The Photoelectric Effect in IGCSE OCR Physics | IGCSE OCR 物理：光电效应考点精讲

📚 The Photoelectric Effect in IGCSE OCR Physics | IGCSE OCR 物理：光电效应考点精讲

When electromagnetic radiation of sufficiently high frequency strikes the surface of a metal, the metal may emit electrons. This phenomenon, known as the photoelectric effect, cannot be explained by classical wave theory and played a pivotal role in the development of quantum physics. For IGCSE OCR Physics, you need to understand the experimental observations, Einstein’s photon model, the photoelectric equation, and the concepts of work function, threshold frequency and stopping potential.

当频率足够高的电磁辐射照射到金属表面时，金属可能会发射电子。这种现象称为光电效应，无法用经典波动理论解释，并对量子物理的发展起到了关键作用。在 IGCSE OCR 物理中，你需要理解实验观察、爱因斯坦的光子模型、光电效应方程以及功函数、阈值频率和遏止电压等概念。

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

The photoelectric effect is the emission of electrons from the surface of a metal when electromagnetic radiation above a certain minimum frequency falls on it. The emitted electrons are often called photoelectrons.

光电效应是指，当金属表面受到高于某个最小频率的电磁辐射照射时，会发射电子的现象。发射出的电子常被称为光电子。

This effect was first observed by Heinrich Hertz in 1887 and later investigated in detail by others, including Philipp Lenard. It provided direct evidence that light can behave as a stream of particles (photons) rather than just as a continuous wave.

该效应最初由赫兹在 1887 年观察到，后来由勒纳德等人进行了详细研究。它为光可以表现为粒子流（光子）而不仅仅是连续波提供了直接证据。

2. Key Experimental Observations | 关键实验观察

Experiments using a vacuum photocell (a cathode coated with the metal under study and an anode to collect electrons) revealed several important features of the photoelectric effect. You should be able to recall and explain these observations.

使用真空光电管（阴极涂有待研究金属，阳极收集电子）进行的实验揭示了光电效应的几个重要特征。你应该能够回忆并解释这些观察结果。

Observation 1: For a given metal, photoelectrons are only emitted if the frequency of the incident light exceeds a certain minimum frequency, called the threshold frequency (f₀). Below this frequency, no electrons are emitted, no matter how intense the light is.

观察1：对于给定的金属，只有当入射光的频率超过某个最小频率（称为阈值频率 f₀）时，才会有光电子发射。低于该频率时，无论光有多强，都不会有电子发射。

Observation 2: The emission of photoelectrons is instantaneous – there is no measurable time delay between the light arriving and the electrons being emitted, even at very low intensities.

观察2：光电子的发射是瞬时的——即使光强非常低，从光照射到电子发射之间也没有可测量的时间延迟。

Observation 3: Increasing the intensity (brightness) of the radiation does not increase the maximum kinetic energy of the emitted photoelectrons. It only increases the number of electrons emitted per second (the photocurrent).

观察3：增加辐射的强度（亮度）并不会提高发射出的光电子的最大动能。它只会增加每秒发射的电子数目（光电流）。

Observation 4: The maximum kinetic energy (Eₖ) of the photoelectrons depends linearly on the frequency of the incident light. Higher frequency light ejects electrons with greater maximum kinetic energy.

观察4：光电子的最大动能（Eₖ）与入射光的频率呈线性关系。频率越高的光，击出的电子最大动能越大。

3. Why Wave Theory Fails | 为什么波动理论会失败

Classical wave theory pictures light as a continuous electromagnetic wave. According to this model, electrons in the metal would gradually absorb energy from the wave until they had enough to escape. This leads to three predictions that contradict experimental facts.

经典波动理论把光描绘成连续的电磁波。根据这个模型，金属中的电子会逐渐从波中吸收能量，直到拥有足够的能量逸出。这就产生了三个与实验事实相矛盾的预测。

Firstly, wave theory predicts that given enough time, even very low-intensity light of any frequency should eventually give electrons sufficient energy to leave the metal. In reality, there is a sharp threshold frequency, and no amount of waiting helps below that frequency.

首先，波动理论预测，只要时间足够长，任何频率的极低强度光最终都会赋予电子足够的能量使其离开金属。但实际上存在一个明确的阈值频率，低于该频率时无论等待多久都不行。

Secondly, wave theory predicts a time delay at low intensities because the wave energy is spread out. In reality, photoemission is instant, even at very low intensities.

其次，波动理论预测在低强度下会有一个时间延迟，因为波的能量分散。实际上，即使在极低强度下，光电发射也是瞬时的。

Thirdly, wave theory predicts that increasing intensity should increase the maximum kinetic energy of photoelectrons, since a more intense wave carries more energy. Experiments show that kinetic energy depends only on frequency, not on intensity.

第三，波动理论预测，增加强度会提高光电子的最大动能，因为更强的波携带更多能量。实验表明动能只取决于频率，与强度无关。

4. Einstein’s Photon Model | 爱因斯坦的光子模型

In 1905, Albert Einstein proposed that light (and all electromagnetic radiation) consists of discrete packets of energy called photons. The energy E of a single photon is directly proportional to its frequency f:
E = hf where h is the Planck constant (h ≈ 6.63 × 10⁻³⁴ J s).

