Energy Levels and Spectra: Edexcel Physics Revision | Edexcel 物理：能级与光谱 考点精讲

📚 Energy Levels and Spectra: Edexcel Physics Revision | Edexcel 物理：能级与光谱 考点精讲

Every time you see the glow of a neon sign or the characteristic yellow of a sodium street lamp, you are observing a fundamental quantum phenomenon: electrons jumping between discrete energy levels inside atoms. In Edexcel A-Level Physics, energy levels and spectra form a core part of the quantum physics topic, linking atomic structure to the unique ‘fingerprints’ of light emitted by each element. This article breaks down everything you need to know for the exam, from the hydrogen energy formula to the Franck-Hertz experiment, and from line spectra to fluorescence.

每当你看到霓虹灯的辉光或钠路灯特有的黄色，你都在观察一个基本的量子现象：电子在原子内部离散能级之间的跃迁。在 Edexcel A-Level 物理中，能级与光谱是量子物理主题的核心部分，它将原子结构与每种元素发出的独特光”指纹”联系起来。本文为你拆解考试所需的所有知识点，从氢原子能级公式到弗兰克-赫兹实验，从线光谱到荧光。

1. Atomic Energy Levels | 原子能级

In the Bohr model of the atom, electrons can only occupy certain allowed orbits, each with a fixed energy. These discrete energies are called energy levels. The lowest energy level is the ground state (n = 1); any higher level is an excited state (n > 1). An electron cannot exist between these levels — it must make a quantum jump from one to another.

在玻尔原子模型中，电子只能占据某些特定的轨道，每个轨道具有固定的能量。这些离散的能量称为能级。最低的能级是基态（n = 1）；任何更高的能级都是激发态（n > 1）。电子不能存在于这些能级之间——它必须从一个能级量子跃迁到另一个能级。

The energy of an electron in an atom is taken as negative because work must be done to remove the electron from the attraction of the nucleus. The highest energy level, at n = ∞, corresponds to zero energy, where the electron is free from the atom — this is ionisation.

原子中电子的能量取为负值，因为要使电子脱离原子核的吸引需要做功。最高能级 n = ∞ 对应于零能量，此时电子脱离原子——这就是电离。

2. The Hydrogen Atom Energy Formula | 氢原子能级公式

For hydrogen, the energy of the nth level is given by the relation that appears frequently in Edexcel papers:

Eₙ = −13.6 / n² (in eV)

where n is the principal quantum number (n = 1, 2, 3, …). Thus the ground state energy is −13.6 eV. An electron in the n = 2 level has energy −3.40 eV, in n = 3 it is −1.51 eV, and so on.

对于氢原子，第 n 能级的能量由 Edexcel 试卷中经常出现的公式给出：

Eₙ = −13.6 / n² （单位 eV）

其中 n 是主量子数（n = 1, 2, 3, …）。因此基态能量为 −13.6 eV。处于 n = 2 能级的电子能量为 −3.40 eV，n = 3 时为 −1.51 eV，依此类推。

When an electron moves from a higher level nᵢ to a lower level n_f, a photon is emitted with energy equal to the difference between the two levels:

ΔE = Eᵢ − E_f = hf = hc / λ

Conversely, a photon of exactly the right energy can be absorbed to promote an electron from a lower to a higher level.

当电子从较高能级 nᵢ 跃迁到较低能级 n_f 时，会发射一个光子，其能量等于两能级之差：

ΔE = Eᵢ − E_f = hf = hc / λ

相反，一个能量恰好合适的光子可以被吸收，从而将电子从低能级激发到高能级。

3. Energy Level Diagrams | 能级图

Energy level diagrams plot energy vertically, with n = 1 (ground state) at the bottom and n = ∞ (ionisation limit) at the top. Horizontal lines represent the allowed energy levels, and arrows between them indicate electron transitions. Downward arrows correspond to photon emission; upward arrows correspond to photon absorption.

能级图以纵轴表示能量，底部为 n = 1（基态），顶部为 n = ∞（电离极限）。水平线代表允许的能级，它们之间的箭头表示电子跃迁。向下的箭头对应光子发射；向上的箭头对应光子吸收。

You must be able to calculate the wavelength of the photon emitted when an electron falls from, say, n = 3 to n = 2. First find ΔE in eV, convert to joules (× 1.60 × 10⁻¹⁹), then use λ = hc / ΔE. Remember h = 6.63 × 10⁻³⁴ J s and c = 3.00 × 10⁸ m s⁻¹.

你必须能够计算电子从例如 n = 3 跃迁到 n = 2 时所发射光子的波长。首先求出以 eV 为单位的 ΔE，转换为焦耳（× 1.60 × 10⁻¹⁹），然后利用 λ = hc / ΔE。记住 h = 6.63 × 10⁻³⁴ J s，c = 3.00 × 10⁸ m s⁻¹。

You should also be able to identify which transition corresponds to a particular spectral line, and explain why only certain photon energies appear in a line spectrum.

