum kinetic energy of the emitted electrons. Increasing the intensity only increases the number of photons (and hence the number of electrons), not the energy of any individual photon.

考试常考的内容包括：根据阈值频率计算逸出功（φ = hf₀）、利用光电方程求电子最大动能、以及解释光强和频率对电子发射的不同影响。注意把频率换算成光子能量时单位要保持一致，逸出功通常以电子伏（eV）或焦耳给出。你还应能画出最大动能随频率变化的图像，其斜率就是普朗克常数 h。

Common exam content includes: calculating the work function from the threshold frequency (φ = hf₀), using the photoelectric equation to find the maximum kinetic energy of electrons, and explaining how intensity and frequency affect electron emission differently. Keep units consistent when converting frequency to photon energy; the work function may be given in electron-volts (eV) or joules. You should also be able to sketch the graph of maximum kinetic energy against frequency, whose gradient is Planck’s constant h.

十、能级与光子发射：原子为何发出特定波长的光 | Energy Levels and Photon Emission: Why Atoms Emit Light at Specific Wavelengths

原子内的电子只能占据某些特定的、离散的能级（energy level），而不能处于任意能量状态。电子处于最低能级时称为基态（ground state），吸收能量后会跃迁到较高的能级，称为激发态（excited state）。这个能级是量子化的（quantised），也就是说能量只能取一系列分立的值，这正是”量子”一词的由来。

Electrons inside an atom can occupy only certain specific, discrete energy levels, never arbitrary energy states. When an electron is in the lowest level it is in the ground state; after absorbing energy it jumps to a higher level, called an excited state. These levels are quantised, meaning the energy can take only a set of discrete values, which is exactly where the word “quantum” comes from.

当电子从高能级跃迁回低能级时，它会把两能级之间的能量差以一个光子的形式发射出来。光子的能量等于两个能级的能量差：hf = E₁ – E₂。由于能级是离散的，发射的光子只能具有某些特定频率，这就解释了为什么每种元素都有自己独特的发射光谱（emission spectrum），就像指纹一样独一无二。

When an electron drops from a higher level back to a lower one, it emits the energy difference between the two levels as a single photon. The photon energy equals the difference between the two energy levels: hf = E₁ – E₂. Because the levels are discrete, the emitted photons can have only certain specific frequencies, which explains why every element has its own unique emission spectrum, as distinctive as a fingerprint.

氢原子的能级可以用公式计算，基态能量为 -13.6 eV。从 n = 2 跃迁到 n = 1 时发射的光子能量约为 10.2 eV，属于紫外线；从 n = 3 到 n = 2 的跃迁发射约 1.9 eV，属于可见光。考试常要求你根据能级图计算发射或吸收的光子能量、频率和波长。注意：能级图中的数值是相对基态的能量，计算能级差时直接相减即可。

The energy levels of the hydrogen atom can be calculated, with a ground-state energy of -13.6 eV. The transition from n = 2 to n = 1 emits a photon of about 10.2 eV, in the ultraviolet; the transition from n = 3 to n = 2 emits about 1.9 eV, in the visible range. Exams often ask you to calculate the energy, frequency and wavelength of an emitted or absorbed photon from an energy-level diagram. Note that the values on an energy-level diagram are measured relative to the ground state, so you simply subtract the two levels to find the difference.

十一、波粒二象性与德布罗意波长 | Wave-Particle Duality and the de Broglie Wavelength

光表现出波粒二象性（wave-particle duality）：在干涉和衍射实验中它表现得像波，而在光电效应中它表现得像粒子（光子）。德布罗意（de Broglie）大胆地提出，如果光这种”波”能表现出粒子性，那么电子这类”粒子”也应该能表现出波动性。他认为任何运动的粒子都对应一个波长，称为德布罗意波长。

Light shows wave-particle duality: in interference and diffraction experiments it behaves like a wave, while in the photoelectric effect it behaves like a particle (a photon). De Broglie boldly proposed that if light, a “wave”, can behave like a particle, then “particles” such as electrons should also behave like waves. He suggested that any moving particle has an associated wavelength, called the de Broglie wavelength.

德布罗意波长的公式为 λ = h/mv = h/p，其中 p 是粒子的动量，m 是质量，v 是速度。这个公式揭示了为什么我们平时观察不到宏观物体的波动性：因为普朗克常数 h 极其微小，一个宏观物体的质量 m 又很大，所以它的德布罗意波长小到无法测量。只有像电子这样质量极小的粒子，其德布罗意波长才足够大，能够被实验观测到。

The de Broglie wavelength is given by λ = h/mv = h/p, where p is the particle’s momentum, m its mass and v its speed. This formula reveals why we never observe wave behaviour in everyday objects: Planck’s constant h is extremely small while a macroscopic object’s mass m is large, so its de Broglie wavelength is far too small to measure. Only particles with tiny mass, such as electrons, have a de Broglie wavelength large enough to be observed experimentally.

电子衍射实验证实了电子的波动性：一束电子穿过薄晶体时，会形成与 X 射线衍射相同的衍射图样，这说明电子确实表现得像波。这个发现最终导致了电子显微镜的发明，因为电子的德布罗意波长比可见光短得多，所以电子显微镜的分辨率远高于光学显微镜。考试中常要求你计算运动电子的德布罗意波长，注意先把动能换算成速度或动量。

Electron diffraction confirmed the wave nature of electrons: a beam of electrons passing through a thin crystal produces the same diffraction pattern as X-rays, showing that electrons really do behave like waves. This discovery eventually led to the invention of the electron microscope, because the de Broglie wavelength of an electron is far shorter than visible light, giving the electron microscope a much higher resolution than an optical microscope. Exams often ask you to calculate the de Broglie wavelength of a moving electron; remember to convert kinetic energy into speed or momentum first.

Summary | 总结

本单元”粒子与辐射”是 AQA A-Level 物理的基础，它把物理学的视野从宏观世界带入了原子与亚原子的微观世界。我们学习了原子的三种基本粒子、同位素与核符号，掌握了 α、β、γ 三种放射性衰变；理解了光子模型和 E = hf 公式，并据此对粒子进行分类，认识了强子、轻子、夸克以及重子数、轻子数和奇异数三条守恒定律；最后，通过光电效应、能级与波粒二象性，我们看到了量子理论的威力。

The “Particles and Radiation” unit is the foundation of AQA A-Level Physics, taking the perspective of physics from the macroscopic world down into the microscopic world of atoms and subatomic particles. We learned the three fundamental particles of the atom, isotopes and nuclide notation, and mastered the three radioactive decays (alpha, beta and gamma). We understood the photon model and the formula E = hf, used this to classify particles, and met hadrons, leptons, quarks and the three conservation laws of baryon number, lepton number and strangeness. Finally, through the photoelectric effect, energy levels and wave-particle duality, we saw the power of quantum theory.

在备考时，建议你重点练习以下题型：原子组成与核符号的换算、核反应方程的书写与守恒验证、光子能量与波长的计算、夸克组成与粒子分类的判断、光电效应的三条规律与爱因斯坦光电方程、以及德布罗意波长的计算。这些题型覆盖了本单元几乎所有考试要点，熟练掌握后，你就能在这一部分的考试中取得理想的成绩。

When revising, focus on the following question types: converting atomic composition and nuclide notation, writing nuclear equations and checking conservation, calculating photon energy and wavelength, judging quark composition and particle classification, the three laws of the photoelectric effect together with Einstein’s photoelectric equation, and calculating the de Broglie wavelength. These cover almost every exam point in the unit, and once you master them you will be well placed to score highly on this section of the exam.

更多咨询请联系16621398022（同微信）