CIE A-Level Physics: The Photoelectric Effect — Complete Guide | 光电效应完全指南

The photoelectric effect is one of the most important topics in CIE A-Level Physics (9702). It not only appears regularly in Paper 2 and Paper 4 examinations but also represents a pivotal moment in the history of physics — the experiment that classical wave theory could not explain, and the phenomenon that launched quantum physics. This comprehensive bilingual guide covers every aspect of the topic, from experimental observations to Einstein’s Nobel Prize-winning explanation, complete with worked examples and examination tips.

光电效应是CIE A-Level物理（9702）中最重要的主题之一。它不仅经常出现在Paper 2和Paper 4考试中，还代表了物理学史上的一个关键时刻——经典波动理论无法解释的实验，以及开创量子物理学的现象。这份全面的双语指南涵盖了该主题的各个方面，从实验观察到爱因斯坦获得诺贝尔奖的解释，包括完整例题和考试技巧。

1. What Is the Photoelectric Effect? | 什么是光电效应？

The photoelectric effect is the emission of electrons from a metal surface when electromagnetic radiation (light) of sufficiently high frequency shines on it. The emitted electrons are called photoelectrons.

光电效应是指当频率足够高的电磁辐射（光）照射到金属表面时，电子从金属表面发射出来的现象。发射出的电子称为光电子。

The effect was first observed by Heinrich Hertz in 1887 during his experiments on electromagnetic waves. He noticed that a spark jumped more readily between two electrodes when ultraviolet light illuminated the negatively charged electrode. This accidental discovery would later revolutionize our understanding of light and matter.

这一效应最早由海因里希·赫兹于1887年在进行电磁波实验时观察到。他注意到，当紫外光照射到带负电的电极时，两个电极之间更容易产生火花。这一偶然发现后来彻底改变了我们对光和物质的理解。

2. Experimental Observations — The Gold Leaf Electroscope | 实验观察 — 金箔验电器

A classic demonstration of the photoelectric effect uses a gold leaf electroscope with a zinc plate attached to its top. The key observations are:

光电效应的经典演示使用金箔验电器，其顶部附有一块锌板。关键观察结果如下：

• Ultraviolet light on a negatively charged zinc plate → the gold leaf collapses (electrons are ejected, neutralising the negative charge)
• Visible light on a negatively charged zinc plate → no effect (frequency too low)
• UV light on a positively charged zinc plate → no effect (positive charge attracts electrons back)

• 紫外光照射带负电的锌板 → 金箔下垂（电子被发射出去，中和了负电荷）
• 可见光照射带负电的锌板 → 无效果（频率太低）
• 紫外光照射带正电的锌板 → 无效果（正电荷将电子吸引回来）

3. The Four Key Observations | 四个关键观察结果

Through careful experimentation, scientists identified four crucial characteristics of the photoelectric effect. These observations form the foundation of examination questions on this topic.

通过仔细的实验，科学家们确定了光电效应的四个关键特征。这些观察结果构成了该主题考试题目的基础。

Observation 1: Threshold Frequency | 观察一：阈值频率

For a given metal, there exists a minimum frequency of incident radiation below which no photoelectrons are emitted, regardless of the intensity (brightness) of the light. This minimum frequency is called the threshold frequency (f₀).

对于给定的金属，存在一个入射辐射的最低频率，低于该频率时，无论光的强度（亮度）如何，都不会有光电子发射出来。这个最低频率称为阈值频率（f₀）。

Metal 金属	Work Function φ / eV 功函数	Threshold Frequency f₀ / Hz 阈值频率
Sodium 钠 (Na)	2.3 eV	5.56 × 10¹⁴
Zinc 锌 (Zn)	4.3 eV	1.04 × 10¹⁵
Potassium 钾 (K)	2.0 eV	4.84 × 10¹⁴
Calcium 钙 (Ca)	2.9 eV	7.01 × 10¹⁴
Gold 金 (Au)	5.1 eV	1.23 × 10¹⁵

Observation 2: Instantaneous Emission | 观察二：瞬时发射

Photoelectrons are emitted instantaneously — there is no time delay between the light hitting the surface and the emission of electrons, even at very low intensities. This was impossible to explain with classical wave theory, which predicted that electrons would need time to accumulate enough energy from the incoming waves.

