Electrons in Atoms | 原子中的电子

📚 Electrons in Atoms | 原子中的电子

The behaviour of electrons within an atom determines virtually every aspect of chemistry — from the position of an element in the periodic table to the types of bonds it can form. This article explores the electronic structure of atoms in detail, tailored specifically for the Cambridge A-Level Chemistry syllabus.

原子中电子的行为几乎决定了化学的每一个方面——从元素在周期表中的位置到它能形成的化学键类型。本文将针对剑桥A-Level化学考纲，详细探讨原子的电子结构。

1. The Role of Electrons in Atoms | 电子在原子中的作用

An atom consists of a dense, positively charged nucleus surrounded by a diffuse cloud of negatively charged electrons. The number of electrons equals the number of protons in a neutral atom, and it is the arrangement of these electrons that governs the chemical properties of the element.

原子由一个致密带正电的原子核以及周围弥散的带负电电子云组成。中性原子中电子数等于质子数，正是这些电子的排布方式决定了元素的化学性质。

Electrons occupy discrete energy levels within the atom. These levels are quantised, meaning that only certain energy values are permitted. An electron cannot exist between energy levels; it must absorb or release a specific quantum of energy to transition between them.

电子在原子中占据分立的能级。这些能级是量子化的，意味着只允许某些特定的能量值。电子不能存在于能级之间；它必须吸收或释放特定量子能量才能完成能级跃迁。

Energy levels are labelled by the principal quantum number, n.
能级用主量子数 n 标记。
Electrons fill lower energy levels first (aufbau principle).
电子首先填充较低能级（构造原理）。
The further an electron is from the nucleus, the higher its energy.
电子离核越远，其能量越高。

2. Wave–Particle Duality and the Quantum Model | 波粒二象性与量子模型

In the early 20th century, experiments revealed that electrons behave both as particles and as waves. This wave–particle duality is central to the quantum mechanical model of the atom, which replaces the earlier Bohr model’s fixed circular orbits with probabilistic electron clouds.

20世纪初，实验揭示电子既表现出粒子性又表现出波动性。这种波粒二象性是原子量子力学模型的核心，该模型取代了早期玻尔模型中固定的圆形轨道，代之以概率性的电子云。

Erwin Schrödinger developed a wave equation that describes the behaviour of electrons in atoms. Solutions to this equation, called wave functions (ψ), provide information about the probability of finding an electron in a particular region of space. The square of the wave function, ψ², represents the electron density at a given point.

埃尔温·薛定谔建立了描述原子中电子行为的波动方程。该方程的解称为波函数（ψ），提供在空间某一区域找到电子的概率信息。波函数的平方 ψ² 表示某一点的电子密度。

Rather than describing an electron’s exact path, quantum mechanics defines an atomic orbital as a region within which there is a high probability (typically about 95%) of finding the electron.

量子力学不是描述电子的精确路径，而是将原子轨道定义为在其中找到电子的高概率区域（通常约为95%）。

3. Principal Quantum Number and Energy Levels | 主量子数与能级

The principal quantum number, n, takes integer values 1, 2, 3, 4 , etc. It determines the main energy level of the electron and is directly related to the average distance of the electron from the nucleus. Larger n corresponds to higher energy and greater distance.

主量子数 n 取整数数值 1、2、3、4 等。它决定电子的主能级，并直接关系到电子离核的平均距离。n 越大，能量越高，离核越远。

n value	n 值	1	2	3	4
Maximum electrons	最大电子数 (2n²)	2	8	18	32
Subshells present	所含亚层	s	s, p	s, p, d	s, p, d, f

The maximum number of electrons in a main energy level is given by 2n². For example, the third energy level (n = 3) can hold up to 18 electrons. However, in ground-state atoms of the first 20 elements, the third level is only partially filled before the fourth level begins to fill.

主能级中电子的最大数目由 2n² 给出。例如，第三能级（n = 3）最多可容纳18个电子。然而，前20号元素的基态原子中，第三能级在尚未填满时第四能级便开始填充。

4. Subshells and Atomic Orbitals | 亚层与原子轨道

Each main energy level is divided into subshells designated s, p, d and f. The number of subshells in a level equals the value of n. For example, n = 2 contains two subshells: 2s and 2p.

