📚 Electrons in Atoms | 原子中的电子
Understanding how electrons are arranged within atoms is fundamental to explaining chemical properties and periodicity. The modern quantum mechanical model describes electrons occupying specific energy levels, sub-levels, and orbitals, governed by principles such as the Aufbau principle, Hund’s rule, and the Pauli exclusion principle. Ionisation energies provide experimental evidence for this electronic structure.
理解原子中电子的排列方式是解释化学性质和周期性的基础。现代量子力学模型描述电子占据特定的能级、亚层和轨道，并遵循构造原理、洪特规则和泡利不相容原理等原则。电离能为这种电子结构提供了实验证据。
1. The Nuclear Atom and Energy Levels | 核原子与能级
Early models proposed electrons orbiting the nucleus in fixed circular paths, but the current model is based on quantum mechanics. Electrons exist in discrete energy levels, often called shells, labelled with the principal quantum number n = 1, 2, 3, …
早期模型提出电子在固定的圆形轨道上绕核运动，但现在的模型基于量子力学。电子存在于分立的能级中，通常称为电子层，用主量子数 n = 1, 2, 3, … 标记。
A higher n means a higher energy level and a greater average distance from the nucleus. The energy required to remove an electron from an atom depends largely on which shell it occupies.
n 越大，能级越高，电子离核的平均距离也越远。移走原子中的一个电子所需的能量，主要取决于它所占据的电子层。
2. Principal Quantum Number and Shells | 主量子数与电子层
The principal quantum number n determines the overall size and energy of a shell. The maximum number of electrons a shell can hold is given by 2n². Thus the first shell (n=1) holds up to 2 electrons, the second (n=2) holds up to 8, the third (n=3) holds up to 18, and so on.
主量子数 n 决定了电子层的大小和能量。一个电子层最多能容纳的电子数由 2n² 给出。因此第一层（n=1）最多容纳 2 个电子，第二层（n=2）最多容纳 8 个，第三层（n=3）最多容纳 18 个，依此类推。
In the periodic table, the period number corresponds to the highest principal quantum number being filled for the elements in that period.
在周期表中，周期数对应于该周期元素正在填充的最高主量子数。
3. Sub-shells: s, p, d, f | 亚层：s、p、d、f
Each shell (except n=1) is split into sub-shells. The number of sub-shells equals n. The sub-shells are designated s, p, d, and f. An s sub-shell consists of 1 orbital and holds a maximum of 2 electrons, a p sub-shell has 3 orbitals holding up to 6 electrons, a d sub-shell has 5 orbitals holding up to 10 electrons, and an f sub-shell has 7 orbitals holding up to 14 electrons.
除 n=1 外，每个电子层都分成若干亚层，亚层的数目等于 n。亚层用 s、p、d、f 标记。一个 s 亚层包含 1 个轨道，最多容纳 2 个电子；一个 p 亚层有 3 个轨道，最多容纳 6 个电子；一个 d 亚层有 5 个轨道，最多容纳 10 个电子；一个 f 亚层有 7 个轨道，最多容纳 14 个电子。
For example, the n=2 shell contains 2s and 2p sub-shells; the n=3 shell contains 3s, 3p, and 3d sub-shells. The order of sub-shell energies is not always straightforward: 4s is lower in energy than 3d, which affects the order of filling.
例如，n=2 的电子层包含 2s 和 2p 亚层；n=3 的电子层包含 3s、3p 和 3d 亚层。亚层能量的高低顺序并不总是简单的：4s 的能量低于 3d，这影响了填充顺序。
4. Atomic Orbitals: Shapes and Orientation | 原子轨道：形状与取向
An atomic orbital is a region of space around the nucleus where the probability of finding an electron is high. Each orbital can hold a maximum of two electrons. The shape of an s orbital is spherical. All s orbitals are spherical, with larger sizes as n increases.
