Discovering the Electron | 电子的发现

📚 Discovering the Electron | 电子的发现

The discovery of the electron at the end of the nineteenth century transformed physics. It showed that atoms are divisible and that electric charge exists in discrete units. For CIE A-Level Physics, the story links cathode rays, field deflections, Thomson’s e/m measurement and Millikan’s oil drop experiment.

十九世纪末电子的发现彻底改变了物理学。它表明原子是可分的，电荷以分立单元存在。对 CIE A-Level 物理而言，这段历史将阴极射线、场偏转、汤姆孙的 e/m 测量和密立根油滴实验联系在一起。

1. Cathode rays and gas discharge tubes | 阴极射线与气体放电管

When a high potential difference is applied across a gas at low pressure in a discharge tube, the gas glows and invisible rays travel from the cathode. These cathode rays are streams of electrons.

当低压气体放电管两端施加高电压时，气体会发光，并且有不可见的射线从阴极射出。这些阴极射线就是电子流。

At pressures near atmospheric pressure the gas conducts little; as pressure is reduced, striations and a dark space appear, and the glass near the anode fluoresces.

在接近大气压时气体几乎不导电；随着气压降低，会出现辉纹和暗区，阳极附近的玻璃产生荧光。

The rays are emitted from the cathode, travel in straight lines, and are independent of the gas used, which suggests they are fundamental particles.

射线从阴极发出，沿直线传播，并且与所用气体无关，这表明它们是基本粒子。

2. Thermionic emission | 热电子发射

Modern electron guns use thermionic emission. A metal filament is heated by an electric current, giving some free electrons enough kinetic energy to escape from the metal surface.

现代电子枪利用热电子发射。金属灯丝被电流加热，使一些自由电子获得足够的动能从金属表面逸出。

The emitted electrons are then accelerated by an anode at a high positive potential. The work function of the metal is the minimum energy needed for an electron to escape.

发射出的电子随后被高正电位的阳极加速。金属的逸出功是电子逃逸所需的最小能量。

In a vacuum, the beam can be made narrow and directed, which is essential for deflection experiments.

在真空中，电子束可以变窄并被定向，这对偏转实验至关重要。

3. Properties of cathode rays | 阴极射线的性质

Cathode rays carry negative charge. They are deflected by electric fields towards the positive plate and by magnetic fields in a direction given by the left-hand rule for negative charge.

阴极射线带负电荷。它们在电场中向正极板偏转，在磁场中按负电荷左手定则确定的方向偏转。

They travel in straight lines, produce fluorescence, and can be stopped by thin metal foils. Their charge-to-mass ratio is the same for all gases.

它们沿直线传播，产生荧光，并可被薄金属箔阻挡。它们的荷质比对所有气体都相同。

These observations led J. J. Thomson to conclude that cathode rays are negatively charged particles, later named electrons, common to all matter.

这些观察使 J. J. 汤姆孙得出结论：阴极射线是带负电的粒子，后来称为电子，普遍存在于所有物质中。

4. Deflection in electric fields | 电场中的偏转

A uniform electric field between parallel plates exerts a constant force on an electron. The force is F = eE, where E is the electric field strength V/d.

平行板之间的均匀电场对电子施加恒定的力。力为 F = eE，其中 E 是电场强度 V/d。

Since the force is constant and perpendicular to the initial velocity in a typical arrangement, the electron follows a parabolic path and its vertical acceleration is a = eE/m.

由于该力恒定且通常垂直于初速度，电子沿抛物线轨迹运动，其竖直加速度为 a = eE/m。

The deflection y on a screen can be measured. It depends on the electron’s speed, the field strength, and the geometry, allowing e/m to be found if the speed is known.

可以测量屏幕上的偏转量 y。它取决于电子速度、电场强度和几何尺寸，因此若已知速度，就能求出 e/m。

5. Deflection in magnetic fields | 磁场中的偏转

A uniform magnetic field exerts a force on a moving electron only when there is a component of velocity perpendicular to the field. The force is F = Bev, where v is the component perpendicular to B.

均匀磁场仅当电子速度有垂直于磁场的分量时才施加力。该力为 F = Bev，其中 v 是垂直于 B 的速度分量。

This magnetic force is always perpendicular to the velocity, so it acts as a centripetal force. The electron moves in a circular arc with radius r = mv/(Be).

该磁力始终垂直于速度，因此充当向心力。电子做圆弧运动，半径为 r = mv/(Be)。

From the radius of curvature, the quantity e/m can be obtained directly if v and B are known. A common method is to balance electric and magnetic deflections.

如果已知 v 和 B，可以从曲率半径直接得到 e/m。常用的方法是使电场偏转和磁场偏转相互平衡。

6. Thomson’s e/m experiment | 汤姆孙的 e/m 实验

Thomson used a discharge tube with perpendicular electric and magnetic fields acting on the electron beam. First, the electric field alone deflected the beam onto a fluorescent screen.

汤姆孙使用放电管，让互相垂直的电场和磁场作用于电子束。首先，仅用电场使电子束偏转到荧光屏上。

Then a magnetic field was applied so that the magnetic force exactly cancelled the electric force. At the balance condition, eE = Bev, giving v = E/B.

