E: Nuclear and Quantum Physics | E：核与量子物理

📚 E: Nuclear and Quantum Physics | E：核与量子物理

IB Physics Option E: Nuclear and Quantum Physics brings together two of the most profound revolutions in modern physics. From the particle‑like behaviour of light to the probabilistic nature of matter and the immense energy locked inside atomic nuclei, this option builds a foundation for understanding phenomena that classical physics cannot explain. The following notes cover the key concepts, equations, and applications required for both SL and HL students, with careful attention to the IB syllabus.

IB 物理选项 E：核与量子物理汇集了现代物理中两次最深刻的革命。从光的粒子行为到物质的概率本质，再到原子核内蕴藏的巨大能量，这一选项为了解经典物理无法解释的现象奠定了基石。以下笔记涵盖了 SL 和 HL 学生需要掌握的关键概念、方程及应用，严格依据 IB 大纲编写。

1. Photoelectric Effect and Photon Model | 光电效应与光子模型

The photoelectric effect is the emission of electrons from a metal surface when light of sufficiently high frequency shines on it. Classical wave theory predicts that any frequency of light, given enough intensity, should eventually eject electrons, and that there should be a time delay. Neither prediction matches experiment.

光电效应是指当足够高频率的光照射金属表面时，会有电子发射出来。经典波动理论预言，任何频率的光只要强度足够，最终都能打出电子，并且应该存在时间延迟。但这两个预言都与实验不符。

Einstein explained the effect by treating light as a stream of photons, each carrying energy E = hf, where h is Planck's constant and f is the frequency. When a photon strikes a metal, its energy is transferred to a single electron. The electron must do work Φ (the work function) to escape the surface, so its maximum kinetic energy is given by the equation:

爱因斯坦用光子理论解释了这一效应：光被视作一束光子流，每个光子携带能量 E = hf，其中 h 为普朗克常量，f 为频率。当光子撞击金属时，能量将转移给单个电子。电子必须克服逸出功 Φ 才能脱离表面，因此其最大动能由下式给出：

Eₖ = hf – Φ

. Increasing the intensity of light increases the number of photons, hence the photoelectric current, but does not change the maximum kinetic energy of the ejected electrons.

阈值频率 f₀ 是能够发射电子的最低频率，f₀ = Φ/h。增大光强只会增加光子数目，从而提高光电流，却不会改变发射电子的最大动能。

2. De Broglie Matter Waves and Wave–Particle Duality | 德布罗意物质波与波粒二象性

can behave as both a wave and a particle, then particles of matter might also exhibit wave‑ e with momentum p has an associated wavelength λ = h/p. This is the de Broglie wavelength.

既然光可以同时表现出波和粒子的性质，那么物质粒子也可能展现波动性。路易·德布罗意提出，任何动量为 p 的运动粒子都对应一个波长 λ = h/p，即德布罗意波长。

Experimental evidence came from the diffraction of electrons by a thin metal foil (Davisson–Germer experiment) and from electron diffraction through graphite. Both experiments produced interference patterns identical to those expected for waves, confirming that electrons have wave nature.

实验证据来自电子通过薄金属箔的衍射（戴维孙‑革末实验）和电子穿过石墨的衍射。这两个实验都产生了与波完全相同的干涉图样，证实了电子具有波动性。

Wave‑particle duality is a central concept: all quantum entities exhibit both particle and wave behaviour, but which aspect is observed depends on the type of measurement.

波粒二象性是核心概念：所有量子实体都同时表现出粒子和波的行为，但具体观察到哪一面取决于测量方式。

λ = h / p = h / (mv)

3. Atomic Spectra and Energy Levels | 原子光谱与能级

a higher energy level E₂ to a lower level E₁, the energy difference is released as a photon of frequency f given by E₂ – ne spectra. Conversely, an atom can absorb a photon and jump to a higher level, producing absorption spectra.

当原子中的电子从高能级 E₂ 跃迁到低能级 E₁ 时，能量差以光子的形式释放，其频率满足 E₂ – E₁ = hf，由此产生发射线光谱。反之，原子也可吸收光子跃迁到高能级，形成吸收光谱。

(n = 3) is infrared. The discrete lines support the existence of quantised energy levels.

对氢原子而言，巴耳末系在可见光区域，对应终结于 n = 2 的跃迁；莱曼系（n = 1）位于紫外区，帕邢系（n = 3）位于红外区。这些分立的谱线支持了能级量子化的观点。

The energy of each level in hydrogen is given by Eₙ = –13.6 eV/n². Transitions are drawn in an energy‑level diagram, and the photon’s wavelength can be found from ΔE = hc/λ.