每个主能级被划分为s、p、d、f等亚层。能级中亚层数等于 n 的值。例如，n = 2 包含两个亚层：2s 和 2p。

Each subshell consists of one or more orbitals. An orbital can hold a maximum of two electrons with opposite spins. The number of orbitals in each subshell is as follows:

每个亚层由一个或多个轨道组成。一个轨道最多可容纳两个自旋相反的电子。各亚层的轨道数目如下：

s subshell: 1 orbital (holds 2 electrons) — s 亚层：1个轨道（容纳2个电子）
p subshell: 3 orbitals (holds 6 electrons) — p 亚层：3个轨道（容纳6个电子）
d subshell: 5 orbitals (holds 10 electrons) — d 亚层：5个轨道（容纳10个电子）
f subshell: 7 orbitals (holds 14 electrons) — f 亚层：7个轨道（容纳14个电子）

The ordering of subshell energies in a multi-electron atom is approximately:

在多电子原子中，亚层的能量顺序近似为：

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s...

Note the important anomaly: the 4s subshell fills before the 3d subshell because 4s has lower energy than 3d in the ground-state atoms of elements in the first two periods of the d-block.

注意一个重要异常：4s 亚层先于 3d 亚层填充，因为在d区前两周期的基态原子中，4s 的能量低于 3d。

5. Shapes of s and p Orbitals | s 轨道和 p 轨道的形状

An s orbital is spherical in shape, centred on the nucleus. The radius of the sphere increases with the principal quantum number. For example, a 2s orbital is larger than a 1s orbital and has a higher energy. There are no directional preferences for s orbitals; their electron density is distributed uniformly in all directions.

s轨道呈球形，以原子核为中心。球半径随主量子数增大而增大。例如，2s轨道大于1s轨道且能量更高。s轨道没有方向偏好；其电子密度在各个方向上均匀分布。

A p orbital has a dumbbell (figure-of-eight) shape. Each p subshell contains three mutually perpendicular orbitals, designated pₓ, pᵧ and p_z, oriented along the x, y and z axes respectively. Each p orbital has a nodal plane passing through the nucleus, where the probability of finding an electron is zero.

p轨道呈哑铃形（8字形）。每个p亚层含有三个相互垂直的轨道，分别标记为 pₓ、pᵧ 和 p_z，沿 x、y、z 轴方向排布。每个p轨道的中心存在一个节面，该平面穿过原子核，在此平面上找到电子的概率为零。

An understanding of orbital shapes is essential for interpreting bond angles and molecular geometry in the shapes of molecules topic, which is also examined in Cambridge A-Level Chemistry.

理解轨道形状对于解释键角和分子几何形状至关重要，这也是剑桥A-Level化学中”分子形状”专题所考察的内容。

6. Quantum Numbers | 量子数

Each electron in an atom is uniquely described by a set of four quantum numbers. These numbers define the energy, shape, orientation and spin of the electron.

原子中的每个电子由一组四个量子数唯一描述。这些数字定义电子的能量、形状、方向和自旋。

Quantum number	量子数	Symbol 符号	Allowed values 允许值	Meaning 含义
Principal	主量子数	n	1, 2, 3, …	Energy level 主能级
Azimuthal	角量子数	l	0 to n−1	Subshell type 亚层类型
Magnetic	磁量子数	mₗ	−l to +l	Orbital orientation 轨道方向
Spin	自旋量子数	s	+½ or −½	Electron spin 电子自旋

For l = 0, the subshell is s; for l = 1, it is p; for l = 2, it is d; and for l = 3, it is f. The azimuthal quantum number therefore directly corresponds to the subshell notation used in electronic configurations.

l = 0 对应 s 亚层，l = 1 对应 p 亚层，l = 2 对应 d 亚层，l = 3 对应 f 亚层。因此，角量子数直接对应电子排布中使用的亚层符号。

7. The Aufbau Principle, Pauli Exclusion and Hund’s Rule | 构造原理、泡利不相容原理与洪特规则

Three fundamental rules govern how electrons populate atomic orbitals:

三个基本规则支配电子如何填充原子轨道：

1. The Aufbau Principle — electrons fill the lowest available energy orbitals first before occupying higher-energy orbitals.

1. 构造原理 —— 电子首先填充最低可用能级轨道，然后才占据较高能级轨道。

2. The Pauli Exclusion Principle — no two electrons in the same atom can have the same set of all four quantum numbers. Consequently, an orbital can hold at most two electrons, and these must have opposite spins (↑↓).

2. 泡利不相容原理 —— 同一原子中不存在四个量子数完全相同的两个电子。因此，一个轨道最多可容纳两个电子，且这两个电子必须自旋相反（↑↓）。

3. Hund’s Rule — when electrons occupy orbitals of equal energy (degenerate orbitals) in the same subshell, they first enter each orbital singly with the same spin direction. Only after all orbitals are half-filled does pairing begin.