你还应能识别哪条跃迁对应于特定的谱线，并解释为什么线光谱中只出现某些特定的光子能量。

4. Photon Emission and Absorption | 光子发射与吸收

Emission occurs when an excited electron drops to a lower energy level, releasing a photon of energy E = hf. Since the energy levels are fixed, only specific photon energies are possible, giving a line emission spectrum. Absorption is the reverse process: an electron absorbs a photon and jumps to a higher level, provided the photon energy matches the gap exactly.

发射发生在受激电子跃迁到较低能级时，释放出一个能量为 E = hf 的光子。由于能级是固定的，只有特定的光子能量是可能的，从而产生线状发射光谱。吸收是相反的过程：电子吸收一个光子并跃迁到较高能级，条件是该光子的能量恰好与能级差匹配。

A key exam point: an electron can always be excited by any photon with energy greater than or equal to the ionisation energy, because the excess energy becomes kinetic energy of the freed electron. However, for transitions between bound levels, only exact energies will do.

一个关键的考试要点：任何能量大于或等于电离能的光子都可以将电子电离，因为多余的能量会变成自由电子的动能。然而，对于束缚能级之间的跃迁，只有精确的能量匹配才行。

5. Discrete Line Spectra | 分立线光谱

When light from a hot, low-pressure gas is passed through a diffraction grating or prism, it produces a series of bright lines on a dark background — an emission line spectrum. Each line originates from electrons in many atoms moving between the same two energy levels. If white light passes through a cool gas, dark lines appear on a continuous background — an absorption spectrum. The dark lines correspond exactly to the bright lines of the emission spectrum of that element.

当来自炽热低压气体的光通过衍射光栅或棱镜时，会在暗背景上产生一系列亮线——发射线光谱。每条谱线源自许多原子中电子在相同的两个能级之间跃迁。如果白光穿过冷气体，则连续背景上会出现暗线——吸收光谱。这些暗线恰好与该元素发射光谱的亮线相对应。

In Edexcel questions, you may be given a spectrum diagram and asked to identify which gas is responsible by matching the pattern of lines to known data. The uniqueness of each element’s line spectrum makes it a powerful tool for chemical identification — even in distant stars.

在 Edexcel 考题中，你可能会得到一幅光谱图，并被要求通过将谱线图案与已知数据匹配来确定是哪种气体。每种元素的线光谱的独特性使其成为化学鉴定的有力工具——即使对遥远的恒星也是如此。

6. The Balmer, Lyman and Paschen Series | 巴尔末、莱曼和帕邢线系

For hydrogen, the transitions can be grouped into series ending on a common lower level. The Lyman series (ultraviolet) involves transitions down to n = 1; the Balmer series (visible) ends at n = 2; the Paschen series (infrared) ends at n = 3. Jumping from n ≥ 2 down to n = 1 gives the Lyman lines; from n ≥ 3 to n = 2 gives Balmer; from n ≥ 4 to n = 3 gives Paschen.

对于氢原子，跃迁可以按终止于同一较低能级进行分组。莱曼线系（紫外线）涉及跃迁至 n = 1；巴尔末线系（可见光）终止于 n = 2；帕邢线系（红外线）终止于 n = 3。从 n ≥ 2 跃迁至 n = 1 给出莱曼线系；从 n ≥ 3 至 n = 2 给出巴尔末线系；从 n ≥ 4 至 n = 3 给出帕邢线系。

The most familiar is the Balmer series. The line with the longest wavelength in this series (Hα) is due to the transition from n = 3 to n = 2. The series limit (shortest wavelength) occurs when an electron falls from n = ∞ to n = 2. Students are often required to calculate the wavelength of Hα or the series limit using the energy level formula.

最熟悉的是巴尔末线系。该线系中波长最长的谱线（Hα）来自 n = 3 到 n = 2 的跃迁。线系极限（最短波长）发生在电子从 n = ∞ 落到 n = 2 时。学生经常被要求利用能级公式计算 Hα 的波长或线系极限。

7. Continuous Spectra and Their Origin | 连续光谱及其起源

Not all spectra consist of discrete lines. A continuous spectrum contains all wavelengths in a certain range and is produced by hot, dense objects such as the filament of an incandescent bulb or the Sun’s photosphere. The thermal motion of closely packed atoms results in a broad range of photon energies being emitted.

