📚 Alpha-particle Scattering and the Nucleus | α粒子散射与原子核
At the turn of the 20th century, the atom was believed to be a diffuse sphere of positive charge with electrons embedded within it, much like plums in a pudding. This view was overturned by a series of elegant alpha-particle scattering experiments, which revealed the existence of a tiny, massive, positively charged nucleus at the heart of every atom.
在20世纪初，人们认为原子是一个弥漫的正电荷球体，电子如同葡萄干布丁中的葡萄干一样嵌在其中。这一观点被一系列精妙的α粒子散射实验彻底推翻，实验揭示了每个原子中心都存在一个极小、极重且带正电的原子核。
1. The Pre-Rutherford View: Thomson's Plum Pudding Model | 卢瑟福之前的观点：汤姆孙的葡萄干布丁模型
Before 1911, the dominant atomic model was J.J. Thomson's 'plum pudding' model. In this picture, the atom consisted of a uniform sphere of positive charge about 10⁻¹⁰ m in diameter, with negatively charged electrons dotted throughout it, held in place by electrostatic forces. The overall charge was neutral, and the mass was distributed continuously.
在1911年之前，占主导地位的原子模型是J.J.汤姆孙的“葡萄干布丁”模型。在这个模型中，原子由一个直径约10⁻¹⁰ m的均匀正电荷球体构成，带负电的电子散布其中并通过静电力固定在位置上。整体呈电中性，质量是连续分布的。
According to Thomson's model, any alpha particles fired at a thin metal foil would pass through with only tiny deflections, as the electric forces from the diffuse positive charge would be far too weak to produce large-angle scattering.
根据汤姆孙模型，任何射向薄金属箔的α粒子都只会发生极小的偏转才能穿过，因为弥散正电荷产生的电场力太弱，无法造成大角度散射。
2. The Geiger–Marsden Experiment: Apparatus | 盖革-马斯登实验：实验装置
In 1909, under Ernest Rutherford's direction, Hans Geiger and Ernest Marsden set up an experiment to investigate alpha-particle scattering. A narrow beam of alpha particles from a radon or radium source was directed at a very thin gold foil, only a few thousand atoms thick. A movable zinc sulfide screen detected scattered alpha particles by producing tiny flashes of light (scintillations) when struck.
1909年，在欧内斯特·卢瑟福的指导下，汉斯·盖革和欧内斯特·马斯登搭建了一套实验装置来研究α粒子的散射。一束来自氡或镭源的窄α粒子束射向极薄的金箔（仅几千个原子厚）。可移动的硫化锌屏通过产生微小的闪光（闪烁）来探测散射的α粒子。
The entire apparatus was placed in an evacuated chamber to prevent air molecules from scattering the alpha particles. A microscope was used to count the scintillations at various angles around the foil.
整个装置被放置在真空室内，以防空气分子散射α粒子。使用显微镜对金箔周围不同角度的闪烁次数进行计数。
3. Key Observations from the Alpha Scattering Experiment | α粒子散射实验的主要观察结果
1. The vast majority of alpha particles passed straight through the gold foil with no measurable deflection.
1. 绝大多数α粒子径直穿过金箔，没有发生可测量的偏转。
2. A small fraction (about 1 in 8000) were deflected through small angles, typically less than 90°.
2. 一小部分（约8000个中有1个）以小角度偏转，通常小于90°。
3. Amazingly, about 1 in every 8000 alpha particles was scattered through an angle greater than 90°, and a very tiny number rebounded almost straight back towards the source.
3. 令人惊讶的是，每8000个α粒子中约有1个以大于90°的角度被散射，极少数几乎沿原路反弹回放射源方向。
These observations were completely incompatible with Thomson's plum pudding model, which could not explain any large-angle scattering.
这些观察结果与汤姆孙的葡萄干布丁模型完全矛盾，后者无法解释任何大角度散射。
4. Rutherford's Interpretation: The Nuclear Atom | 卢瑟福的解释：原子核
Rutherford realised that the large-angle scattering must result from a single encounter with a very small, massive, positively charged centre. He proposed that all the positive charge and most of the atomic mass were concentrated in a tiny nucleus, surrounded by electrons at relatively large distances.
