📚 E.1 Structure of the Atom | 原子结构
The atom, once believed to be an indivisible particle, is now understood as a complex system of subatomic constituents. In IB Physics Topic E.1, we examine the structure of the atom through historical models, the properties of the nucleus, and the quantised nature of electronic energy levels. This topic forms the bridge between classical physics and the quantum world, underpinning everything from nuclear stability to atomic spectra.
原子曾经被认为是一种不可分割的粒子，如今则被理解为一个由亚原子成分构成的复杂系统。在 IB 物理 E.1 专题中，我们通过历史模型、原子核的性质以及电子能级的量子化特性来研究原子的结构。这一专题构成了经典物理与量子世界之间的桥梁，是理解核稳定性与原子光谱等现象的基础。
1. Historical Development of Atomic Models | 原子模型的历史发展
The concept of the atom originated with ancient Greek philosophers who proposed that matter is composed of tiny, indivisible particles called 'atomos'.
原子的概念起源于古希腊哲学家，他们提出物质由微小的、不可分割的粒子组成，称为“原子”。
In the early 19th century, John Dalton revived the atomic theory with experimental evidence, suggesting that each element consists of identical atoms that combine in fixed ratios.
19 世纪初，约翰·道尔顿用实验证据重新提出了原子论，认为每种元素由相同的原子组成，这些原子以固定比例结合。
J.J. Thomson's discovery of the electron in 1897 disproved the idea of indivisibility and led to the 'plum pudding' model, in which negatively charged electrons were embedded in a sphere of positive charge.
1897 年 J.J. 汤姆逊发现了电子，颠覆了原子的不可分割性，并提出了“葡萄干布丁”模型，即带负电的电子嵌在带正电的球体中。
Ernest Rutherford's gold foil experiment in 1911 provided evidence for a dense, positively charged nucleus, leading to the planetary model of the atom.
1911 年欧内斯特·卢瑟福的金箔实验为致密带正电的原子核提供了证据，由此诞生了原子的行星模型。
2. The Nuclear Atom and Rutherford Scattering | 核式原子与卢瑟福散射
In the Geiger-Marsden experiment, a beam of alpha particles was directed at a thin gold foil. Most particles passed through with little deflection, but a small fraction were scattered through large angles, some even bouncing back.
在盖革-马斯登实验中，一束 α 粒子射向一片薄金箔。大多数粒子几乎未偏转地穿过，但有一小部分被大角度散射，个别粒子甚至被反弹回来。
These observations could only be explained if the atom's positive charge and most of its mass are concentrated in a tiny central nucleus, with electrons orbiting in the largely empty space around it.
只有假设原子的正电荷及其绝大部分质量集中在一个极小的中心原子核上，而电子在周围空旷的空间中绕行，这些观察结果才能得到解释。
Rutherford scattering thus established the nuclear model of the atom and gave an early method for estimating the size of the nucleus.
卢瑟福散射因此确立了原子的核式模型，并提供了估算原子核大小的早期方法。
3. Protons, Neutrons and Isotopes | 质子、中子和同位素
The nucleus is composed of protons and neutrons, collectively called nucleons. The atomic number Z equals the number of protons and determines the element, while the mass number A is the total number of nucleons.
原子核由质子和中子组成，统称为核子。原子序数 Z 等于质子数，决定了元素的种类，而质量数 A 是核子的总数。
Atoms of the same element that have the same Z but different A are called isotopes. They possess identical chemical properties but different nuclear masses.
同一种元素中 Z 相同但 A 不同的原子称为同位素。它们具有相同的化学性质，但原子核质量不同。
A nuclide is symbolically represented as ᴬᶻX, where X is the chemical symbol. For example, carbon-12 is written as ¹²₆C.
核素用符号ᴬᶻX表示，其中 X 是化学符号。例如，碳-12 写作 ¹²₆C。
4. Nuclear Radii | 原子核半径
Scattering experiments reveal that the radius R of a nucleus depends on its mass number A. This relationship is given by the empirical formula:
散射实验表明，原子核的半径 R 取决于其质量数 A。这一关系由经验公式给出：
R = R₀ A¹⁄³
where R₀ is an empirical constant approximately equal to 1.2 × 10⁻¹⁵ m (1.2 fm).