并非所有光谱都由分立谱线组成。连续光谱包含某一范围内的所有波长，由炽热、致密的物体（如白炽灯泡的灯丝或太阳的光球层）产生。紧密排列原子的热运动导致发射出的光子能量范围很宽。

In the lab, an incandescent solid or liquid at high temperature produces a continuous spectrum. If this light then passes through a cooler gas, dark absorption lines are superimposed on the continuum, providing a fingerprint of the elements in the gas. The Sun’s spectrum is a classic example — the Fraunhofer lines are absorption lines caused by elements in the Sun’s outer atmosphere.

在实验室中，高温的炽热固体或液体会产生连续光谱。如果这束光然后穿过较冷的气体，连续谱上会叠加暗的吸收线，从而提供气体中元素的指纹。太阳光谱就是一个典型例子——夫琅禾费线是由太阳外层大气中的元素造成的吸收线。

8. The Franck-Hertz Experiment | 弗兰克-赫兹实验

Direct evidence for the existence of discrete energy levels in atoms came from the Franck-Hertz experiment. Electrons are accelerated through mercury vapour by a variable voltage. As the voltage increases, the current collected at the anode initially rises. However, at a specific voltage (about 4.9 V for mercury), the current drops sharply.

原子中存在分立能级的直接证据来自弗兰克-赫兹实验。电子通过可变电压在汞蒸气中被加速。随着电压增加，阳极收集到的电流最初上升。然而，在某一特定电压下（汞约为 4.9 V），电流急剧下降。

This drop occurs because the accelerated electrons now have exactly enough kinetic energy (4.9 eV) to excite mercury atoms from their ground state to the first excited state. The electrons lose this energy in inelastic collisions and can no longer reach the anode. The current then rises again as the voltage is increased further, until multiples of the excitation energy cause further dips. The experiment confirms that atoms can only absorb energy in discrete amounts, corresponding to the gaps between energy levels.

这种下降的发生是因为被加速的电子此时恰好具有足够的动能（4.9 eV）将汞原子从基态激发到第一激发态。电子在非弹性碰撞中损失这部分能量，从而无法到达阳极。随着电压进一步升高，电流再次上升，直到激发能量的倍数导致更多的下降。该实验证实原子只能吸收离散的能量，与能级间的间隙相对应。

9. Fluorescence and Phosphorescence | 荧光与磷光

When certain materials absorb ultraviolet radiation and immediately re-emit visible light, the phenomenon is called fluorescence. In terms of energy levels, a UV photon excites an electron to a high energy level; the electron then cascades down through intermediate levels, emitting photons of lower energy (longer wavelengths) in the visible range. The process is rapid and stops as soon as the UV source is removed.

当某些材料吸收紫外线辐射并立即重新发射可见光时，这种现象称为荧光。从能级角度看，一个紫外光子将电子激发到高能级；然后电子通过中间能级逐级回落，发射出能量更低（波长更长）的可见光光子。该过程很快，一旦移走紫外光源就停止。

Phosphorescence is similar but delayed. The electrons become trapped in a metastable excited state from which transitions to the ground state are ‘forbidden’ by quantum mechanical selection rules. The trapped electrons return to the ground state slowly over seconds or even hours, causing a persistent glow after the excitation source is removed. Glow-in-the-dark stickers are a common example.

磷光类似但有所延迟。电子被困在一个亚稳态激发态中，量子力学选择定则”禁止”其直接跃迁到基态。被捕获的电子在数秒甚至数小时内缓慢返回基态，导致激发光源移除后仍持续发光。夜光贴纸就是一个常见例子。

10. Applications of Atomic Spectra | 原子光谱的应用

Line spectra are used extensively in chemical analysis. Each element has a unique emission and absorption spectrum, acting like a barcode. In astronomy, the composition of stars, interstellar gas, and exoplanet atmospheres is determined from absorption or emission lines in their spectra. Redshifts of these lines also indicate the motion of galaxies.

线光谱广泛用于化学分析。每种元素都有独特的发射和吸收光谱，就像条形码一样。在天文学中，恒星、星际气体以及系外行星大气的成分都是根据其光谱中的吸收或发射线来确定的。这些谱线的红移还指示了星系的运动。

In laboratories, atomic absorption spectroscopy (AAS) detects trace metals by measuring the absorption of characteristic wavelengths by a sample vaporised in a flame. Similarly, lasers (Light Amplification by Stimulated Emission of Radiation) rely on stimulated emission between energy levels to produce intense, monochromatic, coherent light. Understanding energy levels is also vital in designing LED lighting, where the band gap of a semiconductor determines the colour of emitted light.

在实验室中，原子吸收光谱法（AAS）通过测量在火焰中气化的样品对特征波长的吸收来检测痕量金属。同样，激光（受激辐射光放大）依赖于能级之间的受激辐射，以产生强、单色、相干的光。理解能级对于设计 LED 照明也至关重要，其中半导体的带隙决定了发射光的颜色。

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Published by TutorHao | Physics Revision Series | aleveler.com

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