📚 Looking inside the atom | 原子内部探秘
If you could zoom into a single grain of sand, you would eventually find a world of incredible emptiness and tiny, energetic building blocks. The interior of an atom is mostly void, yet it contains a dense nucleus surrounded by a cloud of electrons. Understanding what lies inside the atom is not only a triumph of modern physics but also the foundation for explaining everything from chemical bonding to nuclear energy and radioactivity. In this article, we explore the key experimental evidence and theoretical models that reveal the inner structure of the atom, covering the vital concepts required for CIE A‑Level Physics.
如果你能把一颗沙子无限放大，最终会看到一个极度空旷却充满微小活力部件的世界。原子的内部几乎是一片真空，却包含着一个致密的原子核以及环绕的电子云。理解原子内部的结构不仅是现代物理学的伟大成就，也是解释化学键、核能以及放射性等一切现象的基础。本文将探讨揭示原子内部结构的关键实验证据和理论模型，涵盖 CIE A‑Level 物理所需的重要概念。
1. Early models of the atom | 早期原子模型
The idea that matter is made of indivisible particles dates back to ancient Greece, but the first scientific atomic model was proposed by John Dalton in the early 19th century. Dalton suggested that all matter consists of tiny, solid, indivisible spheres called atoms, and each element had its own type of atom. This model explained the laws of conservation of mass and definite proportions, but it could not account for electrical phenomena.
物质由不可分割的粒子组成的观点可以追溯到古希腊，但第一个科学原子模型是 19 世纪初由约翰·道尔顿提出的。道尔顿认为所有物质都由微小的、实心的、不可分割的球体（即原子）构成，每种元素都有自己独特的原子类型。该模型解释了质量守恒定律和定比定律，但无法解释电学现象。
J.J. Thomson's discovery of the electron in 1897 radically changed this picture. He proposed the "plum pudding" model, in which negatively charged electrons were embedded like raisins in a sphere of uniform positive charge. Although this model acknowledged the existence of subatomic particles, it was soon overturned by an elegant experiment.
J.J. 汤姆孙在 1897 年发现电子后，彻底改变了这一图景。他提出了“葡萄干布丁”模型，即带负电的电子像葡萄干一样嵌在均匀分布的正电荷球体中。虽然该模型承认了亚原子粒子的存在，但很快就被一个精妙的实验推翻了。
2. Rutherford scattering and the nuclear model | 卢瑟福散射与核式模型
In 1909, Hans Geiger and Ernest Marsden, under the direction of Ernest Rutherford, fired a beam of alpha particles at a thin gold foil. According to the plum pudding model, most alpha particles should have passed through with minimal deflection. Surprisingly, while most did pass straight through, a small fraction were scattered through large angles, and some even bounced back.
1909 年，汉斯·盖革和欧内斯特·马斯登在欧内斯特·卢瑟福的指导下，用一束 α 粒子轰击薄金箔。按照葡萄干布丁模型，大多数 α 粒子应当几乎不受偏转地穿过。令人惊讶的是，尽管大多数粒子确实径直穿过，但一小部分发生了大角度散射，有的甚至反弹回来。
Rutherford interpreted these results by proposing that all the positive charge and almost all the mass of an atom are concentrated in a tiny central region, which he called the nucleus. The electrons orbit this nucleus at relatively large distances, leaving the rest of the atom mostly empty space. This nuclear model successfully explained the large‑angle scattering: only when an alpha particle came very close to the dense, positively charged nucleus would the Coulomb repulsion be strong enough to cause significant deflection.
卢瑟福将这些结果解释为：原子的全部正电荷和几乎全部质量都集中在微小的中心区域，他称之为原子核。电子在相对很大的距离上绕核运行，使得原子其余部分几乎是空的空间。这一核式模型成功解释了发生大角度散射的原因：只有当 α 粒子非常靠近致密且带正电的原子核时，库仑斥力才会足够强，从而引起显著的偏转。
Force of repulsion ∝ 1 / r²
斥力 ∝ 1 / r²
3. Nucleons: protons and neutrons | 核子：质子和中子
Rutherford’s nucleus was initially thought to contain only protons, since the hydrogen nucleus is a single proton. However, this posed a problem: the mass number (A) of most atoms was roughly twice their atomic number (Z), implying the existence of neutral particles with roughly the proton mass. In 1932 James Chadwick discovered the neutron through experiments with beryllium and alpha particles, confirming the presence of uncharged nucleons.
