Quantum Physics for CIE A-Level: Photons, the Photoelectric Effect and Wave-Particle Duality | CIE A-Level 量子物理：光子、光电效应与波粒二象性

📚 Quantum Physics for CIE A-Level: Photons, the Photoelectric Effect and Wave-Particle Duality | CIE A-Level 量子物理：光子、光电效应与波粒二象性

Quantum physics is the study of physical processes at the scale of atoms, photons and electrons. For CIE A-Level Physics, the quantum physics topic focuses on the particle nature of electromagnetic radiation, the photoelectric effect, energy levels in atoms and the wave-particle duality of both light and matter.

量子物理研究原子、光子和电子尺度的物理过程。在 CIE A-Level 物理中，量子物理主题重点包括电磁辐射的粒子性、光电效应、原子能级以及光与物质的波粒二象性。

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1. Energy Quantisation and Photons | 能量量子化与光子

The energy of a photon is directly proportional to the frequency of the radiation. This relationship was first proposed by Planck to explain black-body radiation, and it is now written as:

光子的能量与辐射频率成正比。这一关系最初由普朗克为解释黑体辐射而提出，现在写成：

E = h f

Here E is the photon energy in joules (J), h is the Planck constant (6.63 × 10⁻³⁴ J s), and f is the frequency in hertz (Hz). Using c = f λ, the photon energy can also be written as E = h c / λ, which shows that shorter wavelength radiation carries more energy per photon.

其中 E 是光子能量（单位焦耳 J），h 是普朗克常量（6.63 × 10⁻³⁴ J s），f 是频率（单位赫兹 Hz）。利用 c = f λ，光子能量也可写成 E = h c / λ，说明波长越短，单个光子携带的能量越大。

In atomic and quantum physics, the electronvolt is often more convenient: 1 eV = 1.60 × 10⁻¹⁹ J. To convert a photon energy from joules to electronvolts, divide by 1.60 × 10⁻¹⁹.

在原子物理和量子物理中，电子伏特更为常用：1 eV = 1.60 × 10⁻¹⁹ J。要把光子能量从焦耳换算为电子伏特，除以 1.60 × 10⁻¹⁹ 即可。

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2. The Photoelectric Effect: Key Observations | 光电效应：关键实验现象

The photoelectric effect is the emission of electrons from a metal surface when electromagnetic radiation above a certain frequency falls on it. A classic demonstration uses a clean zinc plate attached to a negative electroscope. When ultraviolet light is shone on the zinc, the gold leaf collapses because photoelectrons are emitted and the negative charge leaks away.

光电效应是当频率高于某一值的电磁辐射照射金属表面时，金属发射电子的现象。经典演示使用连接在负验电器上的洁净锌板。当紫外线照射锌板时，金箔下垂，因为发射出光电子，负电荷泄漏。

The key experimental observations are:

关键实验现象如下：

• Emission is instantaneous when the frequency is above the threshold frequency.

  当频率高于极限频率时，发射是瞬时的。

• No electrons are emitted below the threshold frequency, no matter how intense the light is.

  低于极限频率时，无论光强多大，都没有电子发射。

• Increasing intensity increases the photoelectric current but does not increase the maximum kinetic energy of the electrons.

  增大光强会增加光电流，但不会增大光电子的最大动能。

• Increasing frequency above the threshold increases the maximum kinetic energy of the emitted electrons.

  增大高于极限频率的光的频率，会增加发射电子的最大动能。

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3. Work Function and Threshold Frequency | 逸出功与极限频率

The work function φ is the minimum energy required for an electron to escape from the surface of a particular metal. The threshold frequency f₀ is related to the work function by:

逸出功 φ 是电子从特定金属表面逸出所需的最小能量。极限频率 f₀ 与逸出功的关系为：

φ = h f₀

If a photon has energy less than φ, a single photon cannot supply enough energy to liberate an electron. This explains why the photoelectric effect has a sharp frequency cutoff.

如果光子的能量小于 φ，单个光子无法提供足够能量使电子逸出。这就解释了光电效应为什么会有一个明确的频率截止值。

Metal	Work function φ / eV
Sodium	2.28
Calcium	2.87
Zinc	4.24
Copper	4.70
Gold	5.10

Metals with a low work function, such as sodium, emit photoelectrons from visible light, whereas metals with a high work function, such as gold, need ultraviolet or higher-frequency radiation.

逸出功较低的金属（如钠）可在可见光下发射光电子，而逸出功较高的金属（如金）则需要紫外线或更高频率的辐射。

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4. Einstein’s Photoelectric Equation | 爱因斯坦光电方程

Einstein proposed that light consists of photons and that each photoelectron absorbs a single photon. Energy conservation gives Einstein’s photoelectric equation:

爱因斯坦提出光由光子组成，每个光电子吸收一个光子。能量守恒给出爱因斯坦光电方程：

h f = φ + Kₘₐₓ

Here Kₘₐₓ is the maximum kinetic energy of the emitted electron. The minimum energy needed to remove the electron is the work function φ; any remaining photon energy appears as electron kinetic energy.

其中 Kₘₐₓ 是发射光电子的最大动能。移走电子所需的最小能量是逸出功 φ；剩余的光子能量则转化为电子的动能。

The maximum kinetic energy can be measured by applying a retarding potential difference. When the photocurrent just falls to zero, the stopping potential Vₛ satisfies e Vₛ = Kₘₐₓ, so:

最大动能可通过施加反向电压来测量。当光电流刚好降为零时，遏止电压 Vₛ 满足 e Vₛ = Kₘₐₓ，因此：

e Vₛ = h f – φ

This equation shows a linear relationship between the stopping potential and the frequency. The gradient is h/e and the frequency-axis intercept gives the threshold frequency f₀.

该方程表明遏止电压与频率成线性关系。斜率为 h/e，频率轴截距给出极限频率 f₀。

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5. Photon Model vs Wave Model | 光子模型与波动模型的对比

The classical wave model predicted that any frequency of light could eventually eject electrons if the light was intense enough, and that there should be a time delay while energy accumulated. These predictions contradict the experimental observations.

经典波动模型预测，只要光强足够，任何频率的光最终都能打出电子，并且能量积累需要一定的时间延迟。这些预测与实验观察相矛盾。

Observation	Wave model prediction	Photon model prediction
Threshold frequency	No sharp cutoff expected	Emission requires h f ≥ φ
Time delay	Energy builds up over time	Emission is immediate
Effect of intensity	Higher intensity gives higher Kₘₐₓ	Higher intensity gives more photons per second, so larger current
Effect of frequency	Frequency should not affect Kₘₐₓ	Higher frequency gives higher photon energy, so larger Kₘₐₓ

The photon model successfully accounts for all four key observations: one photon interacts with one electron, and the electron is emitted only if the photon energy is at least equal to the work function.

光子模型成功解释了全部四个关键现象：一个光子与一个电子相互作用，并且只有光子能量至少等于逸出功时电子才会被发射。

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6. Wave-Particle Duality for Light | 光的波粒二象性

Light shows wave behaviour in interference and diffraction experiments, but it shows particle behaviour in the photoelectric effect and in Compton scattering. The two descriptions are complementary: neither one alone explains all observations.

光在干涉和衍射实验中表现出波动行为，但在光电效应

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