光电子是瞬时发射的——在光照射到表面与电子发射之间没有时间延迟，即使在非常低的强度下也是如此。经典波动理论无法解释这一点，该理论预测电子需要时间来从入射波中积累足够的能量。

Observation 3: Maximum Kinetic Energy Depends on Frequency | 观察三：最大动能取决于频率

The maximum kinetic energy of the emitted photoelectrons depends only on the frequency of the incident light, not on its intensity. Increasing the intensity of light above the threshold frequency increases the number of photoelectrons emitted (the photocurrent), but does not increase their maximum kinetic energy.

发射光电子的最大动能仅取决于入射光的频率，而非其强度。在阈值频率之上增加光强度会增加发射光电子的数量（光电流），但不会增加它们的最大动能。

Observation 4: Light Intensity and Photocurrent | 观察四：光强度与光电流

For frequencies above the threshold frequency, the photocurrent (number of photoelectrons emitted per second) is directly proportional to the intensity of the incident light. This makes sense because higher intensity means more photons arriving per second, each capable of liberating one electron.

对于高于阈值频率的频率，光电流（每秒发射的光电子数量）与入射光的强度成正比。这很合理，因为更高的强度意味着每秒有更多的光子到达，每个光子都能释放一个电子。

4. Classical Wave Theory Fails | 经典波动理论的失败

Classical electromagnetic wave theory made three predictions about the photoelectric effect — and all three were contradicted by experimental evidence:

经典电磁波理论对光电效应做出了三个预测——而这三个预测都被实验证据推翻了：

Prediction of Classical Theory 经典理论预测	Experimental Fact 实验事实	Conclusion 结论
Any frequency should work if light is intense enough	Threshold frequency exists — no electrons below f₀ regardless of intensity	Classical theory FAILS
There should be a time delay at low intensities as electrons absorb energy from the wave	Emission is instantaneous even at the lowest intensities	Classical theory FAILS
Higher intensity should produce higher-energy electrons	Maximum K.E. depends on frequency, not intensity	Classical theory FAILS

The resolution came from a completely new way of thinking about light — proposed by Albert Einstein in 1905.

解决方案来自于一种全新的思考光的方式——由阿尔伯特·爱因斯坦于1905年提出。

5. Einstein’s Photon Model (1905) | 爱因斯坦的光子模型（1905年）

Einstein proposed that electromagnetic radiation consists of discrete packets (quanta) of energy called photons. Each photon has energy:

爱因斯坦提出，电磁辐射由称为光子的离散能量包（量子）组成。每个光子具有能量：

E = hf

Where:

• E = energy of one photon (J) | 一个光子的能量（焦耳）
• h = Planck constant = 6.63 × 10⁻³⁴ J s | 普朗克常数
• f = frequency of the radiation (Hz) | 辐射频率（赫兹）

Using the wave equation c = fλ, we can also write:

使用波动方程 c = fλ，我们也可以写成：

E = hc / λ

Where:

• c = speed of light = 3.00 × 10⁸ m s⁻¹ | 光速
• λ = wavelength of the radiation (m) | 辐射波长（米）

In the photon model, each photon interacts with a single electron in the metal in a one-to-one process. The electron either absorbs the entire photon energy or none at all — there is no partial absorption. This is the key insight that explains all the experimental observations.

在光子模型中，每个光子以一对一的方式与金属中的一个电子相互作用。电子要么吸收整个光子能量，要么完全不吸收——没有部分吸收。这是解释所有实验观察结果的关键见解。

6. Work Function and the Photoelectric Equation | 功函数与光电方程

To escape from the metal surface, an electron must overcome the attractive forces binding it to the metal. The minimum energy required to remove an electron from the surface of a metal is called the work function (φ).