原子轨道是原子核周围空间中的一个区域，在该区域内找到电子的概率很高。每个轨道最多能容纳两个电子。s 轨道的形状是球形的。所有 s 轨道都是球形的，随着 n 增加，轨道尺寸变大。
A p orbital has a dumbbell shape with two lobes on opposite sides of the nucleus. There are three p orbitals per sub-shell, designated px, py and pz, aligned along the x-, y- and z-axes respectively. Each p orbital has the same energy (they are degenerate).
p 轨道呈哑铃形，在原子核两侧各有一个瓣。每个 p 亚层有三个 p 轨道，称为 px、py 和 pz，分别沿 x、y、z 轴对称排列。这三个 p 轨道能量相同（它们是简并的）。
d orbitals have more complex shapes, often described as cloverleaf (four lobes) or as two lobes with a doughnut ring. There are five d orbitals: dxy, dxz, dyz, dx²−y², and dz².
d 轨道的形状更复杂，通常被描述为四叶草形（四个瓣）或两个瓣加上一个甜甜圈环。一共有五个 d 轨道：dxy、dxz、dyz、dx²−y² 和 dz²。
5. Electron Spin and Pauli Exclusion Principle | 电子自旋与泡利不相容原理
Electrons possess a property called spin, which can be thought of as clockwise or anticlockwise spin, represented by two spin states: +½ and −½. The Pauli exclusion principle states that no two electrons in the same atom can have the same set of four quantum numbers; therefore, an orbital can hold at most two electrons, and they must have opposite spins.
电子具有一种称为自旋的性质，可以看作顺时针或逆时针自旋，用两种自旋状态表示：+½ 和 −½。泡利不相容原理指出，同一原子中不能有两个电子的四个量子数完全相同；因此，一个轨道最多只能容纳两个电子，并且它们必须自旋相反。
In orbital box diagrams, this is shown by arrows pointing up (↑) and down (↓). When filling degenerate orbitals, electrons occupy separate orbitals with parallel spins before pairing up, as stated by Hund’s rule.
在轨道方框图中，这用向上 (↑) 和向下 (↓) 的箭头表示。在填充简并轨道时，电子会先以平行自旋的方式单独占据不同的轨道，然后再配对，这符合洪特规则。
6. Filling Orbitals: Aufbau Principle, Hund’s Rule | 轨道填充：构造原理、洪特规则
The Aufbau principle states that electrons fill the lowest available energy orbitals first. The order is approximately:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, …
构造原理指出，电子首先填充能量最低的可用轨道。填充顺序大致为：
1s、2s、2p、3s、3p、4s、3d、4p、5s、4d、5p、6s、4f、5d、6p……
Hund’s rule of maximum multiplicity says that when electrons occupy orbitals of equal energy (degenerate orbitals), they first fill them singly with parallel spins, minimising electron–electron repulsion. Pairing only occurs after each degenerate orbital has one electron.
洪特最大多重度规则指出，当电子占据能量相等的轨道（简并轨道）时，它们首先会以平行自旋的方式单独填入每个轨道，使电子间排斥最小。只有在每个简并轨道都填充了一个电子后，才会发生配对。
For example, nitrogen (atomic number 7) has the electron configuration 1s² 2s² 2p³. The three 2p electrons occupy the three separate p orbitals with parallel spins, giving three unpaired electrons.
例如，氮（原子序数 7）的电子排布为 1s² 2s² 2p³。三个 2p 电子以平行自旋的方式分别占据三个 p 轨道，因此有三个未配对电子。
7. Electron Configurations of Atoms | 原子的电子排布
Electron configurations are written by listing the sub-shells occupied, with superscript numbers indicating the number of electrons in each sub-shell. For example, oxygen: 1s² 2s² 2p⁴; sodium: 1s² 2s² 2p⁶ 3s¹; calcium: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s².
电子排布式通过列出被占据的亚层，并用上标数字表示每个亚层中的电子数来书写。例如，氧：1s² 2s² 2p⁴；钠：1s² 2s² 2p⁶ 3s¹；钙：1s² 2s² 2p⁶ 3s² 3p⁶ 4s²。
Shorthand notation uses the previous noble gas in brackets. For instance, potassium: [Ar] 4s¹; vanadium: [Ar] 3d³ 4s². Note that 4s is filled before 3d for most transition metals, but it is usually written in order of increasing principal quantum number after filling.
简写表示法使用方括号中的上一个稀有气体。例如，钾：[Ar] 4s¹；钒：[Ar] 3d³ 4s²。注意，对于大多数过渡金属，4s 亚层先于 3d 填充，但在书写时通常按主量子数递增的顺序排列。
Important exceptions: chromium (Z=24) and copper (Z=29). Their configurations are [Ar] 3d⁵ 4s¹ and [Ar] 3d¹⁰ 4s¹ respectively, rather than the expected 3d⁴ 4s² or 3d⁹ 4s². This is due to the extra stability of a half-filled (d⁵) or fully filled (d¹⁰) d sub-shell.