其中 R₀ 是一个经验常数，约等于 1.2 × 10⁻¹⁵ m（1.2 fm）。
The A¹⁄³ dependence implies that the volume of the nucleus is proportional to the number of nucleons, so nuclear matter has a roughly constant density, on the order of 10¹⁷ kg m⁻³.
与 A¹⁄³ 的依赖关系意味着原子核的体积与核子数成正比，因此核物质具有大致恒定的密度，数量级约为 10¹⁷ kg m⁻³。
Nuclear radii are typically measured using electron scattering, where the de Broglie wavelength of high-energy electrons is small enough to probe nuclear dimensions.
原子核半径通常通过电子散射来测量，高能电子的德布罗意波长足够小，可以探测核的尺度。
5. The Strong Nuclear Force | 强核力
The nucleus is held together despite the electrostatic repulsion between protons. This is explained by the strong nuclear force, one of the four fundamental forces.
尽管质子之间存在静电排斥，原子核仍能保持在一起。这可以通过强核力来解释，强核力是四种基本力之一。
The strong force acts between all nucleons (protons and neutrons) independently of charge. It is a very short-range force, effective only at separations of about 10⁻¹⁵ m.
强核力作用于所有核子（质子和中子）之间，与电荷无关。它是一种非常短程的力，仅在约 10⁻¹⁵ m 的距离内有效。
At distances around 1 fm, the strong force is attractive and much stronger than the electrostatic repulsion, binding the nucleons tightly. At separations smaller than 0.5 fm, it becomes repulsive, preventing the nucleus from collapsing.
在约 1 fm 的距离上，强核力表现为吸引力，且远强于静电排斥，将核子紧密束缚在一起。当间距小于 0.5 fm 时，它变为排斥力，防止原子核坍缩。
The short range of the strong force explains why lighter nuclei have roughly equal numbers of protons and neutrons, while heavier nuclei require more neutrons to add binding without extra electrostatic repulsion.
强核力的短程性解释了为什么较轻的原子核中质子数和中子数大致相等，而较重的原子核需要更多的中子来增加结合能而不引入额外的静电排斥。
6. The Bohr Model of Hydrogen | 氢原子的玻尔模型
Niels Bohr proposed a model for the hydrogen atom in which electrons move in allowed circular orbits without radiating energy – these are called stationary states.
尼尔斯·玻尔为氢原子提出了一个模型，其中电子在允许的圆形轨道上运动而不辐射能量——这些状态称为定态。
The angular momentum of the electron in an orbit is quantised: mvr = n(h/2π), where n is an integer called the principal quantum number (n = 1, 2, 3, ...).
轨道中电子的角动量是量子化的：mvr = n(h/2π)，其中 n 是一个称为主量子数的整数（n = 1, 2, 3, ...）。
The total energy of an electron in level n is given by: Eₙ = –13.6 eV / n² e ground state (n = 1) has the lowest energy, while higher n correspond to excited states.
在能级 n 中的电子总能量为：Eₙ = –13.6 eV / n²。基态（n = 1）具有最低能量，而更高的 n 对应激发态。
An electron transitions between levels by absorbing or emitting a photon whose energy equals the difference between the two levels: ΔE = E₂ – E₁ = hf.
电子通过吸收或发射一个光子在不同能级之间跃迁，光子的能量等于两能级之差：ΔE = E₂ – E₁ = hf。
7. Atomic Energy Levels and Transitions | 原子能级与跃迁
Atoms have discrete energy levels. The lowest possible energy level is the ground state, and all higher levels are excited states. If an electron receives enough energy to leave the atom entirely, ionisation occurs.
原子具有分立的能级。可能的最低能级为基态，所有更高的能级均为激发态。如果电子获得足够能量完全离开原子，就会发生电离。
Excitation can happen through collisions with other particles or by absorbing a photon of exactly the right energy. De-excitation often results in the emission of a photon with energy equal to the energy lost by the electron.
激发可以通过与其他粒子的碰撞或吸收一个能量恰好匹配的光子来实现。退激发通常导致发射一个光子，其能量等于电子损失的能量。
The frequency f and wavelength λ of the emitted or absorbed photon are found using ΔE = hf = hc/λ, where h is the Planck constant and c is the speed of light.