然后施加磁场，使磁力恰好抵消电力。在平衡条件下，eE = Bev，得到 v = E/B。

With the electric field removed, the magnetic field alone bent the beam into a circle. The radius r was measured, and e/m was found from e/m = v/(Br) = E/(B²r).

撤去电场后，仅由磁场使电子束弯曲成圆。测量半径 r，由 e/m = v/(Br) = E/(B²r) 求出荷质比。

Thomson obtained e/m ≈ 1.76 × 10¹¹ C kg⁻¹, much larger than the known value for hydrogen ions, implying the electron is either very light or highly charged.

汤姆孙测得 e/m ≈ 1.76 × 10¹¹ C kg⁻¹，远大于当时已知氢离子的荷质比，表明电子要么非常轻，要么带电量很大。

7. Balanced field method and velocity selection | 平衡场法与速度选择

The balanced field arrangement is called a velocity selector. When electric and magnetic forces cancel, only electrons with speed v = E/B pass straight through undeflected.

平衡场装置称为速度选择器。当电场力和磁场力相抵消时，只有速度为 v = E/B 的电子能直线通过而不偏转。

This principle is widely used in mass spectrometers and particle accelerators to select particles of a specific velocity before further analysis.

这一原理广泛用于质谱仪和粒子加速器中，在进一步分析前选择特定速度的粒子。

In solving problems, remember that the electric force is independent of velocity, while the magnetic force increases with velocity. The cancellation condition is therefore unique.

解题时要记住，电场力与速度无关，而磁场力随速度增大而增大。因此抵消条件是唯一的。

8. Millikan’s oil drop experiment | 密立根油滴实验

Thomson’s e/m ratio gave the charge and mass only as a combination. Millikan’s oil drop experiment determined the elementary charge e directly.

汤姆孙的 e/m 只给出电荷与质量的比值。密立根油滴实验直接测定了基本电荷 e。

Tiny oil droplets were sprayed between two horizontal plates. Some droplets became charged by friction. By adjusting the electric field, a negatively charged droplet could be held stationary or made to rise and fall.

在两块水平极板之间喷入微小油滴。一些油滴因摩擦而带电。通过调节电场，带负电的油滴可被保持静止，或上升和下降。

When the droplet is stationary, the electric force equals the weight minus the upthrust. For a spherical droplet of radius a and density ρ in air of density σ, the charge is:

当油滴静止时，电场力等于重力减去浮力。对于半径为 a、密度为 ρ 的油滴，在空气密度为 σ 中，电荷为：

q = (4πa³g(ρ – σ))/(3E)

The radius a was found by allowing the droplet to fall freely and measuring its terminal speed; Stokes’ law was used with a correction at small droplet sizes.

半径 a 通过让油滴自由下落并测量其终极速度来确定；使用了斯托克斯定律，并在小油滴尺寸时进行修正。

9. Quantisation of charge | 电荷的量子化

Millikan observed that the charge on every droplet was always an integer multiple of a smallest value, about 1.6 × 10⁻¹⁹ C. This showed that electric charge is quantised.

密立根观察到每个油滴上的电荷总是某个最小值的整数倍，约为 1.6 × 10⁻¹⁹ C。这表明电荷是量子化的。

The elementary charge e is now accepted as 1.602 × 10⁻¹⁹ C. Because the oil drop charge values showed discrete jumps, the existence of single electrons was strongly supported.

基本电荷 e 现在公认值为 1.602 × 10⁻¹⁹ C。由于油滴电荷值呈现离散跳跃，单个电子的存在得到了有力支持。

Combining e from Millikan with Thomson’s e/m gives the electron mass:

将密立根测得的 e 与汤姆孙的 e/m 结合，可得到电子质量：

mₑ = e / (e/m) ≈ 1.602 × 10⁻¹⁹ C / 1.759 × 10¹¹ C kg⁻¹ ≈ 9.11 × 10⁻³¹ kg

10. Electron charge and mass: accepted values | 电子电荷与质量：公认值

The electron has charge -e, where e = 1.602 × 10⁻¹⁹ C, and mass mₑ = 9.109 × 10⁻³¹ kg. Its charge-to-mass ratio is approximately 1.76 × 10¹¹ C kg⁻¹.

电子带电荷 -e，其中 e = 1.602 × 10⁻¹⁹ C，质量 mₑ = 9.109 × 10⁻³¹ kg。其荷质比约为 1.76 × 10¹¹ C kg⁻¹。

The electron is much lighter than a proton: mₚ/mₑ ≈ 1836. This large ratio is why e/m for electrons is far greater than for ions.

电子比质子轻得多：mₚ/mₑ ≈ 1836。正是这个很大的比率使电子的 e/m 远大于离子。

In calculations, be careful with powers of ten, sign conventions, and units. e/mₑ is often used in electron deflection and cyclotron problems.

计算时要注意十的幂次、符号惯例和单位。e/mₑ 常用于电子偏转和回旋问题。

11. Significance of the discovery | 电子发现的意义

The discovery of the electron ended the idea of the atom as indivisible

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Discovering the Electron | 电子的发现