Common Physical Constants and How They Are Tested | 常见物理常数及其考查方式

📚 Common Physical Constants and How They Are Tested | 常见物理常数及其考查方式

In A-level physics, a small set of fundamental constants appears again and again in exam questions. Knowing their values, units, and the contexts in which they arise is essential for solving problems quickly and accurately.

在 A-level 物理中，一小部分基本常数会在考题中反复出现。熟记它们的数值、单位及其应用的物理情境，是快速、准确解题的关键。

1. Speed of Light in Vacuum c | 真空光速 c

The speed of light in vacuum is perhaps the most famous physical constant, with a value of exactly 299 792 458 m s⁻¹. In most exam calculations, it is taken as 3.00 × 10⁸ m s⁻¹.

真空中的光速或许是最著名的物理常数，其精确值为 299 792 458 m s⁻¹。在多数考试计算中，通常取 3.00 × 10⁸ m s⁻¹。

This constant appears in the wave equation c = fλ for electromagnetic waves, in the photon energy formula E = hf, and in mass–energy equivalence E = mc². It also defines the relationship between the electric constant and the magnetic constant: c² = 1/(ε₀μ₀).

光速出现在电磁波的波动方程 c = fλ、光子能量公式 E = hf，以及质能等价关系 E = mc² 中。它还定义了电常数与磁常数之间的关系：c² = 1/(ε₀μ₀)。

Common exam usage: Calculating the wavelength of light from its frequency, or finding the energy of a photon when given its wavelength. You may also be asked to convert between electronvolts and joules.

常见考法：由频率计算光的波长，或由波长求光子能量。题目还可能要求你在电子伏特与焦耳之间进行换算。

2. Gravitational Constant G | 万有引力常数 G

The gravitational constant G has a value of 6.67 × 10⁻¹¹ N m² kg⁻². It is a universal constant appearing in Newton’s law of gravitation F = Gm₁m₂/r².

万有引力常数 G 的数值为 6.67 × 10⁻¹¹ N m² kg⁻²。它是牛顿万有引力定律 F = Gm₁m₂/r² 中的普适常数。

In exam questions, G is often used together with the mass of the Earth or the Sun to calculate orbital speeds, gravitational field strength, or the escape velocity. A typical calculation is g = GM/R², where M and R are the mass and radius of a planet.

在考试题中，G 常与地球或太阳的质量一起使用，用于计算轨道速度、引力场强度或逃逸速度。典型计算为 g = GM/R²，其中 M 和 R 分别是行星的质量和半径。

Common exam usage: Questions may provide the radius of a planet’s orbit and ask for its orbital period using Kepler’s third law, or they may ask you to estimate the mass of a planet from the surface gravitational field strength.

常见考法：题目可能给出行星轨道半径，要求利用开普勒第三定律求轨道周期；也可能要求你根据表面引力场强度估算行星质量。

3. Planck Constant h | 普朗克常数 h

The Planck constant h has a value of 6.63 × 10⁻³⁴ J s. It is the fundamental constant of quantum mechanics, linking the energy of a photon to its frequency: E = hf.

普朗克常数 h 的数值为 6.63 × 10⁻³⁴ J s。它是量子力学的基本常数，将光子能量与其频率联系起来：E = hf。

In the photoelectric effect, the work function φ and the maximum kinetic energy of emitted electrons are related by hf = φ + Eₖₘₐₓ. The Planck constant also appears in the de Broglie wavelength λ = h/p for matter waves.

在光电效应中，逸出功 φ 与发射电子的最大动能满足 hf = φ + Eₖₘₐₓ。普朗克常数还出现在物质波的德布罗意波长 λ = h/p 中。

Common exam usage: You may be given the stopping potential and the frequency of incident light, then asked to determine the work function or the Planck constant from a graph of V_s against f.

常见考法：题目可能给出截止电压和入射光频率，要求你根据 V_s–f 图像确定逸出功或普朗克常数。

4. Elementary Charge e | 元电荷 e

The elementary charge e is the magnitude of charge carried by a single proton or electron, equal to 1.60 × 10⁻¹⁹ C. It is a central constant in electromagnetism and atomic physics.

元电荷 e 是单个质子或电子所带电荷的大小，等于 1.60 × 10⁻¹⁹ C。它是电磁学和原子物理的核心常数。

You will encounter e in the force between charges F = kq₁q₂/r², in electric field calculations, and in the energy conversion when a charge moves through a potential difference: W = eV. The electronvolt is defined as the energy gained by one electron moving through a potential difference of one volt.

你会在电荷之间的作用力 F = kq₁q₂/r²、电场计算以及电荷通过电势差时的能量转换 W = eV 中遇到 e。电子伏特定义为单个电子通过 1 伏特电势差时获得的能量。

Common exam usage: Calculating the number of charge carriers using I = nAve, or determining the energy of accelerated particles. The electron charge is also used with the Avogadro constant to determine the Faraday constant.

常见考法：利用 I = nAve 计算载流子数密度，或求加速粒子的能量。元电荷还常与阿伏伽德罗常数联用求法拉第常数。

5. Electron Rest Mass mₑ | 电子静止质量 mₑ

The electron rest mass is approximately 9.11 × 10⁻³¹ kg. In nuclear physics, mass is often expressed in atomic mass units, and the electron mass corresponds to about 0.00055 u.