发射或吸收的光子的频率 f 和波长 λ 通过ΔE = hf = hc/λ求得，其中 h 为普朗克常数，c 为光速。
the ultraviolet Lyman series, and transitions to n = 3 yield the infrared Paschen series.
跃迁至 n = 2 能级产生可见光的巴尔末系，跃迁至 n = 1 给出紫外区的莱曼系，而跃迁至 n = 3 产生红外区的帕邢系。
8. Emission and Absorption Spectra | 发射光谱与吸收光谱
When light from excited atoms is passed through a spectroscope, bright lines on a dark background are observed – this is an emission spectrum. Each element produces a unique set of spectral lines, acting like a fingerprint.
当受激原子发出的光通过分光镜时，可以观察到暗背景上的亮线——这就是发射光谱。每种元素都产生一组独特的光谱线，就像指纹一样。
An absorption spectrum appears as dark lines on a continuous rainbow background. These lines occur when a cooler gas absorbs specific wavelengths of light passing through it, corresponding to the energy gaps in its atoms.
吸收光谱表现为连续彩虹背景上的暗线。当较冷的气体吸收穿过它的特定波长的光时，就会出现这些暗线，这些波长对应于原子中的能级间隙。
The dark absorption lines of the sun, called Fraunhofer lines, provide evidence for the elements present in the solar atmosphere and were instrumental in encouraging the development of atomic structure models.
太阳光谱中的暗吸收线被称为夫琅禾费线，它们为太阳大气中存在的元素提供了证据，并对原子结构模型的发展起到了推动作用。
9. Nuclear Energy Levels | 原子核能级
Just as electrons exist in discrete energy levels within the atom, the nucleus itself has quantised energy levels. Nucleons occupy specific shells inside the nucleus, analogous to electron shells.
就像原子中的电子存在于分立的能级中一样，原子核本身也具有量子化的能级。核子在核内占据特定的壳层，类似于电子壳层。
When a nucleus transitions from an excited nuclear state to a lower energy state (often following alpha or beta decay), it emits a high-energy photon called a gamma ray. The energy of the gamma photon equals the difference between the two nuclear energy levels.
当原子核从激发核态跃迁到较低能量状态时（通常发生在 α 衰变或 β 衰变之后），它会发射一个高能光子，称为 γ 射线。γ 光子的能量等于两个核能级之间的差值。
Gamma ray spectra are discrete and provide crucial evidence for the existence of nuclear energy levels, supporting the nuclear shell model.
γ 射线谱是分立的，为原子核能级的存在提供了关键证据，从而支持了核壳层模型。
10. Limitations and the Quantum Picture | 局限性与量子图像
Bohr's model was remarkably successful for hydrogen but failed to predict spectra for atoms with more than one electron. It could not explain the relative intensities of spectral lines or why some electron orbits were not observed.
玻尔模型在氢原子上非常成功，但无法预测多于一个电子的原子的光谱。它不能解释光谱线的相对强度，也不能说明为什么某些电子轨道未被观察到。
The model was a hybrid of classical and quantum ideas, treating electrons as particles in fixed orbits while imposing an arbitrary quantisation condition. Modern quantum mechanics describes electrons in terms of probability clouds, or orbitals, solving the Schrodinger equation for the atom.
该模型是经典与量子思想的混合体，既将电子视为在固定轨道上的粒子，又强加了一个任意的量子化条件。现代量子力学用概率云（即轨道）来描述电子，通过求解薛定谔方程来处理原子。
The wave-particle duality of the electron and the Heisenberg uncertainty principle further refined the picture, showing that the precise position and momentum of an electron cannot be simultaneously known.
电子的波粒二象性和海森堡不确定性原理进一步修正了物理图像，表明电子的准确位置和动量无法同时被确定。
Despite its shortcomings, the Bohr model remains an essential stepping stone, introducing the crucial concept of energy quantisation that permeates all of modern physics.
尽管存在不足，玻尔模型仍然是一个重要的里程碑，它引入了能量量子化这一贯穿现代物理学的重要概念。
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