卢瑟福意识到，大角度散射必定是由于与一个极小、极重且带正电的中心发生单次碰撞所致。他提出，所有正电荷和绝大部分原子质量都集中在一个微小的原子核中，周围是相距很远的电子。
The large deflections events occurred when an alpha particle approached the nucleus closely enough to experience a strong Coulomb repulsive force. The fact that most alpha particles passed through undeflected indicated that the atom is mostly empty space.
当α粒子接近原子核到足够近的距离，就会受到强大的库仑排斥力，从而发生大角度偏转。而大多数α粒子无偏转通过则表明原子内部绝大部分是空的。
5. The Nuclear Model of the Atom | 原子的核式模型
In Rutherford's nuclear model (1911), the atom consists of a central nucleus of radius roughly 10⁻¹⁵ m, carrying positive charge +Ze, where Z is the atomic number. Negatively charged electrons orbit the nucleus at distances of the order of 10⁻¹⁰ m, held in their orbits by electrostatic attraction. The nucleus contains over 99.9 % of the mass of the atom.
在卢瑟福的核式模型（1911年）中，原子由一个半径约为10⁻¹⁵ m的中心原子核构成，核带正电荷+Ze，Z为原子序数。带负电的电子在距核约10⁻¹⁰ m的轨道上绕行，靠静电引力维持。原子核含有原子99.9%以上的质量。
This model immediately explained the scattering results: the alpha particle only comes close enough to the nucleus to interact strongly in head-on or near-head-on collisions. The empty space between nuclei allows most alphas to pass through unaffected.
该模型立刻解释了散射结果：只有在对心碰撞或近对心碰撞中，α粒子才能靠近原子核到足以发生强相互作用。核之间的广阔空间使得大部分α粒子能够不受影响地穿过。
6. Estimating Nuclear Size: The Method of Closest Approach | 估算原子核大小：最接近距离法
Rutherford used the scattering data to estimate the nuclear size by considering a head-on collision. At the distance of closest approach d, all the initial kinetic energy Eₖ of the alpha particle is converted into electric potential energy.
卢瑟福利用散射数据，通过考虑对心碰撞来估算原子核的大小。在最近距离d处，α粒子的全部初始动能Eₖ转化为电势能。
Using conservation of energy: Eₖ = (1/(4πε₀)) · (q₁q₂)/d icle) and q₂ = +Ze (charge of the gold nucleus). Hence the distance of closest approach is d = (1/(4πε₀)) · (2Ze²)/Eₖ. This gives an upper limit for the nuclear radius, because the alpha particle cannot actually touch the nucleus if it is deflected before reaching that distance.
由能量守恒：Eₖ = (1/(4πε₀)) · (q₁q₂)/d，其中q₁ = +2e（α粒子的电荷），q₂ = +Ze（金原子核的电荷）。因此最接近距离为d = (1/(4πε₀)) · (2Ze²)/Eₖ。这一距离给出了原子核半径的上限，因为α粒子若在到达该距离前就已偏转，则实际接触不到核。
7. The Closest Approach Formula and a Worked Example | 最接近距离公式与计算实例
For gold, Z = 79, and the alpha particles used typically had kinetic energy of about 5 MeV (5 × 10⁶ eV). Converting to joules: Eₖ = 5 × 10⁶ × 1.602 × 10⁻¹⁹ ≈ 8.01 × 10⁻¹³ J. The constant 1/(4πε₀) = 8.99 × 10⁹ N m² C⁻², and e = 1.602 × 10⁻¹⁹ C.
对于金，Z = 79，实验中使用的α粒子动能通常约为5 MeV（5 × 10⁶ eV）。换算成焦耳：Eₖ = 5 × 10⁶ × 1.602 × 10⁻¹⁹ ≈ 8.01 × 10⁻¹³ J。常数1/(4πε₀) = 8.99 × 10⁹ N m² C⁻²，e = 1.602 × 10⁻¹⁹ C。
he formula: d = (8.99 × 10⁹) × (2 × 79 × (1.602 × 10⁻¹⁹)²) / (8.01 × 10⁻¹³) ≈ 4.55 × 10⁻¹⁴ m. This is around 40 times larger than modern values of the gold nuclear radius (~7 × 10⁻¹⁵ rming it as an upper bound. Today, nuclear radii are more accurately described by r = r₀ ³√A, with r₀ ≈ 1.2 × 10⁻¹⁵ m.