3. 洪特规则 —— 当电子占据同一亚层中能量简并的轨道时，它们首先以相同自旋方向分别进入各个轨道。只有当所有轨道都半充满后，配对才开始发生。

For example, the electronic configuration of nitrogen (Z = 7) is 1s² 2s² 2p³. The three 2p electrons occupy the three p orbitals singly with parallel spins, rather than pairing in one orbital while leaving another empty. This arrangement minimises electron–electron repulsion and lowers the total energy.

例如，氮（Z = 7）的电子构型为 1s² 2s² 2p³。三个2p电子以平行自旋分别占据三个p轨道，而不是在同一个轨道中配对而留下另一个空轨道。这种排布使电子间斥力最小化并降低了总能量。

8. Writing Electronic Configurations | 书写电子构型

Electronic configurations are written by listing the occupied subshells in order of increasing energy, with a superscript indicating the number of electrons in each subshell. The order of filling follows the sequence: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p.

书写电子构型时，按能量递增顺序列出已占据的亚层，并用上标表示每个亚层中的电子数。填充顺序遵循：1s、2s、2p、3s、3p、4s、3d、4p、5s、4d、5p、6s、4f、5d、6p、7s、5f、6d、7p。

For example, consider the element sulfur (Z = 16). It has 16 electrons, which fill in the following order: 1s² 2s² 2p⁶ 3s² 3p⁴. Written in full: 1s² 2s² 2p⁶ 3s² 3p⁴.

以硫（Z = 16）为例，它有16个电子，按以下顺序填充：1s² 2s² 2p⁶ 3s² 3p⁴。完整书写为：1s² 2s² 2p⁶ 3s² 3p⁴。

An alternative condensed form uses the nearest noble gas core in square brackets. For sulfur, this gives [Ne] 3s² 3p⁴. This shorthand simplifies long configurations and is expected in Cambridge A-Level answers.

另一种简写形式使用方括号中的最近稀有气体核心。硫可写为 [Ne] 3s² 3p⁴。这种简写简化了长配置，是剑桥A-Level答题中期望使用的写法。

Key examples to memorise for the syllabus include nitrogen (Z = 7): 1s² 2s² 2p³; chlorine (Z = 17): 1s² 2s² 2p⁶ 3s² 3p⁵; and calcium (Z = 20): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s².

考纲中需要牢记的关键例子包括：氮（Z = 7）：1s² 2s² 2p³；氯（Z = 17）：1s² 2s² 2p⁶ 3s² 3p⁵；钙（Z = 20）：1s² 2s² 2p⁶ 3s² 3p⁶ 4s²。

9. Anomalous Configurations: Chromium and Copper | 异常构型：铬与铜

Two notable exceptions to the aufbau rule appear in the first transition series. Chromium (Z = 24) has the configuration [Ar] 3d⁵ 4s¹ rather than the expected [Ar] 3d⁴ 4s². Copper (Z = 29) has [Ar] 3d¹⁰ 4s¹ instead of [Ar] 3d⁹ 4s².

第一过渡系中出现两个值得注意的构造原理例外。铬（Z = 24）的构型为 [Ar] 3d⁵ 4s¹，而非预期的 [Ar] 3d⁴ 4s²。铜（Z = 29）的构型为 [Ar] 3d¹⁰ 4s¹，而非 [Ar] 3d⁹ 4s²。

These configurations are more stable because the 3d⁵ half-filled subshell and the 3d¹⁰ fully-filled subshell both possess a special stability. This stability arises from the symmetrical distribution of electron charge and the reduced electron–electron repulsion within the d subshell.

这些构型更稳定，因为 3d⁵ 半充满亚层和 3d¹⁰ 全充满亚层都具有特殊的稳定性。这种稳定性源于d亚层内电子电荷的对称分布以及电子间斥力的降低。

When writing configurations of transition metal ions, the 4s electrons are removed first. For example, Fe²⁺ (Z = 26) has the configuration [Ar] 3d⁶, not [Ar] 3d⁵ 4s¹. The 4s orbital lies at higher energy than 3d in the ion, so it is emptied first during ionisation.

书写过渡金属离子的构型时，4s 电子首先被移除。例如，Fe²⁺（Z = 26）的构型为 [Ar] 3d⁶，而非 [Ar] 3d⁵ 4s¹。在离子中4s轨道能量高于3d，因此在电离过程中4s先被清空。

10. Ionisation Energies and Periodic Trends | 电离能与周期性趋势

The first ionisation energy is defined as the minimum energy required to remove one mole of electrons from one mole of gaseous atoms to form one mole of gaseous unipositive ions. This definition and the associated equation are frequently tested in the exam.