卢瑟福的原子核最初被认为只包含质子，因为氢原子核就是一个质子。但这带来一个问题：大多数原子的质量数（A）大约是原子序数（Z）的两倍，这意味着存在与质子质量相当的中性粒子。1932 年，詹姆斯·查德威克通过铍与 α 粒子的实验发现了中子，从而证实了不带电核子的存在。
mass of approximately 1.67 × 10⁻²⁷ kg. A neutron is electrically neutral and has a slightly larger mass. Both nucleons are themselves composite particles made of quarks, a topic we will mention later.
如今我们知道，核子（质子和中子）在原子核内结合在一起。质子携带一个正的基本电荷 +e，静止质量约为 1.67 × 10⁻²⁷ kg。中子不带电，质量略大一些。两种核子本身都是由夸克组成的复合粒子，稍后我们会提到。
4. Atomic number, mass number and isotopes | 原子序数、质量数与同位素
The chemical identity of an atom is determined by the number of protons in its nucleus, called the atomic number Z. The total number of nucleons (protons + neutrons) is the mass number A. A nuclide is represented by the notation ᴬₓX where X is the chemical symbol. For example, the most common isotope of carbon is written as ¹²₆C.
原子的化学特性由原子核中的质子数决定，称为原子序数 Z。核子的总数（质子与中子之和）为质量数 A。核素用符号 ᴬₓX 表示，X 为元素符号。例如，最常见的碳同位素写作 ¹²₆C。
Isotopes are atoms of the same element (same Z) that have different numbers of neutrons, hence different mass numbers. They share nearly identical chemical properties because their electron configurations are the same, but they may have very different nuclear stabilities. Examples include the stable isotopes ¹²₆C, ¹³₆C and the radioactive isotope ¹⁴₆C, which is used in carbon dating.
同位素是指质子数相同（Z 相同）而中子数不同的同种元素原子，因此质量数不同。它们的化学性质几乎相同，因为电子排布一致，但核稳定性可能差异很大。例如，稳定同位素 ¹²₆C、¹³₆C 以及放射性同位素 ¹⁴₆C，后者便被用于碳年代测定法。
| Isotope | 同位素 | Z | N (neutrons) | A |
|---|---|---|---|
| Hydrogen-1 | 氢-1 | 1 | 0 | 1 |
| Hydrogen-2 (deuterium) | 氢-2 (氘) | 1 | 1 | 2 |
| Uranium-235 | 铀-235 | 92 | 143 | 235 |
5. The strong nuclear force | 强核力
If the nucleus is filled with closely packed protons, the electromagnetic repulsion between them should blow it apart. The fact that nuclei are stable points to a very strong attractive force acting between nucleons. This is the strong nuclear force, which is far stronger than the electrostatic repulsion but acts only over extremely short distances (about 1–2 femtometres).
如果原子核内挤满了质子，它们之间的电磁斥力应当会将原子核撕裂。然而原子核稳定存在，这表明核子之间存在着一种极强的吸引力，这就是强核力。它远比静电斥力强，但作用距离极短（约 1–2 飞米）。
The strong force has several key properties: it is attractive at nucleon separations around 1 fm, but becomes repulsive at even shorter distances to prevent the nucleons from overlapping. It acts between all nucleon pairs (proton-proton, neutron-neutron, proton-neutron) with essentially the same strength, and it does not depend on electric charge. This explains why heavier nuclei require more neutrons to provide additional attractive force without adding extra electrostatic repulsion.
