Atomic Structure | 原子结构

📚 Atomic Structure | 原子结构

Atomic structure is the foundation of chemistry, explaining how matter is built from subatomic particles. Understanding protons, neutrons and electrons, along with their arrangement in energy levels and orbitals, makes it possible to predict chemical properties, bonding behaviour and spectroscopic data. This article covers the Cambridge International A‑level Chemistry specification for atomic structure, from fundamental particles to mass spectrometry and ionisation energy trends.

原子结构是化学的基础，解释了物质如何由亚原子粒子构成。理解质子、中子与电子，以及它们在能级与轨道中的排布方式，使我们能够预测化学性质、成键行为和光谱数据。本文涵盖剑桥国际 A‑level 化学课程中原子结构部分的全部内容，从基本粒子到质谱法与电离能趋势，逐一详细解析。

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1. Fundamental Particles | 基本粒子

All atoms consist of three types of subatomic particle: protons, neutrons and electrons. Protons and neutrons make up the dense, positively charged nucleus, while electrons occupy the space surrounding the nucleus. Each particle has a characteristic relative mass and relative charge, which are summarised in the table below.

所有原子都由三种亚原子粒子组成：质子、中子和电子。质子和中子构成了致密、带正电的原子核，而电子则占据原子核周围的空间。每种粒子都有特征的相对质量和相对电荷，如下表所示。

Particle	Relative mass	Relative charge
Proton	1	+1
Neutron	1	0
Electron	1/1836	-1

The atomic number (Z) is the number of protons in the nucleus and defines the element. The mass number (A) is the total number of protons and neutrons. An atom is electrically neutral when the number of electrons equals the number of protons. Ions form when atoms gain or lose electrons.

原子序数 (Z) 是原子核中的质子数，它决定了元素的种类。质量数 (A) 是质子数与中子数的总和。当电子数与质子数相等时，原子呈电中性。当原子得到或失去电子时，便形成离子。

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2. Nuclear Symbol Notation | 核素符号

The composition of any nuclide can be shown using the notation ⁱ⁺AₓZ Symbol, where A is the mass number written as a superscript and Z is the atomic number written as a subscript, both on the left of the element symbol. For example, a sodium atom with 11 protons and 12 neutrons is written as ²³₁₁Na. This notation immediately tells you the number of protons, neutrons and electrons in a neutral atom.

任何核素的组成都可以用符号 ⁱ⁺AₓZ 元素符号 来表示，其中 A 为质量数，写在左上角，Z 为原子序数，写在左下角。例如，一个具有 11 个质子和 12 个中子的钠原子写作 ²³₁₁Na。通过这种表示法，您可以立即知道中性原子中的质子数、中子数和电子数。

The number of neutrons is equal to A – Z. For a neutral atom, the electron count equals Z. In a charged ion, the charge is shown as a superscript on the right, such as ²³₁₁Na⁺ or ³⁵₁₇Cl⁻.

中子数等于 A – Z。对于中性原子，电子数等于 Z。在带电离子中，电荷显示为右上标，例如 ²³₁₁Na⁺ 或 ³⁵₁₇Cl⁻。

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3. Isotopes | 同位素

Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. They therefore share the same atomic number Z but have different mass numbers A. For instance, carbon has three naturally occurring isotopes: ¹²C, ¹³C and ¹⁴C, with 6, 7 and 8 neutrons respectively.

同位素是指质子数相同而中子数不同的同种元素的原子。因此，它们具有相同的原子序数 Z，但质量数 A 不同。例如，碳有三种天然存在的同位素：¹²C、¹³C 和 ¹⁴C，它们的中子数分别为 6、7 和 8。

Isotopes of an element have essentially identical chemical properties because their electron configurations are the same. Their physical properties, such as density and rate of diffusion, may differ slightly due to the mass difference. Mass spectrometry exploits these mass differences to separate isotopes and measure their relative abundances.