重要的例外情况：铬（Z=24）和铜（Z=29）。它们的电子排布分别是 [Ar] 3d⁵ 4s¹ 和 [Ar] 3d¹⁰ 4s¹，而不是预期的 3d⁴ 4s² 或 3d⁹ 4s²。这是因为半满（d⁵）或全满（d¹⁰）的 d 亚层具有额外的稳定性。
8. Electron Configurations of Ions | 离子的电子排布
When forming positive ions, electrons are removed from the highest energy level (the outermost shell). For transition metals, this means 4s electrons are lost before 3d electrons, because once the 3d sub-shell is populated, the 4s electrons experience greater repulsion and lie at higher energy.
形成正离子时，电子从最高能级（最外层）被移走。对于过渡金属，这意味着 4s 电子先于 3d 电子被失去，因为一旦 3d 亚层被填充，4s 电子受到更大的排斥力，能量更高。
For example, iron: Fe atom [Ar] 3d⁶ 4s²; Fe²⁺ ion [Ar] 3d⁶; Fe³⁺ ion [Ar] 3d⁵. Similarly, copper: Cu atom [Ar] 3d¹⁰ 4s¹; Cu⁺ ion [Ar] 3d¹⁰; Cu²⁺ ion [Ar] 3d⁹.
例如，铁：Fe 原子 [Ar] 3d⁶ 4s²；Fe²⁺ 离子 [Ar] 3d⁶；Fe³⁺ 离子 [Ar] 3d⁵。类似地，铜：Cu 原子 [Ar] 3d¹⁰ 4s¹；Cu⁺ 离子 [Ar] 3d¹⁰；Cu²⁺ 离子 [Ar] 3d⁹。
For non-transition metal ions, electrons are simply removed from the outermost occupied shell. Thus Al³⁺ has the configuration 1s² 2s² 2p⁶, the same as neon.
对于非过渡金属离子，电子只是从已占据的最外层中被移走。因此 Al³⁺ 的排布为 1s² 2s² 2p⁶，与氖相同。
9. Ionisation Energy: First and Successive | 电离能：第一电离能与逐级电离能
The first ionisation energy (IE₁) is the energy required to remove one mole of electrons from one mole of gaseous atoms to form one mole of gaseous ions with a positive charge of +1. The equation is:
X(g) → X⁺(g) + e⁻
第一电离能（IE₁）是指从 1 摩尔气态原子中移走 1 摩尔电子，生成 1 摩尔带 +1 电荷的气态离子所需的能量。方程式如下：
X(g) → X⁺(g) + e⁻
The second ionisation energy (IE₂) refers to the removal of a second electron: X⁺(g) → X²⁺(g) + e⁻. Successive ionisation energies always increase because as electrons are removed, the remaining electrons experience greater effective nuclear charge and are held more tightly.
第二电离能（IE₂）是指移除第二个电子：X⁺(g) → X²⁺(g) + e⁻。逐级电离能总是递增的，因为随着电子被移走，剩余电子感受到的有效核电荷增大，被更牢固地束缚。
10. Trends in Ionisation Energies across Periods and down Groups | 周期与族中的电离能变化趋势
Across a period (e.g. from sodium to argon), the first ionisation energy generally increases. This is because the nuclear charge increases, but the added electrons enter the same principal shell. The shielding effect of inner electrons remains similar, so the outer electrons are attracted more strongly to the nucleus.
在同一周期（例如从钠到氩）中，第一电离能总体上增加。这是因为核电荷增加，而新加入的电子进入同一主量子层。内层电子的屏蔽效应基本不变，因此外层电子被原子核吸引得更强。
There are two notable decreases across Period 3: the drop from magnesium (1s² 2s² 2p⁶ 3s²) to aluminium (1s² 2s² 2p⁶ 3s² 3p¹) occurs because the 3p electron is easier to remove than the 3s electron as it is in a higher energy sub-shell and is slightly better shielded. The drop from phosphorus (3p³) to sulfur (3p⁴) occurs because in sulfur, the paired electrons in one p orbital experience greater repulsion, making it easier to remove one electron.