强核力有几个关键性质：在核子间距约 1 fm 时表现为吸引力，但在更短距离下变为排斥力，从而防止核子重叠。它在所有核子对之间（质子‑质子、中子‑中子、质子‑中子）的作用强度基本相同，且与电荷无关。这解释了为什么较重的原子核需要更多的中子，以便在不增加额外静电斥力的情况下提供更多的吸引力。
6. Radioactivity and unstable nuclei | 放射性与不稳定核
Not all nuclei are stable. If the balance between the strong force and electrostatic repulsion is unfavourable, a nucleus will be radioactive and spontaneously emit particles or electromagnetic radiation to move towards a more stable configuration. Radioactivity is a random, spontaneous process and cannot be influenced by external conditions such as temperature or pressure.
并非所有原子核都稳定。如果强核力与静电斥力之间的平衡不利，该核就会具有放射性，并自发地发射粒子或电磁辐射，以趋向更稳定的状态。放射性是一种随机的自发过程，不受温度或压力等外界条件的影响。
The three main types of radiation are alpha (α), beta (β) and gamma (γ). An alpha particle is a helium nucleus (²⁴₂He), consisting of 2 protons and 2 neutrons. Beta-minus decay involves the emission of an electron (⁰₋₁e) and an antineutrino when a neutron transforms into a proton. Gamma rays are high‑energy photons emitted when a nucleus changes from an excited state to a lower energy state.
三种主要辐射类型是 α、β 和 γ 辐射。α 粒子即氦原子核（²⁴₂He），由 2 个质子和 2 个中子组成。β⁻ 衰变是在一个中子转化为质子时发射电子（⁰₋₁e）和反中微子。γ 射线是原子核从激发态跃迁到低能态时发射的高能光子。
7. Nuclear decay equations | 核衰变方程
In all nuclear reactions, both mass number A and proton number Z are conserved. This allows us to write balanced nuclear equations. For alpha decay, the nucleus loses 2 protons and 2 neutrons, so A decreases by 4 and Z decreases by 2. A typical example is the decay of uranium‑238:
在所有核反应中，质量数 A 和质子数 Z 都是守恒的，这使得我们可以写出配平的核方程。对于 α 衰变，原子核失去 2 个质子和 2 个中子，因此 A 减少 4，Z 减少 2。一个典型例子是铀‑238 的衰变：
²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He
For beta-minus decay, a neutron is converted into a proton, so Z increases by 1 while A remains unchanged. An antineutrino (ν̄) is also emitted. An example is carbon‑14 decay:
在 β⁻ 衰变中，一个中子转化为质子，因此 Z 增加 1，而 A 保持不变，同时还会发射一个反中微子（ν̄）。碳‑14 衰变便是一例：
¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̄
Gamma decay does not change A or Z; it merely lowers the energy of the nucleus and is often emitted alongside alpha or beta decays.
γ 衰变不改变 A 或 Z，它只是降低原子核的能量，并且通常伴随 α 或 β 衰变一起发射。
8. The scale of the atom and nucleus | 原子与原子核的尺度
One of the most startling aspects of looking inside the atom is the sheer difference in scale. The typical radius of an atom is about 10⁻¹⁰ m, while the nucleus has a radius of only about 10⁻¹⁵ m. To put this in perspective, if the nucleus were the size of a marble, the atom would be about the size of a football stadium.
观察原子内部最令人震撼的一点，是尺度的巨大差异。原子的典型半径约为 10⁻¹⁰ m，而原子核的半径仅约为 10⁻¹⁵ m。打个比方，如果原子核有一颗弹珠那么大，整个原子就相当于一个足球场的大小。
f the nucleus is approximately proportional to the number of nucleons, implying that nuclear matter has a roughly constant density. The density of nuclear material is enormous, around 2 × 10¹⁷ kg m⁻³.
原子核半径 R 可以通过公式 R = r₀ A¹/³ 来估算，其中 r₀ ≈ 1.2 fm，A 为质量数。之所以存在这一关系，是因为原子核的体积大致与核子数成正比，说明核物质具有大致恒定的密度。核物质的密度极大，约为 2 × 10¹⁷ kg m⁻³。
9. Electron arrangement and energy levels | 电子排布与能级
While the nucleus contains almost all the mass, the electrons determine the chemical behaviour and the size of the atom. In the Bohr model, electrons occupy discrete energy levels around the nucleus. Although this model has been superseded by the quantum mechanical cloud model, the idea of quantised energy levels remains central. Electrons can move between levels by absorbing or emitting photons of specific energies.