为了从金属表面逃逸，电子必须克服将其束缚在金属上的吸引力。将电子从金属表面移除所需的最小能量称为功函数（φ）。

Einstein’s photoelectric equation is:

爱因斯坦的光电方程是：

hf = φ + KE_max

Where:

• hf = energy of the incident photon | 入射光子能量
• φ = work function of the metal | 金属的功函数
• KE_max = maximum kinetic energy of the emitted photoelectron | 发射光电子的最大动能

This equation can be rearranged to:

该方程可以重新排列为：

KE_max = hf − φ

This is a linear equation of the form y = mx + c, where plotting KE_max against f gives a straight line with gradient h and y-intercept −φ.

这是一个y = mx + c形式的线性方程，其中绘制KE_max对f的图会得到一条斜率为h、y截距为−φ的直线。

7. The Stopping Potential | 遏止电势

The stopping potential (V_s) is the minimum reverse potential difference that must be applied between the photocathode and anode to stop even the most energetic photoelectrons from reaching the anode, reducing the photocurrent to zero.

遏止电势（V_s）是在光电阴极和阳极之间必须施加的最小反向电势差，以阻止即使是最具能量的光电子到达阳极，使光电流降至零。

The relationship is:

关系式为：

eV_s = KE_max

Where e = elementary charge = 1.60 × 10⁻¹⁹ C

其中 e = 基本电荷 = 1.60 × 10⁻¹⁹ C

Substituting into Einstein’s equation:

代入爱因斯坦方程：

eV_s = hf − φ

This means a graph of V_s against f is also a straight line with gradient h/e. This experimental method was used by Robert Millikan in 1916 to accurately determine the value of Planck’s constant, confirming Einstein’s theory.

这意味着V_s对f的图也是一条直线，斜率为h/e。罗伯特·密立根于1916年使用这种实验方法精确测定了普朗克常数的值，证实了爱因斯坦的理论。

8. Key Graphs for CIE Examinations | CIE考试关键图表

The CIE 9702 syllabus expects you to interpret and sketch several important graphs. Here is what you need to know:

CIE 9702课程大纲要求你能够解释和绘制几个重要的图表。以下是需要了解的内容：

Graph 1: KE_max vs Frequency | 图1：最大动能 vs 频率

• Straight line with gradient equal to Planck’s constant h
• x-intercept = threshold frequency f₀
• y-intercept = −φ
• The line is the same for all metals (same gradient h), but different metals have different work functions (different x-intercepts)

• 直线，斜率等于普朗克常数 h
• x截距 = 阈值频率 f₀
• y截距 = −φ
• 所有金属的线相同（相同的斜率h），但不同金属有不同的功函数（不同的x截距）

Graph 2: Photocurrent vs Potential Difference | 图2：光电流 vs 电势差

• Negative potentials → photocurrent decreases until stopping potential V_s where I = 0
• Positive potentials → photocurrent reaches a saturation value
• Higher intensity → greater saturation current (more photons → more electrons)
• Higher frequency → more negative stopping potential (more energetic electrons)

• 负电势 → 光电流减小，直到遏止电势V_s处I = 0
• 正电势 → 光电流达到饱和值
• 更高强度 → 更大的饱和电流（更多光子 → 更多电子）
• 更高频率 → 更负的遏止电势（更高能量的电子）

9. Worked Example 1 (Paper 4 Style) | 例题1（Paper 4风格）

Question: Ultraviolet light of wavelength 200 nm is incident on a clean zinc surface. The work function of zinc is 4.3 eV.

(a) Calculate the energy of a single photon of this ultraviolet radiation in joules.
(b) Determine whether photoelectrons will be emitted.
(c) If photoelectrons are emitted, calculate their maximum kinetic energy in eV.
(d) Calculate the stopping potential required to reduce the photocurrent to zero.

