📚 Key Points of the Simplified Model of Atomic Structure | 原子结构简化模型的核心要点
The simplified model of atomic structure is one of the most important foundations in A-Level Physics. It describes how protons, neutrons and electrons are arranged in an atom, and explains phenomena such as ionisation, energy levels and line spectra. For CIE candidates, a clear understanding of this model is essential for tackling questions on nuclear physics, quantum physics and atomic transitions.
原子结构简化模型是 A-Level 物理中最重要的基础内容之一。它描述了质子、中子和电子在原子中的排列方式，并解释了电离、能级和线状光谱等现象。对于 CIE 考生来说，清晰理解这一模型，是解答核物理、量子物理和原子跃迁相关题目的关键。
1. Basic Components of the Atom | 原子的基本组成
An atom consists of a small, dense, positively charged nucleus surrounded by orbiting electrons. The nucleus contains protons and neutrons, which are collectively called nucleons. Protons carry a positive charge of +1.6 × 10⁻¹⁹ C, neutrons are uncharged, and electrons carry an equal but opposite charge of −1.6 × 10⁻¹⁹ C.
原子由一个微小、致密且带正电的原子核以及围绕其运动的电子组成。原子核中含有质子和中子，二者统称为核子。质子带 +1.6 × 10⁻¹⁹ C 的正电荷，中子不带电，电子带等量异号的 −1.6 × 10⁻¹⁹ C 电荷。
In the simplified model, the atom is often compared to a miniature solar system: the nucleus acts as the “Sun” and electrons act as the “planets”. However, this analogy has limits because electron behaviour is governed by quantum rules, not by classical gravity.
在简化模型中，原子常被比作一个小型太阳系：原子核如同”太阳”，电子如同”行星”。但这种类比有其局限，因为电子的行为由量子规律支配，而非经典引力。
2. The Nucleus: Protons and Neutrons | 原子核：质子与中子
The nucleus is extremely small compared to the whole atom. A typical nucleus has a radius of about 1 × 10⁻¹⁵ m to 1 × 10⁻¹⁴ m, whereas the atomic radius is about 1 × 10⁻¹⁰ m. This means the nucleus occupies only a tiny fraction of the atom’s volume, yet it contains almost all of the atom’s mass.
原子核与整个原子相比极其微小。典型原子核的半径约为 1 × 10⁻¹⁵ m 至 1 × 10⁻¹⁴ m，而原子半径约为 1 × 10⁻¹⁰ m。这意味着原子核只占据原子体积的极小部分，却几乎包含了原子的全部质量。
The number of protons in the nucleus is called the proton number (Z), also known as the atomic number. The total number of protons and neutrons is called the nucleon number (A), also known as the mass number. Using the nuclide notation, a nucleus is written as ₐXᴬ, where X is the chemical symbol.
原子核中的质子数称为质子数 Z，也叫原子序数。质子与中子的总数称为核子数 A，也叫质量数。使用核素记号时，原子核写作 ₐXᴬ，其中 X 是化学符号。
For example, carbon-12 is written as ₆C¹², which means it has 6 protons, 6 neutrons and 6 electrons in its neutral state.
例如，碳-12 写作 ₆C¹²，表示它有 6 个质子、6 个中子，并且在电中性状态下有 6 个电子。
3. Isotopes and Their Notation | 同位素及其记号
Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. Because the number of protons determines the element, isotopes share the same chemical properties but differ in mass.
同位素是同一元素中具有相同质子数但不同中子数的原子。由于质子数决定了元素种类，同位素具有相同的化学性质，但质量不同。
Consider hydrogen and its isotopes: ₁H¹ (protium), ₁H² (deuterium) and ₁H³ (tritium). All three have one proton, but they contain zero, one and two neutrons respectively. In nuclear physics, isotopes are often significant because some are stable while others are radioactive.
以氢及其同位素为例：₁H¹（氕）、₁H²（氘）和₁H³（氚）。三者都含一个质子，但分别含有零个、一个和两个中子。在核物理中，同位素具有重要意义，因为有些是稳定的，有些则具有放射性。
4. The Rutherford Scattering Experiment | 卢瑟福散射实验
The modern simplified model of the atom was established by Ernest Rutherford in 1911 through the gold-foil experiment. In this experiment, alpha particles were fired at a very thin gold foil. Most alpha particles passed straight through, some were deflected by small angles, and a very small number were deflected by more than 90°.
