📚 Line Spectra | 线光谱
When white light is dispersed by a prism or diffraction grating, it forms a continuous spectrum containing all visible wavelengths. However, light emitted or absorbed by individual atoms produces a very different pattern: a line spectrum consisting of discrete, well-defined wavelengths. Understanding line spectra is essential for explaining the quantised nature of atomic energy levels in A-Level Physics.
当白光通过棱镜或衍射光栅发生色散时，会形成包含所有可见波长的连续光谱。然而，单个原子发射或吸收的光会产生截然不同的图案：由分离且明确的波长组成的线状光谱。理解线光谱对于解释 A-Level 物理中原子能级的量子化本质至关重要。
1. Continuous vs Line Spectra | 连续光谱与线状光谱
A continuous spectrum contains all wavelengths over a given range, appearing as an unbroken band of colours. It is produced by hot solids, liquids, or dense gases under high pressure.
连续光谱在给定范围内包含所有波长，表现为一条不间断的色带。它由炽热的固体、液体或高压稠密气体产生。
A line spectrum contains only certain discrete wavelengths, showing either bright lines on a dark background or dark lines on a continuous background. Line spectra are produced by individual atoms in low-pressure gases.
线状光谱只包含特定分立的波长，在暗背景上显示亮线，或在连续背景上显示暗线。线状光谱由低压气体中的单个原子产生。
At A-Level, you must be able to distinguish between emission and absorption line spectra, and relate them to electronic transitions between quantised energy levels.
在 A-Level 课程中，你必须能够区分发射线光谱和吸收线光谱，并将它们与量子化能级之间的电子跃迁联系起来。
2. Emission Line Spectra | 发射线光谱
An emission line spectrum is produced when a hot, low-pressure gas emits light. The gas is excited by heating or by an electric discharge, giving its atoms extra energy.
当炽热的低压气体发光时，会产生发射线光谱。气体通过加热或放电被激发，使原子获得额外能量。
The spectrum consists of bright coloured lines at specific wavelengths on a dark background. Each line corresponds to a particular frequency emitted when an excited electron falls from a higher energy level to a lower one.
光谱由暗背景上特定波长的明亮彩色线条组成。每条线对应于激发态电子从高能级跃迁到低能级时发射的特定频率。
For example, a hydrogen discharge tube gives visible emission lines at 656 nm (red), 486 nm (blue-green), 434 nm (blue-violet) and 410 nm (violet).
例如，氢放电管发出的可见发射谱线分别为 656 nm（红）、486 nm（蓝绿）、434 nm（蓝紫）和 410 nm（紫）。
3. Absorption Line Spectra | 吸收线光谱
An absorption line spectrum is formed when white light passes through a cool gas. The gas absorbs only those photons whose energies exactly match the energy differences between its own atomic levels.
当白光穿过低温气体时，会形成吸收线光谱。气体只吸收能量与其自身原子能级差完全匹配的光子。
The observed spectrum is a continuous rainbow with dark lines missing at specific wavelengths. These dark lines occur at exactly the same wavelengths as the bright lines in the same element's emission spectrum.
观察到的光谱是连续彩虹背景上在特定波长处出现暗线。这些暗线出现的波长与该元素发射光谱中亮线的波长完全一致。
This correspondence is strong evidence that atoms can only absorb or emit photons of certain discrete energies, supporting the idea of quantisation.
这种对应关系有力地证明了原子只能吸收或发射某些分立能量的光子，支持了量子化的观点。
4. The Bohr Model and Energy Levels | 玻尔模型与能级
Niels Bohr proposed that electrons in an atom occupy only certain allowed orbits, called energy levels or shells. The energy of each level is fixed, so the possible energies are quantised.
尼尔斯·玻尔提出，原子中的电子只能处于某些允许的轨道，称为能级或壳层。每个能级的能量是固定的，因此可能的能量是量子化的。
are excited states (n = 2, 3, 4, ...). For hydrogen, the ground state energy is −13.6 eV.
最低能级是基态（n = 1）。较高能级为激发态（n = 2, 3, 4, ...）。对于氢原子，基态能量为 −13.6 eV。
The negative sign means the electron is bound to the nucleus. Zero energy corresponds to the electron being free from the atom, which occurs when ionisation has taken place.
负号表示电子被原子核束缚。零能量对应电子完全脱离原子，即发生电离。
5. Photon Energy and Transitions | 光子能量与跃迁
When an electron moves from a higher energy level E₂ to a lower energy level E₁, it emits a photon. The photon energy equals the difference between the two levels.
当电子从高能级 E₂ 跃迁到低能级 E₁ 时，会发射一个光子。光子能量等于两个能级之间的能量差。
ΔE = E₂ − E₁ = hf
ules, h is the Planck constant (6.63 × 10⁻³⁴ J s), and f is the photon frequency in hertz.
其中 ΔE 是能量差（单位焦耳），h 是普朗克常数（6.63 × 10⁻³⁴ J s），f 是光子频率（单位赫兹）。
Since c = fλ, the wavelength of the emitted photon can be found from:
由于 c = fλ，发射光子的波长可由下式求得：
ΔE = hc/λ
fference gives a photon with low energy and long wavelength; a large energy difference gives a photon with high energy and short wavelength.
因此 λ = hc/ΔE。能量差小，则光子能量低、波长长；能量差大，则光子能量高、波长短。
convert energy level differences from electronvolts to joules using 1 eV = 1.60 × 10⁻¹⁹ J.
使用该公式前，需要将能级差从电子伏特转换为焦耳：1 eV = 1.60 × 10⁻¹⁹ J。
6. Hydrogen Spectral Series | 氢光谱线系
Hydrogen has the simplest line spectrum. Its spectral lines are grouped into series, each corresponding to transitions ending at a particular lower energy level n₁.
氢具有最简单的线状光谱。其谱线分为若干个线系，每个线系对应于终止在特定低能级 n₁ 的跃迁。
the ultraviolet region. The Balmer series ends at n₁ = 2 and includes four visible lines.
莱曼线系终止于 n₁ = 1，位于紫外区。巴尔末线系终止于 n₁ = 2，包含四条可见谱线。
| Series | n₁ | Transitions from | Region |
|---|---|---|---|
| Lyman | 1 | n₂ = 2, 3, 4, ... | Ultraviolet |
| Balmer | 2 | n₂ = 3, 4, 5, ... | Visible |
| Paschen | 3 | n₂ = 4, 5, 6, ... | Infrared |
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