📚 Subshells and Atomic Orbitals | 子壳层与原子轨道
In modern chemistry, electrons are not simply particles orbiting the nucleus in fixed circles. Instead, they exist in three‑dimensional regions called atomic orbitals, which are organised into shells and subshells. Understanding subshells and orbitals allows us to explain the electron configurations of atoms, the shape of molecules, and the periodic trends of the elements.
在现代化学中，电子并不是沿着固定圆形轨道绕核运动的简单粒子。它们存在于被称为原子轨道的三维区域中，而这些轨道又组织成壳层与子壳层。理解子壳层与轨道，使我们能够解释原子的电子构型、分子的形状以及元素性质的周期性变化。
1. The Quantum Mechanical Model of the Atom | 原子的量子力学模型
Early atomic models, such as the Bohr model, pictured electrons moving in well‑defined circular paths. However, the quantum mechanical model describes electrons as wavefunctions, giving only the probability of finding an electron in a particular region of space. This probabilistic description naturally leads to the concepts of atomic orbitals, shells and subshells.
早期的原子模型（如玻尔模型）把电子描绘成在明确的圆形轨道上运动。然而，量子力学模型把电子描述为波函数，只能给出在空间某一特定区域找到电子的概率。这种概率性的描述自然地引出了原子轨道、壳层和子壳层的概念。
Each electron in an atom is described by a set of four quantum numbers. The principal quantum number (n) defines the main energy level, or shell, while the subsidiary (azimuthal) quantum number (l) identifies the subshell within that shell. The magnetic quantum number (ml) defines the specific orbital, and the spin quantum number (ms) accounts for the two possible spin states of an electron.
原子中的每一个电子都由一组四个量子数来描述。主量子数 n 规定了主能级（壳层），而角量子数 l 则确定了该壳层内的子壳层。磁量子数 ml 定义了特定的轨道，自旋量子数 ms 则对应电子的两种可能自旋状态。
2. Principal Quantum Number (n) and Electron Shells | 主量子数 (n) 与电子壳层
The principal quantum number, n, can take positive integer values: 1, 2, 3, 4, and so on. It determines the overall energy and the average distance of an electron from the nucleus. Shells are often labelled with letters: K for n = 1, L for n = 2, M for n = 3, N for n = 4, etc.
主量子数 n 只能取正整数：1、2、3、4 等。它决定了电子的总能量以及电子与原子核之间的平均距离。壳层通常用字母标记：n = 1 为 K 层，n = 2 为 L 层，n = 3 为 M 层，n = 4 为 N 层，依此类推。
Within a given shell (fixed n), the number of subshells equals n. For example, the first shell (n = 1) contains only one subshell (1s); the second shell (n = 2) contains two subshells (2s and 2p); the third shell (n = 3) contains three subshells (3s, 3p and 3d). Higher values of n allow access to f subshells and beyond, though for the first 92 elements we mainly encounter s, p, d and f.
在给定的壳层（n 固定）内，子壳层的数目等于 n。例如，第一壳层（n = 1）只有一个子壳层（1s）；第二壳层（n = 2）含有两个子壳层（2s 和 2p）；第三壳层（n = 3）含有三个子壳层（3s、3p 和 3d）。更大的 n 值可出现 f 子壳层甚至更高，不过对于前 92 号元素，我们主要遇到 s、p、d、f 四种子壳层。
3. Subshells: s, p, d and f | 子壳层：s、p、d、f
A subshell is a group of orbitals of the same type within a given shell. The letter designation s, p, d, f originates from early spectroscopic terms (sharp, principal, diffuse, fundamental). The subshell is identified by the azimuthal quantum number l: l = 0 corresponds to an s subshell, l = 1 to a p subshell, l = 2 to a d subshell, and l = 3 to an f subshell.