现代原子简化模型由欧内斯特·卢瑟福于 1911 年通过金箔实验确立。在该实验中，α 粒子被射向极薄的金箔。大多数 α 粒子直接穿过，少数发生小角度偏转，而极少数的偏转角度超过 90°。
These observations led to three key conclusions. First, most of the atom is empty space because most alpha particles passed straight through. Second, the atom contains a small, dense, positively charged nucleus because some alpha particles were repelled backwards. Third, electrons orbit the nucleus at relatively large distances, just like planets around the Sun.
这些观察得出三个关键结论。第一，原子大部分是空的空间，因为大多数 α 粒子直接穿过。第二，原子内部存在一个微小、致密且带正电的原子核，因为一些 α 粒子被反向排斥。第三，电子在距离原子核较远的轨道上运动，就像行星绕太阳运动一样。
5. Limitations of the Classical Model | 经典模型的局限
Although the Rutherford model explained the nuclear structure, it failed to explain the stability of atoms. According to classical electromagnetic theory, an accelerating electron should continuously radiate energy and spiral into the nucleus. This would destroy the atom within a fraction of a second, which clearly does not happen in reality.
尽管卢瑟福模型解释了原子核结构，却无法解释原子的稳定性。根据经典电磁理论，加速运动的电子应不断辐射能量并螺旋坠入原子核。这将在极短时间内使原子毁灭，而现实中显然并非如此。
Furthermore, the classical model could not explain why atoms emit light only at certain discrete wavelengths. When heated or electrically excited, atoms produce line spectra rather than continuous spectra. This contradiction forced physicists to develop a new model based on quantum ideas.
此外，经典模型无法解释为什么原子只在某些特定波长处发光。当原子被加热或电激发时，产生的是线状光谱而非连续光谱。这一矛盾迫使物理学家发展出基于量子思想的新模型。
6. The Bohr Model of the Atom | 玻尔原子模型
In 1913, Niels Bohr proposed a new model that incorporated quantum ideas. Bohr suggested that electrons can only occupy certain allowed orbits, now called stationary states or energy levels. In these orbits, the electron does not radiate energy even though it is accelerating.
1913 年，尼尔斯·玻尔提出了融合量子思想的新模型。玻尔提出，电子只能占据某些允许的轨道，这些轨道现在称为定态或能级。在这些轨道上，电子即使加速运动也不辐射能量。
Bohr introduced two key postulates. First, the angular momentum of the electron in an allowed orbit is quantised, meaning it can only take values equal to n × (h / 2π), where h is Planck’s constant and n is a positive integer. Second, radiation is emitted or absorbed only when an electron jumps between two allowed orbits.
玻尔引入了两个关键假设。第一，电子在允许轨道上的角动量是量子化的，只能取 n × (h / 2π) 的值，其中 h 是普朗克常数，n 是正整数。第二，只有当电子在两个允许轨道之间跃迁时，原子才发射或吸收辐射。
7. Energy Levels and Photon Emission | 能级与光子发射
Each allowed orbit corresponds to a specific energy level. The lowest energy level is called the ground state, and higher levels are called excited states. When an electron falls from a higher energy level E₂ to a lower energy level E₁, the atom emits a photon whose energy equals the difference between the two levels.
每个允许轨道对应一个特定的能级。最低的能级称为基态，较高的能级称为激发态。当电子从较高能级 E₂ 跃迁到较低能级 E₁ 时，原子发射一个光子，其能量等于两个能级之差。
E = hf = E₂ − E₁
Here, f is the frequency of the emitted photon, and h is Planck’s constant. Because the energy levels are discrete, the emitted frequencies are also discrete, which explains why atomic spectra consist of sharp lines rather than continuous bands.
其中 f 是发射光子的频率，h 是普朗克常数。由于能级是分立的，发射频率也是分立的，这解释了为什么原子光谱由尖锐的谱线组成，而不是连续的带。
8. Absorption and Emission Spectra | 吸收光谱与发射光谱
When white light passes through a cool gas, the gas absorbs photons at specific frequencies. The resulting absorption spectrum shows dark lines against a continuous bright background. Each dark line corresponds to a transition from a lower energy level to a higher one.
当白光穿过冷气体时，气体会吸收特定频率的光子。由此产生的吸收光谱在连续明亮背景上呈现暗线。每条暗线对应着从低能级到高能级的跃迁。
Conversely, when atoms in a gas are excited by heat or electricity, they emit photons as electrons return to lower levels. The emission spectrum consists of bright lines on a dark background. The frequencies of these emission lines exactly match the frequencies absorbed by the same element, demonstrating the conservation of energy at the atomic level.
