📚 The Photoelectric Effect | 光电效应
The photoelectric effect is the emission of electrons from a metal surface when electromagnetic radiation of sufficiently high frequency shines on it. This phenomenon provides some of the strongest evidence that light behaves as a stream of particles called photons.
光电效应是指当频率足够高的电磁辐射照射金属表面时，金属表面发射出电子的现象。这一现象为“光表现为称为光子的粒子流”提供了最强有力的证据之一。
1. The Experimental Arrangement | 实验装置
The classic apparatus consists of an evacuated glass tube containing two electrodes: a metal plate (the emitter) and a collecting electrode (the anode). Ultraviolet light, or another high-frequency radiation, is directed onto the emitter, and a sensitive ammeter measures any current in the circuit.
经典实验装置包括一个抽成真空的玻璃管，内有两个电极：一块金属板（发射极）和一个收集电极（阳极）。用紫外线或其他高频辐射照射发射极，并用灵敏的电流计测量电路中的任何电流。
The tube is evacuated so that any measured current must be due to electrons crossing the gap (the photocurrent), rather than gas molecules being ionised. A variable power supply allows the potential difference between the emitter and the anode to be adjusted.
玻璃管被抽成真空，是为了确保测到的任何电流都来自于穿越间隙的电子（即光电流），而不是气体分子被电离。通过可调电源，我们可以调节发射极与阳极之间的电势差。
2. Work Function and Threshold Frequency | 逸出功与阈值频率
Every metal has a minimum energy required to release an electron from its surface. This is called the work function, Φ, measured in joules (J), although electronvolts (eV) are also used in some questions.
每种金属都存在一个从表面释放电子所需的最小能量，称为逸出功Φ，单位是焦耳（J），在某些题目中也使用电子伏特（eV）。
If the photon energy hf is smaller than Φ, no electrons can be emitted, no matter how many photons arrive. This gives the threshold frequency f₀, the minimum frequency of radiation that can cause photoemission.
如果光子能量hf小于Φ，那么无论有多少光子到达，都无法发射出电子。由此引出阈值频率f₀，即能够引起光电发射的最低辐射频率。
Φ = hf₀ ⇒ f₀ = Φ/h
3. Einstein’s Photon Model | 爱因斯坦的光子模型
In 1905, Einstein proposed that light is quantised into packets of energy called photons, each carrying energy E = hf, where h is Planck’s constant (6.63 × 10⁻³⁴ J s) and f is the frequency of the radiation.
1905年，爱因斯坦提出光由称为光子的能量包量子化组成，每个光子携带能量E = hf，其中h是普朗克常量（6.63 × 10⁻³⁴ J·s），f是辐射的频率。
The interaction is one photon transferring all of its energy to one electron in a single, instantaneous collision. A single photon cannot share its energy among several electrons, and several photons cannot combine to eject a single electron.
相互作用的机制是一个光子将其全部能量一次性转移给一个电子。单个光子不能把能量分给多个电子，多个光子也不能合并起来打出一个电子。
4. The Photoelectric Equation | 光电效应方程
Applying conservation of energy to the one-photon–one-electron interaction gives the photoelectric equation:
对“一光子–一电子”的相互作用应用能量守恒，得到光电效应方程：
hf = Φ + ½mv²(max)
Here, hf is the energy of the incident photon, Φ is the work function of the metal, and ½mv²(max) is the maximum kinetic energy of the emitted electron, often written as Eₖ(max).
其中，hf是入射光子的能量，Φ是金属的逸出功，½mv²(max)是发射出电子的最大动能，通常记为Eₖ(max)。
Eₖ(max) = hf − Φ
The word ‘maximum’ is important: electrons deeper in the metal lose extra energy through collisions before escaping, so most emitted electrons have less than Eₖ(max).
“最大”一词很重要：金属内部较深处的电子在逸出前会因碰撞而损失额外能量，因此大多数发射电子的动能小于Eₖ(max)。
5. Why the Wave Model Fails | 经典波动理论的困境
The wave model of light predicts three behaviours that are contradicted by experiment.
经典波动理论对光的预测有三点与实验事实相矛盾。
| Observation | 实验现象 | Why the wave model fails | 波动理论为何无法解释 |
| No time lag – emission is almost instantaneous. | Waves spread energy evenly over the wavefront; a long time should be needed to accumulate enough energy, but emission happens at once. |
| No emission below the threshold frequency. | Wave theory predicts that any frequency can eject electrons if the intensity is high enough. |
| Eₖ(max) depends on frequency, not intensity. | A more intense wave carries more energy per second, so wave theory predicts a larger electron energy, which is not observed. |
Only the photon model explains all three facts: a single photon must have energy hf ≥ Φ to eject an electron, and intensity only changes the number of photons per second.
