📚 S1.3 Electron Configurations | 电子排布
Understanding how electrons are arranged inside atoms is fundamental to explaining chemical bonding, periodicity and the physical properties of elements. In this section, we investigate the quantum mechanical model of the atom, the evidence from atomic emission spectra, and the rules that allow us to write electron configurations for atoms and ions. These ideas underpin everything from the shape of the periodic table to trends in ionisation energy.
理解电子在原子内部的排布方式是解释化学键合、元素周期律及物理性质的基础。本节探讨原子的量子力学模型、原子发射光谱提供的证据，以及书写原子和离子电子排布所遵循的规则。这些概念支撑着从周期表形状到电离能趋势的方方面面。
1. Electromagnetic Radiation and Atomic Spectra | 电磁辐射与原子光谱
Electromagnetic radiation travels through space as waves and covers a vast range of wavelengths, from gamma rays to radio waves. When a sample of an element is energised by heating or an electric discharge, its electrons absorb specific amounts of energy and jump to higher energy levels. As these excited electrons fall back to lower levels, they release the excess energy as photons of light. Because the energy differences between allowed levels are fixed, the emitted light consists of only certain frequencies, producing a line spectrum rather than a continuous rainbow.
电磁辐射以波的形式在空间传播，覆盖从伽马射线到无线电波的广阔波长范围。当元素样品通过加热或放电获得能量时，电子吸收特定数量的能量，跃迁到较高能级。这些受激电子在回落到较低能级时，将多余的能量以光子的形式释放出来。由于允许能级之间的能量差是固定的，发射的光只包含特定频率，从而产生线状光谱而非连续的彩虹。
The energy (E) of a photon is directly proportional to its frequency (ν) through the Planck relation, and frequency is related to wavelength (λ) by the speed of light (c).
光子能量（E）与其频率（ν）成正比，由普朗克关系式给出；频率与波长（λ）通过光速（c）相联系。
E = hν and c = λν so E = hc/λ
A continuous spectrum (like that from a white-hot solid) contains all wavelengths blended together. A line spectrum, in contrast, is a series of sharp, coloured lines on a dark background. Each line corresponds to a specific energy transition in an atom, providing a unique fingerprint for that element.
连续光谱（如白热固体发出的光）包含混合在一起的所有波长。相比之下，线状光谱是在暗背景上的一系列锐利彩色谱线。每一条谱线对应原子中一个特定的能量跃迁，为该元素提供了独一无二的指纹。
2. The Hydrogen Emission Spectrum | 氢原子发射光谱
almer series, which arises when electrons drop from higher energy levels (n ≥ 3) down to the n = 2 level.
只有一个电子的氢原子给出最简单的线状光谱，这在量子理论的发展中至关重要。当电流通过低压氢气时，发射出的光分解为若干线系。在可见光区，我们看到巴尔末系，它产生于电子从较高能级（n ≥ 3）跃迁回 n = 2 能级。
The energy of any spectral line equals the difference between two quantised energy levels:
其他线系位于紫外区（莱曼系，跃迁至 n = 1）和红外区（帕邢系，跃迁至 n = 3）。任何谱线的能量等于两个量子化能级之差：
ΔE = Ehigher – Elower = hν
At the high-energy end of each series, the lines merge into a continuum. This convergence limit represents the point at which the electron is removed entirely from the atom, i.e. the ionisation energy. The hydrogen spectrum therefore provides direct experimental evidence that atomic energy levels are quantised.
在每个线系的高能端，谱线汇合成连续谱。这一收敛极限代表电子完全脱离原子的点，即电离能。因此氢光谱提供了原子能级是量子化的直接实验证据。
3. Energy Levels and Quantum Numbers | 能级与量子数
The modern model of the atom describes electrons in terms of orbitals – regions of space where there is a high probability of finding an electron. Each electron is characterised by a set of four quantum numbers. The principal quantum number, n, can take integer values 1, 2, 3, … and defines the main energy level, or shell. As n increases, the energy of the electron and its average distance from the nucleus increase.
现代原子模型用轨道（即空间中电子出现概率高的区域）来描述电子。每个电子由一组四个量子数表征。主量子数 n 可以取整数 1, 2, 3, …，它定义了主能级或壳层。随着 n 增大，电子的能量及其与原子核的平均距离增加。
bshells. Within a subshell, there are a specific number of orbitals, each of which can hold a maximum of two electrons. The following table summarises the relationship between n, subshells and electron capacities.
每个壳层进一步分为标记为 s、p、d 和 f 的亚层。给定壳层中亚层的数目等于 n。例如，n = 1 壳层只有一个 s 亚层；n = 2 壳层有 s 和 p 亚层；n = 3 壳层有 s、p 和 d 亚层。在一个亚层中，存在特定数量的轨道，每个轨道最多可容纳两个电子。下表总结了 n、亚层和电子容量的关系。
| Principal quantum number, n | Subshells present | Number of orbitals | Maximum electrons (2n²) |
|---|---|---|---|
| 1 | 1s | 1 | 2 |
| 2 | 2s, 2p | 1 + 3 = 4 | 8 |
| 3 | 3s, 3p, 3d | 1 + 3 + 5 = 9 | 18 |
| 4 | 4s, 4p, 4d, 4f | 1 + 3 + 5 + 7 = 16 | 32 |
In an isolated atom, all orbitals belonging to the same subshell (e.g. the three 2p orbitals) have identical energy and are described as degenerate.