虽然原子核几乎包含了所有质量，但电子的行为决定着化学性质和原子大小。在玻尔模型中，电子占据核外分立的能级。尽管该模型已被量子力学的电子云模型所取代，但量子化能级的思想仍然至关重要。电子可以通过吸收或发射特定能量的光子在能级之间跃迁。
The maximum number of electrons in the n‑th shell is given by 2n². The outermost electrons (valence electrons) are responsible for chemical bonding and the emission spectra of elements. The study of line spectra provided early evidence for energy quantisation and helped refine our understanding of atomic structure.
第 n 层壳层最多可容纳 2n² 个电子。最外层的电子（价电子）负责化学键合以及元素发射光谱。线状光谱的研究为能量量子化提供了早期证据，并帮助完善了我们对原子结构的理解。
10. Probing the nucleus with alpha particles | 用 α 粒子探测原子核
Rutherford scattering is not only of historical importance; it remains a key method for estimating nuclear sizes. In such experiments, the distance of closest approach of an alpha particle in a head‑on collision can be calculated by equating the kinetic energy of the alpha particle to the electrostatic potential energy at the turning point:
卢瑟福散射不仅具有历史意义，至今仍然是估算核大小的重要方法。在这类实验中，可以通过将 α 粒子的动能与折返点处的静电势能相等，来计算迎面碰撞下 α 粒子的最接近距离：
½ m v² = (Ze)(2e) / (4π ε₀ d)
Here m and v are the mass and initial speed of the alpha particle, Z is the proton number of the target nucleus, e is the elementary charge, and d is the distance of closest approach. This calculation gives an upper limit for the nuclear radius and was how Rutherford first estimated it to be in the femtometre range.
式中 m 和 v 是 α 粒子的质量和初速度，Z 是靶核的质子数，e 为基本电荷，d 为最接近距离。这一计算给出了核半径的上限，卢瑟福正是借此首次估测出核半径处于飞米量级。
11. The modern view: quarks | 现代视角：夸克
rks, held together by gluons via the strong force (in its modern quantum chromodynamics formulation). A proton consists of two up quarks and one down quark (uud), giving a net charge of +⅔e + ⅔e − ⅓e = +e. A neutron consists of one up and two down quarks (udd), yielding zero net charge.
进一步深入探索后，物理学家发现核子并非基本粒子。质子和中子由更小的粒子——夸克——组成，胶子通过强相互作用（在现代量子色动力学框架下）将它们束缚在一起。一个质子由两个上夸克和一个下夸克构成（uud），净电荷为 +⅔e + ⅔e − ⅓e = +e。中子由一个上夸克和两个下夸克构成（udd），净电荷为零。
Quarks have fractional charges and are confined within hadrons; they cannot be observed as isolated particles under normal conditions. The standard model of particle physics classifies all known elementary particles and the forces between them, providing the deepest current understanding of what lies inside the atom.
夸克带有分数电荷，并被禁闭在强子内部；在普通条件下无法观测到孤立的夸克。粒子物理的标准模型对所有已知基本粒子及其相互作用进行了分类，为我们目前对原子内部最深层次的理解提供了框架。
12. Conclusion: from emptiness to structure | 结语：从虚空到结构
Far from being an indivisible solid sphere, the atom is a complex system governed by quantum rules and powerful forces. The journey from Dalton's billiard‑ball model to the discovery of the nucleus, nucleons, and quarks shows how experimental evidence continually reshapes our understanding of matter. For A‑Level Physics students, mastering these concepts provides a solid foundation for further study in nuclear physics, particle physics, and quantum phenomena.
原子远非一个不可分割的实心球体，而是一个受量子规则和强大作用力支配的复杂系统。从道尔顿的台球模型到原子核、核子和夸克的发现，这段历程展示了实验证据如何不断重塑我们对物质的理解。对于 A‑Level 物理学生来说，掌握这些概念将为后续学习核物理、粒子物理和量子现象打下坚实的基础。
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