相反，当气体中的原子被加热或电激发时，电子回到较低能级并发射光子。发射光谱由暗背景上的亮线组成。这些发射线的频率与该元素吸收的频率完全匹配，体现了原子层面的能量守恒。
9. Ionisation and Excitation | 电离与激发
Excitation occurs when an electron absorbs energy and jumps from a lower energy level to a higher one. The electron remains bound to the atom. Ionisation, on the other hand, occurs when an electron receives enough energy to escape the atom completely, leaving behind a positively charged ion.
激发发生在电子吸收能量并从低能级跃迁到高能级时，此时电子仍然被束缚在原子中。而电离则是电子获得足够能量后完全脱离原子，留下一个带正电的离子。
The minimum energy required to remove an electron from the ground state is called the ionisation energy. For a hydrogen atom, this energy is 13.6 eV. If an electron absorbs more energy than the ionisation energy, the excess is carried away as kinetic energy of the free electron.
从基态移走一个电子所需的最小能量称为电离能。对氢原子而言，该能量为 13.6 eV。如果电子吸收的能量超过电离能，多余部分将转化为自由电子的动能。
10. Atomic Excitation by Collision | 碰撞引起的原子激发
Atoms can also be excited or ionised by collisions with free electrons or other particles. In a discharge tube, free electrons are accelerated by an electric field and collide with gas atoms. If a colliding electron has exactly the right energy, it can transfer that energy to an atomic electron and raise it to a higher energy level.
原子也可以通过自由电子或其他粒子的碰撞而被激发或电离。在放电管中，自由电子被电场加速并与气体原子碰撞。如果碰撞电子具有恰好合适的能量，它可以将该能量传递给原子电子，使其跃迁到更高的能级。
The Franck-Hertz experiment famously demonstrated this effect. It showed that electrons can lose energy to mercury atoms only in discrete amounts, confirming that atomic energy levels are quantised. This experiment provided direct experimental evidence for the Bohr model.
弗兰克-赫兹实验经典地证明了这一效应。该实验表明，电子只能以分立的方式将能量传递给汞原子，从而证实原子能级是量子化的。这个实验为玻尔模型提供了直接的实验证据。
11. Line Spectra and Energy Level Diagrams | 线状光谱与能级图
Energy level diagrams are a convenient way to represent the allowed energies of an atom. In such diagrams, horizontal lines represent energy levels, and vertical arrows represent transitions. The length of each arrow corresponds to the photon energy, and therefore to the frequency of the emitted or absorbed radiation.
能级图是表示原子允许能量的便捷方式。在这类图中，水平线代表能级，竖直箭头代表跃迁。每条箭头的长度对应光子能量，因此也对应发射或吸收辐射的频率。
In the hydrogen atom, the Lyman series corresponds to transitions that end at the ground state (n = 1), and these lines lie in the ultraviolet region. The Balmer series ends at n = 2 and lies in the visible region. The Paschen series ends at n = 3 and lies in the infrared region.
在氢原子中，莱曼系对应于结束于基态 n = 1 的跃迁，这些谱线位于紫外区。巴尔末系结束于 n = 2，位于可见光区。帕邢系结束于 n = 3，位于红外区。
12. Relative Mass, Charge and Size of Particles | 粒子的相对质量、电荷与大小
For numerical calculations, it is useful to compare the masses and charges of the proton, neutron and electron. The masses of the proton and neutron are approximately equal, while the electron is roughly 1/1836 times the mass of a proton. This is why the nucleus contains nearly all the mass of the atom.
在数值计算中，比较质子、中子和电子的质量与电荷非常有用。质子与中子的质量近似相等，而电子质量约为质子质量的 1/1836。这就是为什么原子核几乎包含了原子的全部质量。
The following table summarises the relative properties of the three particles:
下表总结了三种粒子的相对性质：
| Particle | 粒子 | Relative Charge | 相对电荷 | Relative Mass | 相对质量 |
| Proton | 质子 | +1 | 1 |
| Neutron | 中子 | 0 | 1 |
| Electron | 电子 | −1 | 1/1836 |
In addition, the radius of the nucleus is of the order of 1 × 10⁻¹⁵ m, while the radius of the atom is of the order of 1 × 10⁻¹⁰ m. This difference of about 10⁵ in radius means that the nucleus is extremely small compared to the atom as a whole.
此外，原子核半径的量级为 1 × 10⁻¹⁵ m，而原子半径的量级为 1 × 10⁻¹⁰ m。两者半径相差约 10⁵ 倍，这意味着原子核与整个原子相比极其微小。
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