同一元素的同位素具有基本相同的化学性质，因为它们的电子构型相同。但由于质量差异，它们的物理性质（如密度和扩散速率）可能略有不同。质谱法正是利用这些质量差异来分离同位素并测量其相对丰度。

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4. Relative Atomic Mass and Mass Spectrometry | 相对原子质量与质谱

Relative atomic mass (Aᵣ) is defined as the weighted average mass of an atom of an element, compared to 1/12 of the mass of a carbon‑12 atom. It is a dimensionless quantity that reflects the natural mixture of isotopes. The formula is:

相对原子质量 (Aᵣ) 定义为一种元素的一个原子的加权平均质量与一个碳‑12 原子质量的 1/12 的比值。它是个无量纲量，反映了同位素的天然混合情况。计算公式为：

Aᵣ = Σ (isotopic mass × percentage abundance) / 100

Mass spectrometry is used to determine the relative isotopic masses and their abundances. In brief, a sample is vaporised, ionised (often by electron impact), accelerated through an electric field, deflected by a magnetic field according to mass‑to‑charge ratio (m/z), and detected. The resulting mass spectrum shows peaks whose heights correspond to relative abundance and whose positions on the m/z axis give the mass of each isotope.

质谱法用来测定相对同位素质量及其丰度。简而言之，样品被气化、电离（通常通过电子轰击），在电场中加速，然后在磁场中根据质荷比 (m/z) 发生偏转，最后被检测。得到的质谱图显示出若干峰，峰的高度对应相对丰度，峰在 m/z 轴上的位置给出每种同位素的质量。

For example, chlorine has two major isotopes: ³⁵Cl (75.5%) and ³⁷Cl (24.5%). Its relative atomic mass is calculated as: Aᵣ(Cl) = (35 × 75.5 + 37 × 24.5) / 100 ≈ 35.5.

例如，氯有两种主要同位素：³⁵Cl（占 75.5%）和 ³⁷Cl（占 24.5%）。其相对原子质量的计算为：Aᵣ(Cl) = (35 × 75.5 + 37 × 24.5) / 100 ≈ 35.5。

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5. Electronic Energy Levels and Orbitals | 电子能级与轨道

Electrons occupy specific energy levels, or shells, around the nucleus. Each shell is associated with a principal quantum number n, where n = 1, 2, 3, 4… The maximum number of electrons a shell can hold is given by 2n². Shells are divided into sub‑shells designated s, p, d and f, each containing a fixed number of orbitals.

电子占据原子核周围特定的能级，或称壳层。每一个壳层都与一个主量子数 n 相关联，n = 1、2、3、4……每个壳层最多能容纳的电子数为 2n²。壳层进一步分为 s、p、d、f 亚层，每个亚层含有一定数量的轨道。

Principal quantum number n	Shell	Sub‑shells present	Maximum electrons (2n²)
1	K	1s	2
2	L	2s, 2p	8
3	M	3s, 3p, 3d	18
4	N	4s, 4p, 4d, 4f	32

Each sub‑shell consists of a specific number of orbitals: an s sub‑shell has 1 orbital, a p sub‑shell has 3 orbitals, a d sub‑shell has 5 orbitals and an f sub‑shell has 7 orbitals. Each orbital can hold a maximum of two electrons with opposite spins.

每个亚层由特定数量的轨道组成：s 亚层有 1 个轨道，p 亚层有 3 个轨道，d 亚层有 5 个轨道，f 亚层有 7 个轨道。每个轨道最多可容纳两个自旋相反的电子。

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6. Orbital Shapes and Sub‑levels | 轨道形状与亚层

An s orbital is spherical in shape and symmetrical around the nucleus. The 1s orbital is the smallest; 2s and 3s orbitals are progressively larger. A p orbital has a dumbbell shape with two lobes on opposite sides of the nucleus. The three p orbitals (pₓ, pᵧ, p₂) are oriented at right angles to each other. d orbitals have more complex shapes, with four of the five having a clover‑leaf appearance and the fifth being dumbbell‑shaped with a doughnut ring.

s 轨道呈球形，围绕原子核对称分布。1s 轨道最小，2s 和 3s 轨道依次增大。p 轨道呈哑铃形，在原子核的两侧各有一瓣。三个 p 轨道（pₓ, pᵧ, p₂）相互垂直。d 轨道的形状更为复杂，五个轨道中有四个呈四叶草状，第五个呈带有甜甜圈环的哑铃形。

The energy ordering of orbitals in a multi‑electron atom follows the (n+l) rule, also called the Madelung rule. Orbitals with lower n+l values are filled first. If two orbitals have the same n+l, the one with lower n is filled first. The typical order is: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p...

