📚 Line Spectra | 线状光谱
Line spectra are one of the most compelling pieces of evidence for the quantised nature of energy in atoms. Unlike a continuous rainbow of colours, a line spectrum consists of discrete bright or dark lines at specific wavelengths, corresponding to photons emitted or absorbed as electrons jump between fixed energy levels.
线状光谱是证明原子能量量子化最有力的证据之一。不同于连续的彩虹色带，线状光谱由特定波长处的分立亮线或暗线组成，这些谱线与电子在固定能级之间跃迁时发射或吸收的光子相对应。
1. Introduction to Line Spectra | 线状光谱简介
When light from a glowing gas is passed through a prism or diffraction grating, it does not produce a continuous spread of colours. Instead, a pattern of sharp, narrow lines appears against a dark background. This is called a line spectrum. Each line corresponds to light of a single wavelength or frequency. The positions and intensities of these lines are unique to each element, much like a fingerprint.
当炽热气体发出的光通过棱镜或衍射光栅时，它并不会产生连续的色彩分布。相反，在黑暗背景上会出现一系列清晰而狭窄的谱线，这就是线状光谱。每一条谱线对应单一波长或频率的光。这些谱线的位置和强度对每种元素都是独一无二的，就像指纹一样。
2. Emission and Absorption Spectra | 发射光谱与吸收光谱
There are two main types of line spectra. An emission spectrum is produced when low-pressure gas is electrically excited or heated. Electrons in the atoms absorb energy and jump to higher energy levels. When they fall back to lower levels, they emit photons of specific energies, creating bright lines on a dark background.
线状光谱主要有两种类型。当低压气体被电激发或加热时会产生发射光谱。原子中的电子吸收能量跃迁到较高能级，当它们回落到较低能级时，会发射具有特定能量的光子，从而在黑暗背景上形成亮线。
An absorption spectrum is observed when white light passes through a cooler gas. Atoms in the gas absorb photons of exactly the right energy to promote electrons to higher levels. These absorbed wavelengths are missing from the transmitted light, producing a continuous spectrum crossed by dark absorption lines. The dark lines in an absorption spectrum occur at exactly the same wavelengths as the bright lines in the emission spectrum of the same element.
当白光穿过较冷的气体时，会观察到吸收光谱。气体中的原子准确地吸收使电子跃迁到较高能级所需能量的光子。这些被吸收的波长在透射光中缺失，从而形成被暗吸收线穿越的连续光谱。吸收光谱中的暗线与同一元素发射光谱中的亮线出现在完全相同的波长处。
3. Continuous vs. Line Spectra | 连续光谱与线状光谱对比
A continuous spectrum contains all wavelengths within a certain range and is produced by glowing solids, liquids, or high-pressure gases. In contrast, line spectra are produced by low-pressure gases or individual atoms where the electrons are bound to discrete energy levels. The table below summarises the key differences.
连续光谱包含一定范围内的所有波长，由炽热的固体、液体或高压气体产生。相比之下，线状光谱由低压气体或单个原子产生，其中电子被束缚在分立的能级上。下表总结了主要区别。
| Feature | Continuous Spectrum | Line Spectrum |
|---|---|---|
| Source | Incandescent solids, liquids, high-pressure gases | Low-pressure gases, excited atoms |
| Appearance | Unbroken rainbow of colours | Sharp bright or dark lines at specific wavelengths |
| Energy levels | Not quantised effectively; atoms interact strongly | Electrons occupy discrete, quantised energy states |
| Example | Sun's photosphere (before absorption), tungsten filament | Hydrogen discharge tube, sodium vapour lamp |
4. Atomic Energy Levels and Photon Emission | 原子能级与光子发射
In the Bohr model of the atom, electrons can only exist in certain allowed orbits with specific energies. These discrete energy levels are the key to understanding line spectra. When an electron moves from a higher energy level E₂ to a lower one E₁, the atom emits a photon whose energy equals the difference between the two levels:
在玻尔原子模型中，电子只能存在于某些特定能量的允许轨道上。这些分立的能级是理解线状光谱的关键。当电子从较高能级 E₂ 跃迁到较低能级 E₁ 时，原子会发射一个光子，其能量等于两个能级之差：
ΔE = E₂ − E₁ = h f = h c / λ
where h is Planck' requency, c is the speed of light, and λ is the wavelength. Each transition produces a single spectral line. A collection of many atoms undergoing various transitions results in the observed line spectrum. The fact that only certain photon energies are observed confirms that the energy difference is fixed and quantised.
其中 h 是普朗克常数（6.63 × 10⁻³⁴ J s），f 是频率，c 是光速，λ 是波长。每一次跃迁产生一条单一谱线。大量原子经历不同的跃迁，共同构成观察到的线状光谱。只有特定能量的光子被观测到，这一事实证实了能量差是固定且量子化的。
5. The Hydrogen Spectrum | 氢原子光谱
on the final energy level of the electron transition. The Lyman series (ultraviolet) involves transitions to the n = 1 ground state. The Balmer series (visible and near-UV) involves transitions to n = 2. The Paschen series (infrared) involves transitions to n = 3, and so on.
氢是最简单的原子，只有一个电子，它产生的线状光谱最为简明。谱线根据电子跃迁的最终能级分成不同的线系。莱曼系（紫外区）涉及跃迁到 n = 1 的基态；巴尔末系（可见光区及近紫外）涉及跃迁到 n = 2；帕邢系（红外区）涉及跃迁到 n = 3，依此类推。
The visible Balmer lines were the first to be observed and are of particular importance. They are labelled Hα (red), Hβ (blue-green), Hγ (violet), and so on. These lines arise
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