1905 年，爱因斯坦提出光（以及所有电磁辐射）由离散的能量包组成，称为光子。单个光子的能量 E 与其频率 f 成正比：E = hf，其中 h 是普朗克常数（h ≈ 6.63 × 10⁻³⁴ J s）。

Since wavelength (λ) is related to frequency by c = fλ, the photon energy can also be written as E = hc / λ. Photons travel at the speed of light and have no mass, but they carry both energy and momentum.

由于波长 λ 通过 c = fλ 与频率关联，光子能量也可以写成 E = hc / λ。光子以光速传播，没有静止质量，但携带着能量和动量。

In the photon model, a single photon interacts with a single electron in the metal. The photon gives all its energy to the electron instantly. If the photon energy is large enough to overcome the forces holding the electron in the metal, the electron is emitted. This explains all the experimental observations at once.

在光子模型中，一个单个光子与金属中的一个单个电子相互作用。光子瞬间将所有能量传递给电子。如果光子能量足够大，能够克服将电子束缚在金属中的力，电子就会被发射出来。这就一下子解释了所有的实验观察。

5. Work Function and Threshold Frequency | 功函数与阈值频率

The work function (φ) of a metal is the minimum energy required to remove a single electron from the surface of that metal. It is usually expressed in joules (J) or electronvolts (eV), where 1 eV = 1.60 × 10⁻¹⁹ J.

金属的功函数（φ）是指从该金属表面移走一个电子所需的最小能量。它通常用焦耳（J）或电子伏特（eV）表示，1 eV = 1.60 × 10⁻¹⁹ J。

For photoemission to occur, the energy of the incident photon must be at least equal to the work function of the metal. The minimum frequency that can cause emission is called the threshold frequency (f₀), given by:

hf₀ = φ → f₀ = φ / h

要发生光电发射，入射光子的能量必须至少等于该金属的功函数。能够引起发射的最低频率称为阈值频率 f₀，满足：hf₀ = φ → f₀ = φ / h。

If f < f₀, the photon energy is less than the work function and no electrons are emitted, regardless of the light intensity. This explains the existence of a threshold frequency.

如果 f 低于 f₀，光子能量小于功函数，无论光强多大，都不会有电子发射。这就解释了阈值频率的存在。

Typical work functions for metals range from about 2 to 5 eV. For example, sodium has a work function of about 2.3 eV, while platinum has a work function around 5.6 eV.

常见金属的功函数范围大约在 2 到 5 eV 之间。例如，钠的功函数约为 2.3 eV，而铂的功函数约为 5.6 eV。

6. The Photoelectric Equation | 光电效应方程

Einstein’s photoelectric equation relates the photon energy, the work function and the maximum kinetic energy of the emitted photoelectron:

Eₖ(max) = hf – φ

爱因斯坦光电效应方程将光子能量、功函数和发射出的光电子的最大动能联系起来：

Eₖ(max) = hf – φ

Here, hf is the energy of one incident photon, φ is the work function of the metal, and Eₖ(max) is the maximum kinetic energy that a photoelectron can have after escaping the surface. Any remaining photon energy after overcoming the work function appears as kinetic energy of the electron.

这里，hf 是一个入射光子的能量，φ 是金属的功函数，Eₖ(max) 是光电子逃离表面后所能具有的最大动能。克服功函数后剩余的光子能量就表现为电子的动能。

The equation also shows that the maximum kinetic energy increases linearly with frequency f. If we plot Eₖ(max) against f, we obtain a straight line with gradient h and intercept –φ on the energy axis (or intercept on the frequency axis at f₀).

该方程还表明，最大动能随频率 f 线性增加。如果我们画出 Eₖ(max) 对 f 的图，会得到一条斜率为 h、在能量轴上截距为 –φ 的直线（或者在频率轴上的截距为 f₀）。

7. Effect of Light Intensity and Frequency | 光强和频率的影响

Light intensity is the power per unit area delivered by the radiation. In the photon model, intensity is proportional to the number of photons arriving per second per unit area – not to the energy of individual photons.

光强是辐射在单位面积上传递的功率。在光子模型中，强度与每秒钟到达单位面积的光子数成正比，而不是与单个光子的能量成正比。

Therefore, increasing the intensity of light does not change the energy of each photon. It simply supplies more photons. If these photons have the same frequency (and thus the same energy), more electrons will be emitted per second, leading to a larger photocurrent. However, the maximum kinetic energy of the electrons remains unchanged.

因此，增大光强并不会改变每个光子的能量，而只是提供了更多的光子。如果这些光子具有相同的频率（因而有相同的能量），那么每秒就会有更多电子发射，导致光电流增大。但电子的最大动能保持不变。

When the frequency of the incident light is increased (keeping intensity constant, which means fewer photons per second because each photon carries more energy), the maximum kinetic energy of the emitted electrons increases according to Eₖ = hf – φ. This is confirmed by measuring the stopping potential.