问题：波长为200 nm的紫外光照射到干净的锌表面上。锌的功函数为4.3 eV。

(a) 计算该紫外辐射单个光子的能量（以焦耳为单位）。
(b) 判断是否会发射光电子。
(c) 如果会发射光电子，计算它们的最大动能（以eV为单位）。
(d) 计算将光电流降至零所需的遏止电势。

Solution | 解答：

(a) E = hc/λ = (6.63 × 10⁻³⁴)(3.00 × 10⁸) / (200 × 10⁻⁹) = 9.945 × 10⁻¹⁹ J

Convert to eV: E = 9.945 × 10⁻¹⁹ / 1.60 × 10⁻¹⁹ = 6.22 eV

(b) Since 6.22 eV > 4.3 eV (the work function of zinc), the photon energy exceeds the work function. Photoelectrons WILL be emitted.

(b) 由于6.22 eV > 4.3 eV（锌的功函数），光子能量超过了功函数。光电子将会被发射。

(c) KE_max = hf − φ = 6.22 − 4.3 = 1.92 eV

(d) eV_s = KE_max, so V_s = KE_max / e = 1.92 eV / e = 1.92 V

10. Worked Example 2 (Graph Analysis) | 例题2（图表分析）

Question: In a photoelectric experiment on a clean metal surface, the following stopping potentials were measured for different frequencies of incident light:

问题：在对干净金属表面的光电实验中，测量到以下不同入射光频率下的遏止电势：

Frequency f / 10¹⁴ Hz	Stopping Potential Vs / V
6.0	0.58
7.0	0.98
8.0	1.38
9.0	1.80
10.0	2.23

Use the data to determine: (a) the value of Planck’s constant, (b) the work function of the metal in eV.

使用数据确定：(a) 普朗克常数的值，(b) 金属的功函数（以eV为单位）。

Solution | 解答：

(a) From eV_s = hf − φ, the gradient of V_s vs f is h/e.

Gradient = ΔV_s/Δf = (2.23 − 0.58) / ((10.0 − 6.0) × 10¹⁴) = 1.65 / (4.0 × 10¹⁴) = 4.125 × 10⁻¹⁵ V s

h/e = 4.125 × 10⁻¹⁵, so h = (4.125 × 10⁻¹⁵)(1.60 × 10⁻¹⁹) = 6.60 × 10⁻³⁴ J s

(This is very close to the accepted value of 6.63 × 10⁻³⁴ J s.)

(b) From eV_s = hf − φ, the x-intercept gives f₀ where V_s = 0.

Using the equation of the line: V_s = (h/e)f − φ/e

y-intercept = −φ/e → From the line, when f = 0, V_s = −φ/e

Extrapolating: at f = 6.0 × 10¹⁴, V_s = 0.58

The line equation: V_s = 4.125 × 10⁻¹⁵ f − φ/e

0.58 = 4.125 × 10⁻¹⁵(6.0 × 10¹⁴) − φ/e → 0.58 = 2.475 − φ/e → φ/e = 1.895

φ = 1.895 × e = 1.895 eV ≈ 1.90 eV

Alternatively, using threshold frequency: f₀ = φ/h → f₀ occurs at x-intercept ≈ 4.6 × 10¹⁴ Hz

φ = hf₀ = (6.60 × 10⁻³⁴)(4.6 × 10¹⁴) = 3.04 × 10⁻¹⁹ J = 1.90 eV ✓

11. The Photoelectric Effect in Context | 光电效应在背景中

Einstein’s explanation of the photoelectric effect was revolutionary because it introduced the concept of wave-particle duality — the idea that light behaves as both a wave and a particle. For this work, Einstein received the Nobel Prize in Physics in 1921.