第一电离能被定义为一摩尔气态原子移除一摩尔电子形成一摩尔气态一价正离子所需的最小能量。这一定义及相关方程式在考试中频繁出现。

X(g) → X⁺(g) + e⁻ ΔH = first ionisation energy (kJ mol⁻¹)

Across a period, first ionisation energy generally increases as nuclear charge increases and atomic radius decreases. The increased effective nuclear charge strengthens the attraction between the nucleus and the outer electrons, making them harder to remove.

在同一周期内，第一电离能总体上随核电荷增加和原子半径减小而增大。有效核电荷的增强加强了原子核与外层电子之间的引力，使电子更难移除。

Down a group, first ionisation energy decreases because the outer electrons are further from the nucleus, and there is greater shielding by inner electron shells. The stronger shielding and larger distance outweigh the increased nuclear charge, so electrons are more readily removed.

在同一族内，第一电离能减小，因为外层电子离核更远，且内层电子壳层提供了更强的屏蔽效应。更强的屏蔽和更远的距离超过了核电荷增大的影响，因此电子更容易移除。

Two irregularities within a period are also examined:

周期内还存在两个不规律性需要掌握：

In Period 2, the ionisation energy of boron (Z = 5) is lower than that of beryllium (Z = 4). Beryllium’s outer electrons are in the 2s subshell, while boron’s outer electron enters the higher-energy 2p subshell and is therefore more easily removed.
在第二周期中，硼（Z = 5）的电离能低于铍（Z = 4）。铍的外层电子在2s亚层，而硼的外层电子进入能量更高的2p亚层，因此更容易移除。
The ionisation energy of oxygen (Z = 8) is lower than that of nitrogen (Z = 7). Nitrogen has a half-filled 2p subshell (2p³) with all spins parallel, which is unusually stable. In oxygen, the fourth 2p electron must pair with another in the same orbital, resulting in electron–electron repulsion that facilitates removal.
氧（Z = 8）的电离能低于氮（Z = 7）。氮具有半充满的2p亚层（2p³），所有自旋平行，异常稳定。而氧中第四个2p电子必须与另一个电子在同一轨道配对，产生电子间斥力从而使电子更容易移除。

11. Successive Ionisation Energies | 逐级电离能

Successive ionisation energies refer to the energies required to remove the first, second, third and subsequent electrons from an atom. The values provide evidence for the existence of shells and an estimate of the number of electrons in each shell.

逐级电离能指的是从原子中移走第一、第二、第三及后续电子所需的能量。这些数值为壳层的存在提供了证据，并可估算每个壳层中的电子数。

For example, magnesium (Z = 12) has successive ionisation energies that show a small rise from the first to the second, a further rise to the third, but then a dramatic jump to the tenth. This large increase occurs after the 2p shell of eight electrons is completely removed, as electrons in the inner shell are held much more tightly.

例如，镁（Z = 12）的逐级电离能表现为：第一到第二电离能小幅上升，到第三电离能进一步升高，但到第十电离能出现急剧跳升。这个大幅增加发生在2p壳层的8个电子全部移除之后，因为内壳层电子受到更强束缚。

The large jump between the second and third ionisation energies of magnesium confirms that it has two electrons in its outer shell. This type of analysis is regularly used in Cambridge structured questions to deduce an element’s group number.

镁的第二与第三电离能之间的大幅跳跃证实其外壳层中有两个电子。这种分析在剑桥简答题中经常用于推断元素的族序数。

12. Electron Configuration and the Periodic Table | 电子构型与周期表

Blocks in the periodic table correspond directly to the subshell being filled. The s-block contains Groups I and II, where the outermost electron occupies an s subshell. The p-block contains Groups III to 0 (Group VIII), where the outermost electron occupies a p subshell. The d-block consists of the transition metals, where a d subshell is progressively filled. The f-block consists of the lanthanides and actinides.

周期表中的区域直接对应正在填充的亚层。s区包含第I族和第II族，最外层电子占据s亚层。p区包含第III族至第0族（第VIII族），最外层电子占据p亚层。d区由过渡金属组成，d亚层逐渐填充。f区由镧系和锕系元素组成。

Elements within the same group have the same number of outer-shell electrons, which explains their similar chemical properties. For example, all Group I metals have one valence electron in an s orbital, accounting for their +1 oxidation state and high reactivity.

同族元素具有相同的外层电子数，这解释了它们相似的化学性质。例如，所有第I族金属在s轨道中有1个价电子，这使其表现+1氧化态和高反应活性。

Mastering the link between electronic configuration and periodic position is not only important for the structure of the atom topic but also for predicting trends across the broader inorganic chemistry sections of the syllabus.

掌握电子构型与周期表位置之间的联系，不仅对原子结构专题至关重要，而且对预测考纲中更广泛的无机化学部分的趋势同样重要。

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Electrons in Atoms | 原子中的电子