子壳层是给定壳层内类型相同的一组轨道。字母 s、p、d、f 来源于早期的光谱学术语（sharp、principal、diffuse、fundamental）。子壳层由角量子数 l 标识：l = 0 对应 s 子壳层，l = 1 对应 p 子壳层，l = 2 对应 d 子壳层，l = 3 对应 f 子壳层。
Each type of subshell contains a specific number of orbitals: an s subshell has 1 orbital, a p subshell has 3 orbitals, a d subshell has 5 orbitals, and an f subshell has 7 orbitals. Since each orbital can hold a maximum of two electrons, the maximum electron capacity of an s subshell is 2, p is 6, d is 10, and f is 14.
每一种子壳层包含特定数目的轨道：s 子壳层有 1 个轨道，p 子壳层有 3 个轨道，d 子壳层有 5 个轨道，f 子壳层有 7 个轨道。因为每个轨道最多可容纳两个电子，所以 s 子壳层的最大电子容量为 2，p 为 6，d 为 10，f 为 14。
| Subshell type | Azimuthal quantum number (l) | Number of orbitals | Maximum electrons |
|---|---|---|---|
| s | 0 | 1 | 2 |
| p | 1 | 3 | 6 |
| d | 2 | 5 | 10 |
| f | 3 | 7 | 14 |
4. Orbitals and the Magnetic Quantum Number (ml) | 轨道与磁量子数 (ml)
An atomic orbital is a region in space where there is a high probability (usually taken as 90–95%) of finding an electron. Each orbital is characterised by a unique set of three quantum numbers: n, l, and ml. The magnetic quantum number ml can take integer values from –l to +l, including zero. This gives the orientation of the orbital in space.
原子轨道是空间中的一个区域，在该区域内找到电子的概率很高（通常取 90–95%）。每个轨道由一组三个量子数唯一确定：n、l 和 ml。磁量子数 ml 可以取 –l 到 +l 之间的整数（包括零），它给出了轨道在空间中的取向。
For an s subshell (l = 0), ml can only be 0, so there is only one s orbital. For a p subshell (l = 1), ml can be –1, 0, +1, giving three p orbitals, often labelled px, py and pz. For a d subshell (l = 2), ml has five values (–2, –1, 0, +1, +2), corresponding to five d orbitals. For an f subshell (l = 3), there are seven orbitals.
对于 s 子壳层（l = 0），ml 只能为 0，因此只有一个 s 轨道。对于 p 子壳层（l = 1），ml 可取 –1、0、+1，给出三个 p 轨道，通常标记为 px、py 和 pz。对于 d 子壳层（l = 2），ml 有五个值（–2、–1、0、+1、+2），对应五个 d 轨道。对于 f 子壳层（l = 3），则有七个轨道。
5. Shapes of s Orbitals | s 轨道的形状
All s orbitals are spherical in shape, centred on the nucleus. The 1s orbital is a simple sphere; as n increases, the s orbitals become larger and contain radial nodes – spherical surfaces where the probability of finding the electron is zero. For example, the 2s orbital has one radial node, the 3s orbital has two radial nodes, and so on.
所有 s 轨道都是球形，以原子核为中心。1s 轨道是一个简单的球体；随着 n 的增大，s 轨道变得更大，并包含径向节面——电子存在概率为零的球面。例如，2s 轨道有一个径向节面，3s 轨道有两个径向节面，依此类推。
The electron density in an s orbital is independent of direction; the probability of finding the electron depends only on the distance from the nucleus. This is why s orbitals are described as spherically symmetrical.
s 轨道中的电子密度与方向无关；找到电子的概率只取决于到核的距离。这就是 s 轨道被描述为球对称的原因。
6. Shapes of p Orbitals | p 轨道的形状
Each p subshell contains three dumbbell‑shaped orbitals, oriented at right angles to one another. These are labelled px, py and pz to indicate that the lobes lie along the x‑, y‑ and z‑axes respectively. Each p orbital has a nodal plane passing through the nucleus, where the probability of finding the electron is zero.