代入公式：d = (8.99 × 10⁹) × (2 × 79 × (1.602 × 10⁻¹⁹)²) / (8.01 × 10⁻¹³) ≈ 4.55 × 10⁻¹⁴ m。这比现代测得的金核半径（~7 × 10⁻¹⁵ m）大约40倍，证实其为尺寸上限。如今原子核半径更准确地由 r = r₀ ³√A 描述，式中 r₀ ≈ 1.2 × 10⁻¹⁵ m。
8. Nuclear Composition: Protons and Neutrons | 原子核的组成：质子和中子
The nucleus was later found to be composed of protons and neutrons, collectively called nucleons. A proton carries a single positive charge +e, while the neutron is electrically neutral. The number of protons Z determines the element, and the total number of nucleons A (mass number) determines the isotope.
后来发现原子核由质子和中子组成，统称为核子。质子带一个正电荷+e，而中子不带电。质子数Z决定元素的种类，核子总数A（质量数）决定同位素。
The discovery of the neutron by Chadwick in 1932 completed the picture: the nucleus contains Z protons and (A − Z) neutrons. For example, gold‑197 has 79 protons and 118 neutrons. The nuclear radius increases with the cube root of the mass number, consistent with a roughly constant nuclear density.
查德威克于1932年发现中子，使图像完整：原子核包含Z个质子和(A − Z)个中子。例如金-197有79个质子和118个中子。原子核半径随质量数的立方根增大，这与近似恒定的核密度一致。
9. The Strong Nuclear Force and Stability | 强核力与稳定性
ucleus together. This is the strong nuclear force, which acts between all nucleons (proton–proton, neutron–neutron and proton–neutron) at distances up to about 2–3 × 10⁻¹⁵ m.
由于质子间通过库仑力相互排斥，必定存在一种强得多的吸引力才能将原子核维系在一起。这就是强核力，它作用于所有核子之间（质子-质子、中子-中子、质子-中子），作用范围约2–3 × 10⁻¹⁵ m。
The strong force is charge-independent and very short-range; beyond a few femtometres it drops to nearly zero. In larger nuclei, extra neutrons are needed to provide additional strong-force attraction without adding electrostatic repulsion, leading to the neutron–proton ratio increasing as Z rises. This explains the shape of the nuclear stability curve.
强核力与电荷无关且作用距离极短；超过几飞米就几乎降至零。在较大的原子核中，需要额外的中子来提供更多的强核力吸引而不增加静电排斥，因此随Z增大，中子-质子比也随之上升。这解释了核稳定性曲线的形状。
10. Significance and Legacy of the Gold Foil Experiment | 金箔实验的意义与遗产
The Geiger–Marsden experiment and Rutherford's nuclear model marked the beginning of nuclear physics. It established that the atom is not indivisible but has an internal structure consisting of a dense nucleus and a surrounding electron cloud, a view that underpins all modern chemistry and physics.
盖革-马斯登实验和卢瑟福的核式模型标志着核物理学的开端。它确立了原子并非不可分割，而是具有由致密原子核和周围电子云构成的内部结构，这一观点是现代化学和物理学的基础。
Rutherford's work directly led to the discovery of the proton, the prediction and discovery of the neutron, and later to the development of quantum theory and particle accelerators. The concept of the nucleus also opened the door to nuclear energy, medical imaging, and radiotherapy. The experiment remains one of the most elegant demonstrations of how an unexpected observation can completely reshape our understanding of nature.
卢瑟福的工作直接促成了质子的发现、中子的预言与发现，以及后来量子理论和粒子加速器的发展。原子核的概念也为核能、医学成像和放射治疗打开了大门。该实验至今仍是最优雅的示范之一，说明一次非预期的观测如何彻底重塑我们对自然的认识。
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