氢原子各能级的能量为 Eₙ = –13.6 eV/n²。可在能级图中画出跃迁，并通过 ΔE = hc/λ 求出光子的波长。

4. Heisenberg Uncertainty Principle | 海森堡不确定性原理

The Heisenberg uncertainty principle states that it is impossible to simultaneously measure both the position and momentum of a particle with arbitrary precision. The more accurately we know one, the less accurately we know the other.

海森堡不确定性原理指出，不可能同时以任意精度测量粒子的位置和动量——对其中一个知道得越精确，对另一个就知道得越不精确。

Δx Δp ≥ h / (4π)

The quantity h/(4π) is often written as ħ t. A similar relation exists for energy and time: ΔE Δt ≥ h/(4π), which explains why short‑lived states have a large uncertainty in energy.

h/(4π) 常用约化普朗克常量 ħ/2 表示。类似地，能量和时间也满足 ΔE Δt ≥ h/(4π)，这解释了为什么寿命极短的态其能量不确定性很大。

The uncertainty principle is not a statement about measurement disturbance but a fundamental limit arising from the wave nature of matter. It has far‑reaching consequences, including the explanation of electron diffraction and the stability of atoms.

不确定性原理并非关于测量干扰的声明，而是由物质波动本性产生的基本限制。它影响深远，可解释电子衍射以及原子稳定性。

5. Nuclear Structure, Mass Defect, and Binding Energy | 核结构、质量亏损与结合能

The nucleus consists of protons and neutrons (nucleons) held together by the strong nuclear force. The atomic number Z is the number of protons, and the mass number A is the total number of nucleons. Isotopes are nuclei with the same Z but different N (neutron number).

原子核由质子和中子（统称核子）组成，依靠强核力结合在一起。原子序数 Z 为质子数，质量数 A 为核子总数。同位素是指 Z 相同而中子数 N 不同的核素。

, this mass defect is equivalent to the binding energy Eb that holds the nucleus together:

实测的原子核质量总是略小于其所有核子质量之和，这一亏损的质量 Δm 称为质量亏损。根据 E = mc²，质量亏损相当于将核子束缚在一起的结合能 E_b：

E_b = Δm c²

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Binding energy per nucleon (E_b/A) measures the stability of a nucleus. The iron‑nickel region has the highest binding energy per nucleon, so nuclei lighter than iron tend to release energy through fusion, while heavier ones release energy through fission.

平均结合能（E_b/A）是衡量核稳定性的量。铁‑镍区域拥有最高的平均结合能，因此比铁轻的原子核倾向于通过聚变释放能量，而比铁重的原子核则通过裂变释放能量。

6. Radioactive Decay and Half‑Life | 放射性衰变与半衰期

e nucleus emits radiation. The three common types are alpha decay (emission of ⁴₂He), beta‑minus decay (n → p + e⁻ + ν̅ₑ), beta‑plus decay (p → n + e⁺ + νₑ), and gamma decay (emission of a high‑energy photon).

放射性衰变是一种随机过程，不稳定的原子核会发射辐射。常见的衰变类型有：α 衰变（放出 ⁴₂He）、β⁻ 衰变（n → p + e⁻ + ν̅ₑ）、β⁺ 衰变（p → n + e⁺ + νₑ）以及 γ 衰变（放出高能光子）。

= N₀ e⁻λᵗ, where λ is the decay constant. Activity A = λN decreases exponentially as well.

未衰变核的数目 N 随时间 t 按指数规律衰减：N = N₀ e⁻λᵗ，λ 为衰变常量。放射性活度 A = λN 也呈指数衰减。

The half‑ λ by T₁/₂ = ln 2 / λ. This concept is crucial for radiometric dating and medical tracers.

半衰期 T₁/₂ 是指一半核发生衰变所需的时间，与衰变常量的关系为 T₁/₂ = ln 2 / λ。这一概念在放射性测年和医用示踪剂中至关重要。

7. Nuclear Reactions and Mass–Energy Equation | 核反应与质能方程

nucleons and the total charge are conserved. The energy released or absorbed, called the Q‑ comes from the difference in total rest mass between the reactants and products: Q = (Σmᵢₙ – Σmₒᵤₜ)c².

在核反应中，总核子数和总电荷是守恒的。释放或吸收的能量（Q 值）来源于反应物与生成物总静止质量的差异：Q = (Σm_in – Σm_out)c²。

Einstein’s mass– hy tiny mass changes can yield enormous energies. This is the principle behind both nuclear power and nuclear weapons.