每一个 p 子壳层都包含三个哑铃形的轨道，彼此互相垂直。它们分别标记为 px、py 和 pz，以表示两瓣分别沿着 x 轴、y 轴和 z 轴方向分布。每个 p 轨道都有一个通过原子核的节平面，在该平面上找到电子的概率为零。
All three p orbitals in a given subshell are degenerate – they have exactly the same energy. However, in the presence of external fields or when bonded in molecules, their degeneracy is often lifted.
给定子壳层中，三个 p 轨道是简并的——它们具有完全相同的能量。然而，在外加场存在时或在分子中成键时，它们的简并性经常被消除。
7. Shapes of d Orbitals | d 轨道的形状
A d subshell consists of five orbitals. Four of them (dxy, dxz, dyz and dx²−y²) have a characteristic ‘four‑leaf clover’ shape, with four lobes pointing between or along the axes. The fifth orbital, dz², has two large lobes along the z‑axis and a doughnut‑shaped ring of electron density in the xy‑plane.
d 子壳层由五个轨道组成。其中四个（dxy、dxz、dyz 和 dx²−y²）具有特征性的“四叶草”形状，四瓣分别指向坐标轴之间或沿着坐标轴。第五个轨道 dz² 沿着 z 轴有两个大瓣，并在 xy 平面内有一个环形的电子密度区域。
In an isolated atom or ion, all five d orbitals in a given subshell are degenerate. In transition metal complexes, the interaction with ligands splits the d‑orbital energies, which is the basis for crystal field theory and the explanation of colour and magnetism.
在孤立的原子或离子中，给定子壳层中的五个 d 轨道是简并的。在过渡金属配合物中，配体的作用会使 d 轨道能级发生分裂，这正是晶体场理论的基础，并用以解释配合物的颜色和磁性。
8. Energy Ordering of Subshells and the Aufbau Principle | 子壳层的能量排序与构造原理
The Aufbau principle states that electrons occupy the lowest energy subshells available. The energy order is not simply determined by n alone; it also depends on l. For neutral atoms, the order can be remembered by the Madelung rule: electrons fill in the sequence of increasing (n + l), and for subshells with the same (n + l), the one with the lower n is filled first.
构造原理指出，电子优先占据能量最低的可用子壳层。能级顺序并非仅由 n 决定，还依赖于 l。对于中性原子，可用马德隆规则记忆：电子按照 (n + l) 递增的顺序填充，对于 (n + l) 相同的子壳层，n 较小的优先填充。
The typical energy ordering is: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p. Notice that the 4s subshell is filled before the 3d subshell because 4s has (n + l) = 4 + 0 = 4, whereas 3d has (n + l) = 3 + 2 = 5.
典型的能量顺序为：1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p。注意 4s 子壳层先于 3d 子壳层填充，因为 4s 的 (n + l) = 4 + 0 = 4，而 3d 的 (n + l) = 3 + 2 = 5。
Experimental evidence, such as ionisation energies and photoelectron spectroscopy, confirms that the 4s orbital is higher in energy than the 3d orbital for atoms beyond calcium once the 3d subshell starts to fill. This is why transition metal ions lose 4s electrons before 3d electrons.
实验证据（例如电离能和光电子能谱）证实，当 3d 子壳层开始填充后，对于钙之后的原子，4s 轨道的能量实际上高于 3d 轨道。这就是为什么过渡金属离子在失去电子时，总是先失去 4s 电子，再失去 3d 电子。
9. Filling Rules: Pauli Exclusion and Hund’s Rule | 填充规则：泡利不相容原理与洪特规则
The Pauli exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers. Since each orbital is defined by n, l and ml, it can accommodate at most two electrons, and these must have opposite spins (ms = +½ and –½). This is often represented by paired arrows ↑↓ in an orbital box diagram.