在多电子原子中，轨道的能量顺序遵循 (n+l) 规则，也称为马德隆规则。具有较低 n+l 值的轨道优先填充。如果两个轨道的 n+l 值相同，则 n 较小的轨道优先填充。典型的顺序为：1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p……

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7. Electron Configuration Rules | 电子排布规则

The arrangement of electrons in orbitals is governed by three fundamental rules. The Aufbau principle states that electrons fill the lowest energy orbitals first. The Pauli exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers, which limits an orbital to two electrons with opposite spins. Hund’s rule states that when filling degenerate orbitals (orbitals of the same energy), electrons occupy separate orbitals with parallel spins before pairing up.

电子在轨道中的排布遵循三条基本规则。构造原理（Aufbau principle）指出，电子优先占据能量最低的轨道。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，这使得每个轨道最多容纳两个自旋相反的电子。洪特规则指出，当填充简并轨道（能量相同的轨道）时，电子会先以平行自旋单独占据各个轨道，然后再成对。

Using these rules, the electron configuration of a neutral iron atom (Fe, Z=26) is written as 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶, or in shorthand as [Ar] 4s² 3d⁶. Note that the 4s sub‑shell fills before the 3d because it is of lower energy. However, for transition metal ions, electrons are removed from the 4s orbital before the 3d. Special stability arises from half‑filled and fully filled d sub‑shells, leading to exceptions like Cr ([Ar] 4s¹ 3d⁵) and Cu ([Ar] 4s¹ 3d¹⁰).

利用这些规则，中性铁原子（Fe, Z=26）的电子排布可写作 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶，或简写为 [Ar] 4s² 3d⁶。请注意，4s 亚层在 3d 之前填充，因为其能量更低。然而，对于过渡金属离子，电子会先从 4s 轨道失去，然后才是 3d。半充满和全充满的 d 亚层具有特殊的稳定性，这导致了诸如 Cr ([Ar] 4s¹ 3d⁵) 和 Cu ([Ar] 4s¹ 3d¹⁰) 这样的例外情况。

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8. Ionisation Energy: Definition and Trends | 电离能：定义与趋势

The first ionisation energy of an element is the energy required to remove one mole of electrons from one mole of gaseous atoms to form one mole of gaseous unipositive ions under standard conditions: X(g) → X⁺(g) + e⁻. It is measured in kJ mol⁻¹.

某元素的第一电离能是指在标准条件下，从一摩尔气态原子中移去一摩尔电子，形成一摩尔气态正一价离子所需要的能量：X(g) → X⁺(g) + e⁻。其单位是 kJ mol⁻¹。

Across a period, first ionisation energy generally increases. This is because the nuclear charge increases while electrons are being added to the same outer shell, leading to stronger electrostatic attraction and a decrease in atomic radius. There are slight drops, for instance between Group 2 and Group 3 due to the higher energy of a p orbital compared to an s orbital, and between Group 5 and Group 6 due to spin‑pair repulsion in the doubly occupied p orbital.

在同一周期中，第一电离能总体上呈上升趋势。这是因为核电荷增加，而电子进入同一个外层，导致静电引力增强，原子半径减小。电离能会出现一些小幅下降，例如从第 2 族到第 3 族，由于 p 轨道的能量高于 s 轨道；从第 5 族到第 6 族，则是因为双占 p 轨道中的自旋成对排斥。

Down a group, first ionisation energy decreases. The outer electron is found in a shell with a higher principal quantum number, further from the nucleus, and the shielding effect of inner electron shells reduces the effective nuclear charge felt by the outermost electron.

沿同一族向下，第一电离能减小。这是因为最外层电子处于主量子数更大的壳层中，离原子核更远，且内层电子的屏蔽效应降低了最外层电子所感受到的有效核电荷。

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9. Successive Ionisation Energies as Evidence | 连续电离能提供的证据

Successive ionisation energies refer to the energies required to remove the first, second, third and further electrons from a gaseous atom. The pattern of such energies provides strong evidence for the existence of shells and sub‑shells. Successive values always increase, but large jumps occur when an electron is removed from an inner shell, where it is much closer to the nucleus and much more strongly held.