爱因斯坦的质能等价关系 E = mc² 解释了为何微小的质量变化能产生巨大能量。这是核动力与核武器的基本原理。

A sample reaction is the fission of uranium‑ ₆Kr + 3¹₀n. Calculating the mass defect before and after yields the total energy released.

一个典型的反应是铀‑235 的裂变：²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n。计算反应前后的质量亏损即可得出释放的总能量。

8. Nuclear Fission and Fusion | 核裂变与核聚变

Fission is the splitting of a heavy nucleus into two lighter fragments, accompanied by the release of several neutrons and a large amount of energy. Uranium‑235 undergoes induced fission when it captures a slow (thermal) neutron. A chain reaction is possible if at least one of the released neutrons goes on to cause further fission.

裂变是指重核分裂成两个较轻的碎片，同时释放出几个中子和大量能量。铀‑235 吸收一个慢（热）中子后会发生诱发裂变。如果释放的中子中至少有一个可以继续引发裂变，就可能形成链式反应。

Critical mass and moderators (such as water or graphite) are used in nuclear reactors to control the chain reaction. Control rods absorb excess neutrons to maintain a steady rate.

在核反应堆中，临界质量和慢化剂（如水或石墨）用于控制链式反应。控制棒吸收过剩中子，以维持稳定的反应速率。

Fusion is the joining of two light nuclei, such as deuterium and tritium, to form a heavier nucleus, releasing even more energy per nucleon than fission. Fusion powers the Sun and holds promise for future energy generation, but it requires extremely high temperatures to overcome the Coulomb barrier.

聚变是两个轻核（如氘和氚）结合成一个较重核的过程，每核子释放的能量比裂变还要多。聚变为太阳提供能量，并且有望成为未来的能源，但它需要极高的温度才能克服库仑势垒。

9. Elementary Particles and the Standard Model | 基本粒子与标准模型简介

The Standard Model classifies all known elementary particles into quarks, leptons, and gauge bosons. Quarks (up, down, charm, strange, top, bottom) combine to form hadrons, such as protons (uud) and neutrons (udd). Leptons include the electron, muon, tau, and their associated neutrinos.

标准模型将所有已知的基本粒子分为夸克、轻子和规范玻色子三类。夸克（上、下、粲、奇、顶、底）组合成强子，如质子（uud）和中子（udd）。轻子包括电子、μ子、τ子及相应的中微子。

Each particle has a corresponding antiparticle with the same mass but opposite charge and quantum numbers. For example, the positron (e⁺) is the antiparticle of the electron.

每种粒子都有对应的反粒子，其质量相同但电荷和量子数相反。例如正电子（e⁺）是电子的反粒子。

Gauge bosons mediate the fundamental forces: the photon for electromagnetism, the W⁺, W⁻, and Z⁰ for the weak interaction, and the gluon for the strong interaction. The Higgs boson gives particles mass.

规范玻色子传递基本相互作用：光子传递电磁力，W⁺、W⁻ 和 Z⁰ 传递弱相互作用，胶子传递强相互作用。希格斯玻色子赋予粒子质量。

10. Quarks, Leptons, and Conservation Laws | 夸克、轻子与守恒定律

Quarks carry fractional electric charges: up +⅔e, down –⅓e, charm +⅔e, strange –⅓e, top +⅔e, bottom –⅓e. Mesons are quark‑antiquark pairs, while baryons are three‑quark combinations. The strong force confines quarks within hadrons; they are never observed in isolation.

夸克带有分数电荷：上夸克 +⅔e，下夸克 –⅓e，粲夸克 +⅔e，奇夸克 –⅓e，顶夸克 +⅔e，底夸克 –⅓e。介子由正反夸克对组成，重子由三个夸克组成。强相互作用将夸克禁闭在强子内部，从未观察到孤立夸克。

ese laws determine which reactions are possible. For example, neutron decay n → p + e⁻ + ν̅ₑ conserves both baryon number and lepton number.

守恒定律支配着粒子相互作用：重子数、轻子数（每个轻子家族分别守恒）、电荷数和奇异数（在强相互作用中）均守恒。这些定律决定了哪些反应可以发生。例如，中子衰变 n → p + e⁻ + ν̅ₑ 同时守恒重子数和轻子数。

The observation of neutrino oscillations implies that neutrinos have a tiny mass, an area of active research that goes slightly beyond the IB syllabus but illustrates the evolving nature of particle physics.

中微子振荡的观测暗示中微子具有微小质量，这虽略超出IB大纲，却显示了粒子物理不断发展的特征。

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Published by TutorHao | Physics Revision Series | aleveler.com

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