在孤立原子中，属于同一亚层的所有轨道（如三个 2p 轨道）具有相同的能量，被称为简并。
4. Shapes of Atomic Orbitals | 原子轨道的形状
The shapes of orbitals are derived from the mathematical wave functions that describe electrons. s orbitals are spherical: the probability of finding an electron depends only on distance from the nucleus. The 1s orbital is a simple sphere, while higher s orbitals contain radial nodes where the probability drops to zero.
轨道的形状来源于描述电子的数学波函数。s 轨道是球形的：找到电子的概率仅取决于与核的距离。1s 轨道是一个简单的球体，而更高的 s 轨道包含概率降为零的径向节面。
p orbitals come in sets of three, each with a dumbbell shape oriented along one of the three Cartesian axes: px, py and pz. Each p orbital has a nodal plane passing through the nucleus where the probability of finding the electron is zero.
p 轨道以三个一组出现，每个呈哑铃形，分别沿三个笛卡尔坐标轴取向：px、py 和 pz。每个 p 轨道有一个穿过原子核的节面，该面上找到电子的概率为零。
d orbitals (five in a set) mostly adopt cloverleaf shapes with four lobes. The exception is the dz² orbital, which has two large lobes along the z-axis and a doughnut-shaped ring in the xy plane. Understanding orbital shape is essential for visualising how atoms bond and overlap in covalent bonding.
d 轨道（一组五个）大多呈四叶草形，有四个瓣。例外的是 dz² 轨道，它沿 z 轴有两个大瓣，并在 xy 平面上有一个甜甜圈形环。了解轨道形状对于形象化原子在共价键中如何成键和重叠至关重要。
5. Rules for Filling Orbitals: Aufbau, Hund and Pauli | 轨道填充规则：构造原理、洪特规则和泡利不相容原理
The way electrons fill up the available orbitals is governed by three key rules. The Aufbau principle states that electrons occupy the lowest energy orbitals first. In a multi-electron atom, the energy order is not simply 1s < 2s < 2p < 3s < 3p < 3d < 4s … Instead, the 4s orbital is slightly lower in energy than 3d, so it fills first: after 3p, electrons enter 4s before 3d.
电子填充可用轨道的方式由三条关键规则决定。构造原理指出，电子首先占据能量最低的轨道。在多电子原子中，能量顺序并非简单的 1s < 2s < 2p < 3s < 3p < 3d < 4s …。事实上，4s 轨道能量略低于 3d，因此先填充 4s：在 3p 之后，电子先进入 4s 再进入 3d。
Hund’s rule deals with degenerate orbitals: electrons will occupy degenerate orbitals singly, with parallel spins, before any orbital receives a second electron. This arrangement minimises electron–electron repulsion. For example, in a nitrogen atom (1s² 2s² 2p³), the three 2p electrons occupy three separate 2p orbitals with all spins pointing the same way: ↑ ↑ ↑.
洪特规则处理简并轨道：电子会先以平行自旋单独占据简并轨道，然后才进行配对。这种排布最大限度地减少了电子间排斥。例如，在氮原子（1s² 2s² 2p³）中，三个 2p 电子分别占据三个 2p 轨道，且自旋方向相同：↑ ↑ ↑。
The Pauli exclusion principle places a strict limit on each orbital: no two electrons in an atom can have the identical set of four quantum numbers. Since the first three quantum numbers define an orbital, the spin quantum number ms must differ. Consequently, an orbital can hold at most two electrons, which must have opposite spins (↑↓).
泡利不相容原理对每个轨道施加了严格限制：原子中任意两个电子不能拥有完全相同的四个量子数。由于前三个量子数定义一个轨道，自旋量子数 ms 必须不同。因此，一个轨道最多容纳两个电子，且它们必须自旋相反（↑↓）。
6. Writing Electron Configurations | 书写电子排布
(Z = 8) is 1s² 2s² 2p⁴. The sum of all superscripts equals the total number of electrons.
完整电子排布按能量递增的顺序列出所有占据的亚层，用上标数字表示每个亚层中的电子数。例如，氧（Z = 8）的排布为 1s² 2s² 2p⁴。所有上标之和等于电子总数。
his notation directs attention to the valence electrons that determine chemical behaviour.
对于较重的元素，简写电子排布用方括号中的前一周期稀有气体符号来表示内层芯电子。钠（Na，Z = 11）可写作 [Ne] 3s¹，钙（Ca，Z = 20）写作 [Ar] 4s²。这种记法将注意力引向决定化学行为的价电子。
Orbital box diagrams provide a visual representation. Each orbital is drawn as a box, and electrons are shown as arrows (↑ or ↓). Boxes for degenerate orbitals are grouped together. The diagram for carbon (1s² 2s² 2p²) would show the 2p electrons unpaired in separate boxes, consistent with Hund’s rule.
轨道方框图提供了一种可视化表示。每个轨道画成一个方框，电子用箭头（↑ 或 ↓）表示。简并轨道的方框被画在一起。碳（1s² 2s² 2p²）的方框图会将两个 2p 电子显示为分占不同的方框且不成对，符合洪特规则。
7. Exceptions: Chromium and Copper | 例外情况：铬和铜
ground-state configuration [Ar] 4s¹ 3d⁵ rather than the expected [Ar] 4s² 3d⁴. The half-filled 3d subshell (d⁵) is particularly
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