泡利不相容原理指出，一个原子中不能有两个电子具有完全相同的四个量子数。由于每一个轨道由 n、l 和 ml 定义，它最多只能容纳两个电子，且这两个电子必须具有相反的自旋（ms = +½ 和 –½）。这在轨道方框图中通常用成对的箭头 ↑↓ 表示。
Hund’s rule of maximum multiplicity says that when electrons occupy degenerate orbitals (orbitals of the same energy, such as the three p orbitals), they first fill them singly with parallel spins before any pairing occurs. This arrangement minimises electron–electron repulsion and gives the atom the lowest possible energy.
洪特最大多重度规则指出，当电子占据简并轨道（能量相同的轨道，例如三个 p 轨道）时，它们首先以自旋平行的方式单独填充每个轨道，然后才进行配对。这一排列最小化了电子间的排斥力，使原子处于尽可能低的能量状态。
For example, a nitrogen atom (Z = 7) has the configuration 1s² 2s² 2p³. In the 2p subshell, the three electrons occupy the px, py and pz orbitals singly, all with the same spin. This corresponds to ↑ ↑ ↑ rather than ↑↓ ↑ _ , which would violate Hund’s rule.
例如，氮原子（Z = 7）的电子构型为 1s² 2s² 2p³。在 2p 子壳层中，三个电子分别单独占据 px、py 和 pz 轨道，且自旋方向相同。这对应 ↑ ↑ ↑，而非 ↑↓ ↑ _，后者违反了洪特规则。
10. Writing Electron Configurations Using Subshell Notation | 用子壳层符号书写电子构型
The electron configuration of an atom is written by listing the subshells in order of increasing energy, with a superscript indicating the number of electrons in that subshell. For example, carbon (6 electrons) is 1s² 2s² 2p². Neon (10 electrons) is 1s² 2s² 2p⁶. The noble gas core can be used as a shorthand; sodium (11 electrons) can be written as [Ne] 3s¹.
原子的电子构型通过按能量递增的顺序列出子壳层，并用上标标明该子壳层中的电子数来书写。例如，碳（6 个电子）为 1s² 2s² 2p²。氖（10 个电子）为 1s² 2s² 2p⁶。可用稀有气体原子芯作为缩写：钠（11 个电子）可写为 [Ne] 3s¹。
For the first 30 elements, the configurations follow a predictable pattern, but care must be taken with the 3d and 4s subshells. For potassium (Z = 19) the configuration is [Ar] 4s¹, not [Ar] 3d¹. Calcium (Z = 20) is [Ar] 4s². From scandium (Z = 21) to zinc (Z = 30), the 3d subshell is progressively filled, giving [Ar] 4s² 3d¹ to [Ar] 4s² 3d¹⁰, with two exceptions.
对于前 30 号元素，电子构型遵循可预测的模式，但在 3d 和 4s 子壳层上需要多加留意。钾（Z = 19）的构型是 [Ar] 4s¹，而不是 [Ar] 3d¹。钙（Z = 20）为 [Ar] 4s²。从钪（Z = 21）到锌（Z = 30），3d 子壳层逐渐填充，电子构型从 [Ar] 4s² 3d¹ 变化到 [Ar] 4s² 3d¹⁰，但有两个例外。
11. Anomalous Electron Configurations: Chromium and Copper | 反常电子构型：铬和铜
The two most commonly cited exceptions to the Aufbau order are chromium (Z = 24) and copper (Z = 29). Instead of the expected [Ar] 4s² 3d⁴, chromium adopts [Ar] 4s¹ 3d⁵. Similarly, copper adopts [Ar] 4s¹ 3d¹⁰ rather than the expected [Ar] 4s² 3d⁹.
最常被引用的两个违反构造顺序的例外是铬（Z = 24）和铜（Z = 29）。铬不是预期的 [Ar] 4s² 3d⁴，而是采用 [Ar] 4s¹ 3d⁵。同样，铜采用 [Ar
Published by TutorHao | A-Level Chemistry Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导