只有光子模型能够解释这三点：单个光子必须具有hf ≥ Φ的能量才能打出电子，而光强只改变每秒到达的光子数目。
6. Stopping Potential | 遏止电压
To measure Eₖ(max), the supply polarity is reversed so that the anode becomes negative relative to the emitter. The most energetic electrons are repelled, and the minimum reverse voltage that just stops all electrons from reaching the anode is called the stopping potential Vₛ.
为了测量Eₖ(max)，我们将电源极性反接，使阳极相对于发射极为负。动能最大的电子被电场阻碍，恰好能使所有电子都无法到达阳极的最小反向电压称为遏止电压Vₛ。
eVₛ = Eₖ(max) = hf − Φ
This equation allows Planck’s constant to be found experimentally: the gradient of a graph of Vₛ against f is h/e.
该方程使我们可以通过实验求普朗克常量：在Vₛ随f变化的图像中，斜率为h/e。
7. Intensity and Frequency | 光强与频率的作用
Increasing the intensity of the radiation at a fixed frequency increases the number of photons arriving per second, so more electrons are emitted per second and the photocurrent increases. The maximum kinetic energy of the electrons is unchanged because each photon still has the same energy hf.
在频率不变时增大辐射强度，相当于增加每秒到达的光子数目，因此每秒发射的电子数增多，光电流增大。但由于每个光子的能量hf不变，电子的最大动能不变。
Increasing the frequency at a fixed intensity gives each photon more energy, so Eₖ(max) increases. However, the number of photons per second decreases, so the saturation photocurrent may actually fall.
在光强不变时增大频率，每个光子的能量增大，因此Eₖ(max)增大。但每秒到达的光子数目减少，所以饱和光电流实际上可能减小。
If f is below f₀, no photoelectrons are produced at all — even with extremely high intensity, because no single photon carries enough energy.
如果f低于f₀，则根本不会产生光电子——即使光强极高也不行，因为没有单个光子携带足够的能量。
8. Photocurrent and Saturation Current | 光电流与饱和电流
With the anode positive relative to the emitter, increasing the potential difference attracts more escaping electrons to the anode, so the current rises. When every emitted electron is collected, the current reaches its maximum value, called the saturation current.
当阳极相对于发射极为正时，增大电势差会使更多逸出电子被吸引到阳极，电流随之增大。当所有发射电子都被收集时，电流达到最大值，称为饱和电流。
The saturation current is directly proportional to the intensity of the incident radiation (for a fixed frequency), because intensity is proportional to the number of photons per second and each photon ejects at most one electron.
在频率固定时，饱和电流与入射辐射强度成正比，因为光强与每秒光子数成正比，而每个光子最多打出一个电子。
9. Graphical Analysis | 图像分析
Two graphs are commonly tested in the CIE examination.
CIE考试中常考查两种图像。
| Graph | 图像 | Gradient | 斜率 | Intercepts | 截距 |
| Eₖ(max) against f | h | y-intercept = −Φ; x-intercept = f₀ |
| Vₛ against f | h/e | y-intercept = −Φ/e; x-intercept = f₀ |
All practical measurements confirm that these graphs are straight lines, supporting Einstein’s photon model. The gradient is always the same for every metal, since it only contains universal constants.
所有实测结果都证实这些图像是直线，有力地支持了爱因斯坦的光子模型。斜率对任何金属都相同，因为它只包含普适常量。
10. Applications and Examination Tips | 应用与考点提示
The photoelectric effect is used in light sensors, burglar alarms, automatic doors, and photomultiplier tubes in medical imaging devices. Such devices rely on the immediate response of the photocurrent when light of sufficient frequency is present.
光电效应被应用于光传感器、防盗报警器、自动门以及医疗成像设备中的光电倍增管。这些器件都依赖于在足够频率的光照射下光电流的即时响应。
Examination tips: always link intensity to photocurrent, and frequency to electron kinetic energy; remember that one photon interacts with one electron; convert electronvolts to joules using 1 eV = 1.6 × 10⁻¹⁹ J when required; and state that if f < f₀, no emission occurs regardless of intensity.
考试提示：始终将光强与光电流联系、将频率与电子动能联系；记住一个光子只与一个电子相互作用；需要时用1 eV = 1.6 × 10⁻¹⁹ J进行单位换算；同时要说明，若f < f₀，无论光强多大都不会发生发射。
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