爱因斯坦对光电效应的解释是革命性的，因为它引入了波粒二象性的概念——光既表现为波又表现为粒子。因为这项工作，爱因斯坦于1921年获得诺贝尔物理学奖。

The photon model opened the door to quantum mechanics and has practical applications in:

光子模型为量子力学打开了大门，并在以下方面有实际应用：

• Photoelectric cells — automatic doors, burglar alarms, street light controls | 光电管 — 自动门、防盗报警器、路灯控制
• Solar panels — converting sunlight into electricity | 太阳能电池板 — 将阳光转化为电能
• Image sensors — digital cameras, night vision devices | 图像传感器 — 数码相机、夜视设备
• Photomultiplier tubes — detecting very low light levels in scientific instruments | 光电倍增管 — 在科学仪器中检测极低光水平

12. Examination Tips for CIE 9702 | CIE 9702考试技巧

1. Memorise the photoelectric equation: hf = φ + KE_max. You must be able to write this down instantly.
2. Know the units: Work function φ is often given in eV, but the equation uses joules. Convert using 1 eV = 1.60 × 10⁻¹⁹ J.
3. Graph interpretation is common: Be ready to find h from the gradient and φ from the intercept of a KE_max vs f graph.
4. Explain, don’t just state: When asked why classical theory fails, use the photon model — one photon, one electron, all-or-nothing energy transfer.
5. Intensity vs frequency: Intensity affects the number of photoelectrons (current). Frequency affects their maximum kinetic energy. Never confuse these.
6. Threshold frequency explained: f₀ = φ/h. Below f₀, each individual photon has insufficient energy to overcome the work function, regardless of how many photons arrive.

1. 记住光电方程：hf = φ + KE_max。你必须能够立刻写出这个方程。
2. 了解单位：功函数φ通常以eV给出，但方程使用焦耳。使用1 eV = 1.60 × 10⁻¹⁹ J进行转换。
3. 图表解释很常见：准备从KE_max vs f图的斜率求h，从截距求φ。
4. 解释而不仅仅是陈述：当被问及为什么经典理论失败时，使用光子模型——一个光子，一个电子，全有或全无的能量转移。
5. 强度 vs 频率：强度影响光电子的数量（电流）。频率影响它们的最大动能。永远不要混淆这些。
6. 阈值频率的解释：f₀ = φ/h。低于f₀，每个单独的光子能量不足以克服功函数，无论有多少光子到达。

13. Summary | 总结

Concept 概念	Key Point 要点
Photon energy 光子能量	E = hf = hc/λ
Photoelectric equation 光电方程	hf = φ + KEmax
Threshold frequency 阈值频率	f₀ = φ/h
Stopping potential 遏止电势	eVs = KEmax = hf − φ
Work function 功函数	Minimum energy to eject an electron from a metal surface
Intensity effect 强度效应	Determines number of photoelectrons (current), NOT their K.E.
Frequency effect 频率效应	Determines maximum K.E. of photoelectrons
Graph: KEmax vs f	Gradient = h (Planck’s constant), x-intercept = f₀

The photoelectric effect is a beautiful topic because it demonstrates how a single experiment can overturn centuries of established physics and open up an entirely new way of understanding nature. For CIE A-Level students, mastering this topic provides not just exam marks but a genuine insight into the quantum revolution that shaped modern physics.

光电效应是一个美丽的话题，因为它展示了单一实验如何推翻几个世纪以来建立的物理学，并开辟了理解自然的全新方式。对于CIE A-Level学生来说，掌握这一主题不仅能为考试赢得分数，还能真正洞察塑造现代物理学的量子革命。

Keywords: photoelectric effect, Einstein photoelectric equation, threshold frequency, work function, stopping potential, photon model, Planck’s constant, CIE A-Level Physics 9702, quantum physics, wave-particle duality | 关键词：光电效应，爱因斯坦光电方程，阈值频率，功函数，遏止电势，光子模型，普朗克常数，CIE A-Level物理9702，量子物理，波粒二象性