Alpha-particle Scattering and the Nucleus | α粒子散射与原子核

📚 Alpha-particle Scattering and the Nucleus | α粒子散射与原子核

In Cambridge International AS & A Level Physics, the alpha-particle scattering experiment carried out by Geiger and Marsden under Rutherford’s direction is a cornerstone. It replaced the earlier ‘plum pudding’ model with the nuclear atom, giving the first direct evidence for a small, dense, positively charged nucleus.

在剑桥国际 AS 与 A Level 物理中，盖革和马斯登在卢瑟福指导下完成的 α 粒子散射实验是一个基石。它用核式原子取代了早期的 “葡萄干布丁” 模型，首次提供了原子中存在一个小而致密、带正电的原子核的直接证据。

1. From Thomson’s Plum Pudding to the Nuclear Atom | 从汤姆孙葡萄干布丁模型到核式原子

Before 1911, J. J. Thomson’s model pictured the atom as a sphere of positive charge with electrons embedded in it like plums in a pudding. This model predicted only very small deflections when alpha particles passed through a thin metal foil.

在 1911 年之前，J. J. 汤姆孙的模型将原子描绘成一个带正电的球体，电子像布丁中的葡萄干一样嵌入其中。该模型预言，α 粒子穿过薄金属箔时只会发生非常小的偏转。

Rutherford’s team tested this prediction using alpha particles from a radioactive source. The unexpected large-angle scattering forced physicists to abandon the Thomson model.

卢瑟福团队利用放射源产生的 α 粒子检验了这一预言。出乎意料的大角度散射迫使物理学家放弃了汤姆孙模型。

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2. The Alpha-Particle Scattering Experiment | α粒子散射实验

In the experiment, a narrow beam of alpha particles was directed at an extremely thin gold foil, typically about 10⁻⁶ m thick. A movable zinc sulfide screen detected scattered alpha particles by producing tiny flashes of light.

实验中，一束狭窄的 α 粒子射向极薄的金箔，厚度通常约为 10⁻⁶ m。可移动的硫化锌荧光屏通过产生微小闪光来探测被散射的 α 粒子。

The apparatus was placed in an evacuated chamber so that alpha particles would not be absorbed or scattered by air molecules. The detector could be rotated through angles from 0° to nearly 180° relative to the incident beam.

整个装置置于真空室中，以免 α 粒子被空气分子吸收或散射。探测器可相对于入射束旋转，角度范围为 0° 至接近 180°。

Alpha particles are helium nuclei, carrying charge +2e and about four times the mass of a hydrogen atom. They were chosen because they are energetic, easily detected, and strongly ionising.

α 粒子是氦核，带电荷 +2e，质量约为氢原子的四倍。选择它们是因为其能量较高、易于探测且电离能力强。

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3. Principal Observations | 主要观察结果

Most alpha particles passed straight through the gold foil with little or no deflection. This showed that most of the atom is empty space.

大多数 α 粒子几乎不发生偏转地直接穿过金箔。这表明原子的大部分区域是空的空间。

A small fraction of particles were deflected through small angles, typically less than 10°. A very tiny fraction, about 1 in 8000, were scattered through angles greater than 90°, and a few were reflected almost straight back.

一小部分粒子以小角度偏转，通常小于 10°。极少数粒子（约 1/8000）被散射到大于 90° 的角度，甚至有少数几乎被直接反弹回来。

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4. Explaining the Observations | 对观察结果的解释

Rutherford explained these results by proposing that all the positive charge and almost all the mass of the atom are concentrated in a very small central region called the nucleus. The electrons orbit this nucleus at relatively large distances.

卢瑟福解释这些结果时提出，原子的全部正电荷和几乎全部质量都集中在一个非常小的中心区域，称为原子核。电子在距核相对较远的地方绕核运动。

The large-angle scattering occurs when an alpha particle passes close to a nucleus. The Coulomb repulsion between the positive alpha particle and the positive nucleus produces a large force, causing a large deflection. A head-on approach can stop the alpha particle and send it back.

当 α 粒子靠近原子核时，就会发生大角度散射。带正电的 α 粒子与带正电的原子核之间的库仑斥力产生很大的力，从而引起大角度偏转。正面接近可以使 α 粒子停止并被反弹回去。

Because the nucleus is so small, only alpha particles whose paths pass very close to it experience a strong repulsion. Most particles miss the nucleus entirely and pass through the surrounding empty space.

由于原子核非常小，只有路径非常靠近核的 α 粒子才会受到强斥力。大多数粒子完全错过原子核，从周围的空空间穿过。

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5. The Nuclear Atom Model | 核式原子模型

The nuclear model states that an atom consists of a positively charged nucleus containing protons and neutrons, surrounded by electrons. The nucleus diameter is of the order of 10⁻¹⁴ m to 10⁻¹⁵ m, while the atom diameter is about 10⁻¹⁰ m.

核式模型指出，原子由带正电的原子核（包含质子和中子）以及周围的电子组成。原子核直径约为 10⁻¹⁴ m 至 10⁻¹⁵ m，而原子直径约为 10⁻¹⁰ m。

This means the nucleus is roughly 10,000 to 100,000 times smaller than the atom. If an atom were the size of a football stadium, the nucleus would be roughly the size of a small pea at the centre.

这意味着原子核大约比原子小 10,000 到 100,000 倍。如果把原子放大到足球场大小，原子核大约只有中心一粒小豌豆那么大。

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6. Coulomb Repulsion and Angle of Scattering | 库仑斥力与散射角

The force between an alpha particle and a nucleus is given by Coulomb’s law:

α 粒子与原子核之间的力由库仑定律给出：

F = (2e)(Ze) / (4π ε₀ r²)

Here 2e is the charge of the

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