在第三周期中有两次明显的下降：从镁（1s² 2s² 2p⁶ 3s²）到铝（1s² 2s² 2p⁶ 3s² 3p¹）的下降是因为 3p 电子比 3s 电子更容易移走，因为它处于能量较高的亚层且屏蔽效应略强。从磷（3p³）到硫（3p⁴）的下降是因为硫的一个 p 轨道中配对的电子产生更大的排斥力，从而更容易移走一个电子。
Down a group, first ionisation energies decrease because the outer electrons are in shells with higher principal quantum numbers, farther from the nucleus. The increased distance and the greater shielding by inner electrons outweigh the effect of increased nuclear charge.
沿族向下，第一电离能减小，因为外层电子处于主量子数更大的电子层中，离核更远。距离的增加和内层电子的屏蔽效应增强，超过了核电荷增大的影响。
| Element | Na | Mg | Al | Si | P | S | Cl | Ar |
|---|---|---|---|---|---|---|---|---|
| IE₁ (kJ mol⁻¹) | 496 | 738 | 578 | 786 | 1012 | 1000 | 1251 | 1521 |
11. Evidence for Electron Sub-shells from Ionisation Energies | 电离能提供的电子亚层证据
Successive ionisation energy data provide direct evidence for electron shells and sub-shells. A large jump in successive ionisation energies indicates that the next electron is being removed from a shell closer to the nucleus (with a lower principal quantum number).
逐级电离能数据为电子层和亚层的存在提供了直接证据。逐级电离能值的大幅跃升表明，下一个电子是从离核更近的壳层（主量子数更小）中被移走。
Consider sodium (Na, Z=11). Its electron configuration is 1s² 2s² 2p⁶ 3s¹. The first ionisation energy is relatively low (496 kJ mol⁻¹) as the electron is removed from the 3s shell. The second ionisation energy is very high (4563 kJ mol⁻¹) because the next electron comes from the much more stable 2p sub-shell. The huge jump between IE₁ and IE₂ confirms that the second electron is in a lower energy shell.
以钠（Na, Z=11）为例。其电子排布为 1s² 2s² 2p⁶ 3s¹。第一电离能较低（496 kJ mol⁻¹），因为移走的是 3s 电子。第二电离能非常高（4563 kJ mol⁻¹），因为下一个电子来自稳定得多的 2p 亚层。IE₁ 与 IE₂ 之间的巨大跃升证实第二个电子处于较低的能层中。
Data for aluminium (Z=13, 1s² 2s² 2p⁶ 3s² 3p¹) show a smaller increase from IE₁ to IE₂ (578 → 1817 kJ mol⁻¹) and then to IE₃ (2745 kJ mol⁻¹), all corresponding to removal of 3s and 3p electrons. The large jump occurs between IE₃ and IE₄ (2745 → 11578 kJ mol⁻¹), indicating the removal of an electron from the 2p sub-shell. Within the outer shell, smaller jumps can be attributed to the removal of electrons from different sub-shells or paired orbitals.
铝（Z=13, 1s² 2s² 2p⁶ 3s² 3p¹）的数据显示，IE₁ 到 IE₂ 的增幅较小（578 → 1817 kJ mol⁻¹），再到 IE₃（2745 kJ mol⁻¹），均对应于 3s 和 3p 电子的移除。大幅跃升发生在 IE₃ 和 IE₄ 之间（2745 → 11578 kJ mol⁻¹），表明移除的是 2p 亚层的电子。在外层内部，较小的能量跃升可归因于电子从不同亚层或已配对轨道中被移走。
These patterns of ionisation energies provide experimental verification of the quantum mechanical model of electron arrangement, supporting the existence of principal energy levels and sub-levels.
这些电离能的模式为电子排列的量子力学模型提供了实验验证，支持了主能级和亚能级的存在。
12. Summary and Exam Tips | 总结与考试技巧
In summary, electrons in atoms occupy orbitals grouped into sub-shells (s, p, d, f) and shells (principal quantum number n). The arrangement is governed by the Aufbau principle, Hund’s rule, and the Pauli exclusion principle. Electron configurations explain periodic trends and chemical behaviour. Ionisation energy experiments confirm the shell structure.
总之，原子中的电子占据轨道，轨道归类为亚层（s、p、d、f）和电子层（主量子数 n）。电子的排列受构造原理、洪特规则和泡利不相容原理支配。电子排布解释了元素周期律和化学行为。电离能实验证实了壳层结构。
Key exam points:
- Always write electron configurations clearly, using superscripts and the correct order.
- Remember the
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