连续电离能是指从气态原子中移除第一个、第二个、第三个以及后续电子所需要的能量。这些能量的变化规律为电子壳层和亚层的存在提供了强有力的证据。连续电离能的数值总是增大，但当电子从内层被移除时会出现巨大的跳跃，这是因为内层电子离核更近，受到的束缚更强。

For example, the successive ionisation energies of sodium (Z=11) are (in kJ mol⁻¹): 1st=496, 2nd=4563, 3rd=6913, 4th=9544, 5th=13352, 6th=16610, 7th=20115, 8th=25490, 9th=28932, 10th=141360, 11th=159075. The huge increase between the 9th and 10th ionisation energies clearly shows that the 10th electron is being removed from the inner 2p sub‑shell, confirming the electron configuration 1s² 2s² 2p⁶ 3s¹.

例如，钠 (Z=11) 的连续电离能（单位为 kJ mol⁻¹）分别为：第 1 电离能 496、第 2 电离能 4563、第 3 电离能 6913、第 4 电离能 9544、第 5 电离能 13352、第 6 电离能 16610、第 7 电离能 20115、第 8 电离能 25490、第 9 电离能 28932、第 10 电离能 141360、第 11 电离能 159075。第 9 和第 10 电离能之间出现的巨大跃升清楚地表明，第十个电子是从内层 2p 亚层移走的，这印证了钠的电子构型为 1s² 2s² 2p⁶ 3s¹。

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10. Mass Spectrometer in Detail | 质谱仪详解

The mass spectrometer is an instrument that measures the mass‑to‑charge ratio of ions. The main stages of operation are: (1) Vaporisation – the sample is heated and turned into a gas if necessary. (2) Ionisation – gaseous atoms or molecules are bombarded with high‑energy electrons, knocking off one or more electrons to form positive ions, typically M⁺. (3) Acceleration – positive ions are accelerated by an electric field so that they all have the same kinetic energy. (4) Deflection – the beam of ions passes through a magnetic field, where ions are deflected along a curved path; the degree of deflection depends on m/z: lighter ions with higher charge are deflected more. (5) Detection – ions strike a detector and produce an electric current proportional to abundance.

质谱仪是一种测量离子质荷比的仪器。其主要工作步骤包括：(1) 气化——必要时将样品加热转变为气态。(2) 电离——用高能电子轰击气态原子或分子，打掉一个或多个电子形成正离子，通常是 M⁺。(3) 加速——正离子在电场中被加速，使它们具有相同的动能。(4) 偏转——离子束通过磁场，在磁场中沿弯曲路径发生偏转；偏转程度取决于 m/z：质量越轻、电荷越高的离子偏转越多。(5) 检测——离子撞击检测器，产生与丰度成正比的电流。

To calculate relative atomic mass from a mass spectrum, you multiply the mass of each isotope by its relative abundance (from the peak height), sum these values, and divide by the total of the abundances. The process allows precise determination of Aᵣ values used in stoichiometric calculations.

要从质谱图计算相对原子质量，需要将每种同位素的质量乘以其相对丰度（来自峰高），将所有乘积求和，再除以丰度总和。这一过程可以精确测定用于化学计量计算的 Aᵣ 值。

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11. Summary and Key Equations | 总结与关键公式

Atomic structure theory brings together the identity of an element through atomic number, the makeup of the nucleus via mass number and isotopes, the arrangement of electrons in quantised energy levels, and the energetic evidence from ionisation energies. Key relationships to remember include: number of neutrons = A – Z; maximum electrons per shell = 2n²; electron configuration ordering follows the energy sequence; and Aᵣ = Σ (isotopic mass × abundance) / Σ abundance.

原子结构理论将元素的标识（通过原子序数）、原子核的构成（利用质量数和同位素）、电子在量子化能级中的排布以及来自电离能的能量证据联系在了一起。需要牢记的关键关系包括：中子数 = A – Z；每壳层最大电子数 = 2n²；电子排布顺序遵循能量序列；以及 Aᵣ = Σ (同位素质量 × 丰度) / Σ 丰度。

Mastery of these concepts provides the foundation for understanding periodicity, bonding, redox chemistry and much of physical chemistry. Regular practice with mass spectra calculations, electron configurations for the first 36 elements, and ionisation energy plots will ensure success in Cambridge A‑level examinations.

掌握这些概念将为理解元素周期性、化学键、氧化还原及物理化学的许多内容奠定基础。经常练习质谱计算、前 36 号元素的电子排布以及电离能图，将有助于在剑桥 A‑level 考试中取得成功。

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