当入射光的频率增大时（保持强度不变，这意味着由于每个光子携带的能量更多，每秒光子数会减少），发射电子的最大动能会按照 Eₖ = hf – φ 增大。这可以通过测量遏止电压来证实。

8. Stopping Potential and Maximum Kinetic Energy | 遏止电压与最大动能

The stopping potential (Vₛ) is the minimum reverse voltage that must be applied between the cathode and anode of a photocell to prevent even the most energetic photoelectrons from reaching the anode, thereby reducing the photocurrent to zero.

遏止电压（Vₛ）是必须施加在光电管阴极和阳极之间的最小反向电压，用以阻止即使是能量最高的光电子到达阳极，从而使光电流降至零。

When the stopping potential is applied, the work done by the electric field in stopping the fastest electrons equals their maximum kinetic energy:

e Vₛ = Eₖ(max)

当施加遏止电压时，电场阻止最快电子所做的功等于它们的最大动能：e Vₛ = Eₖ(max)，其中 e 是电子电荷的大小（e = 1.60 × 10⁻¹⁹ C）。

Combining this with the photoelectric equation gives:

e Vₛ = hf – φ

结合光电效应方程可得：e Vₛ = hf – φ。

This relationship is extremely useful because the stopping potential is easy to measure. By plotting Vₛ against frequency f for a given metal, we obtain a straight line whose gradient equals h/e.

这个关系非常有用，因为遏止电压很容易测量。对于给定的金属，绘制 Vₛ 对频率 f 的图，我们会得到一条直线，其斜率等于 h/e。

9. Determining Planck’s Constant Experimentally | 实验测定普朗克常数

A classic IGCSE OCR practical concept is to use the photoelectric effect to determine Planck’s constant h. The procedure involves using a photocell with different colour filters (or a monochromator) to shine monochromatic light of known frequencies onto a clean metal cathode.

IGCSE OCR 中一个经典的实验概念是利用光电效应测定普朗克常数 h。该实验过程使用光电管，通过不同颜色的滤光片（或单色仪）将已知频率的单色光照射到洁净的金属阴极上。

For each frequency, the stopping potential Vₛ is measured by adjusting the reverse voltage until the photocurrent just falls to zero. A graph of Vₛ (on the y-axis) against frequency f (on the x-axis) is plotted.

对每一个频率，通过调节反向电压直到光电流刚好降为零，从而测出遏止电压 Vₛ。然后绘制 Vₛ（纵轴）对频率 f（横轴）的图。

The graph is a straight line with gradient h/e and y-intercept –φ/e. The x-intercept gives the threshold frequency f₀ = φ/h. Since the electronic charge e is known, h can be calculated from the gradient: h = gradient × e.

该图是一条斜率为 h/e、y 轴截距为 –φ/e 的直线。x 轴截距给出了阈值频率 f₀ = φ/h。由于电子电荷 e 已知，h 可以由斜率计算：h = 斜率 × e。

Experimentally determined values obtained in this way agree closely with the accepted value, providing strong support for the photon model.

通过这种方式得到的实验值与公认值非常接近，为光子模型提供了强有力的支持。

10. Summarising the Key Points for Exams | 考点总结

To succeed in IGCSE OCR questions on the photoelectric effect, you must be able to state and use the photoelectric equation and describe each experimental observation with reference to photons, work function and threshold frequency.

要在 IGCSE OCR 光电效应题目中取得成功，你必须能够陈述并运用光电效应方程，并参照光子、功函数和阈值频率来描述每一个实验观察。

Common exam requirements include: explaining why a metal has a threshold frequency; predicting how increasing intensity or frequency affects emission; describing how to find h from a stopping potential–frequency graph; and converting between joules and electronvolts when calculating photon energies or work functions.

常见的考试要求包括：解释为什么金属存在阈值频率；预测增加强度或频率对发射的影响；描述如何从遏止电压–频率图求得 h；以及在计算光子能量或功函数时在焦耳和电子伏特之间进行换算。

Remember the key equations: E = hf, c = fλ, Eₖ = hf – φ, e Vₛ = Eₖ, and f₀ = φ/h. Always check that your units are consistent and that you apply the conversion 1 eV = 1.60 × 10⁻¹⁹ J correctly.

记住关键方程：E = hf，c = fλ，Eₖ = hf – φ，e Vₛ = Eₖ，以及 f₀ = φ/h。务必检查单位一致，并正确应用换算关系 1 eV = 1.60 × 10⁻¹⁹ J。

Finally, be ready to compare the photon model with the wave model, clearly stating why the photoelectric effect cannot be explained by classical wave theory. This contrast of ideas is a favourite in OCR mark schemes.

最后，准备好将光子模型与波动模型进行比较，清楚地说明为什么光电效应不能用经典波动理论解释。这种观念对比是 OCR 评分方案中的常见考点。

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The Photoelectric Effect in IGCSE OCR Physics | IGCSE OCR 物理：光电效应 考点精讲