电子静止质量约为 9.11 × 10⁻³¹ kg。在核物理中，质量常用原子质量单位表示，电子质量约为 0.00055 u。

This constant appears in calculations of specific charge (e/mₑ), in the deflection of charged particles in electric and magnetic fields, and in the energy–momentum relation E² = (pc)² + (m₀c²)².

该常数出现在比电荷（e/mₑ）的计算、带电粒子在电场和磁场中的偏转，以及能量–动量关系 E² = (pc)² + (m₀c²)² 中。

Common exam usage: Questions may involve measuring the charge-to-mass ratio of electrons using a velocity selector, or calculating the mass defect in beta decay where an electron is emitted.

常见考法：题目可能涉及利用速度选择器测量电子的荷质比，或计算 β 衰变中的质量亏损，因为该过程会发射电子。

6. Avogadro Constant Nₐ | 阿伏伽德罗常数 Nₐ

The Avogadro constant Nₐ = 6.02 × 10²³ mol⁻¹ defines the number of particles in one mole of substance. It connects the microscopic world of atoms and molecules to macroscopic quantities like mass and amount of substance.

阿伏伽德罗常数 Nₐ = 6.02 × 10²³ mol⁻¹ 定义了一摩尔物质所含的粒子数。它将原子和分子的微观世界与质量、物质的量等宏观量联系起来。

In the ideal gas equation pV = nRT, the number of moles n can be related to the number of molecules N by n = N/Nₐ. Combining this with the Boltzmann constant k = R/Nₐ gives pV = NkT.

在理想气体方程 pV = nRT 中，摩尔数 n 与分子数 N 的关系为 n = N/Nₐ。结合玻尔兹曼常数 k = R/Nₐ，可得 pV = NkT。

Common exam usage: Estimating the size of molecules, calculating the number of atoms in a sample of known mass, or determining the energy of a single molecule from a molar quantity.

常见考法：估算分子大小、计算已知质量样品中的原子数，或从摩尔量求单个分子的能量。

7. Boltzmann Constant k | 玻尔兹曼常数 k

The Boltzmann constant k has a value of 1.38 × 10⁻²³ J K⁻¹. It relates the average kinetic energy of gas molecules to temperature: <½mv²> = (3/2)kT.

玻尔兹曼常数 k 的数值为 1.38 × 10⁻²³ J K⁻¹。它将气体分子的平均平动动能与温度联系起来：<½mv²> = (3/2)kT。

This constant is essential in thermal physics and also appears in the equation for the root-mean-square speed of gas molecules c_rms = √(3kT/m). In this equation, m is the mass of a single molecule.

该常数在热学中至关重要，也出现在气体分子均方根速率公式 c_rms = √(3kT/m) 中。此处的 m 是单个分子的质量。

Common exam usage: Calculating the average molecular speed in a gas, or finding the temperature at which molecules have a certain kinetic energy. You may need to convert the molar gas constant R to k using Nₐ.

常见考法：计算气体分子的平均速率，或求分子具有某一动能时的温度。你可能需要用 Nₐ 将摩尔气体常数 R 转换为 k。

8. Permittivity and Permeability of Free Space | 真空介电常数与磁导率

The electric constant ε₀ = 8.85 × 10⁻¹² F m⁻¹ appears in Coulomb’s law F = q₁q₂/(4πε₀r²). The magnetic constant μ₀ = 4π × 10⁻⁷ H m⁻¹ appears in the force between current-carrying conductors and in the magnetic field of a solenoid B = μ₀nI.

真空介电常数 ε₀ = 8.85 × 10⁻¹² F m⁻¹ 出现在库仑定律 F = q₁q₂/(4πε₀r²) 中。真空磁导率 μ₀ = 4π × 10⁻⁷ H m⁻¹ 出现在载流导体之间的作用力以及螺线管磁场 B = μ₀nI 中。

The two constants are related to the speed of light: c = 1/√(ε₀μ₀). This relationship is sometimes used in exam questions that ask you to verify the consistency of the given values.

这两个常数与光速的关系为 c = 1/√(ε₀μ₀)。考试有时会利用这一关系，要求你验证给定数值之间的一致性。

Common exam usage: Calculating electric field strength between parallel plates, or the magnetic field inside a solenoid. You may also be asked to derive the units of ε₀ or μ₀ from other equations.

常见考法：计算平行板之间的电场强度，或螺线管内部的磁场。题目还可能要求你从其他方程推导 ε₀ 或 μ₀ 的单位。

9. Unified Atomic Mass Unit u | 原子质量单位 u

The unified atomic mass unit is defined as one-twelfth of the mass of a carbon-12 atom, equal to 1.66 × 10⁻²⁷ kg. In energy terms, 1 u is equivalent to 931.5 MeV.

原子质量单位的定义是碳-12 原子质量的十二分之一，等于 1.66 × 10⁻²⁷ kg。按能量换算，1 u 相当于 931.5 MeV。

This constant is indispensable in nuclear physics, particularly for calculating binding energy and mass defect. The mass difference Δm between reactants and products is converted to energy using E = Δmc².

该常数在核物理中不可或缺，尤其是在计算结合能和质量亏损时。反应物与产物之间的质量差 Δm 通过 E = Δmc² 转换为能量。

Common exam usage: Calculating the energy released in a nuclear fission or fusion reaction, or finding the binding energy per nucleon from a given mass defect.

常见考法：计算核裂变或核聚变反应释放的能量，或根据给定的质量亏损求每个核子的结合能。

10. How Constants Are Tested in Questions | 考试中常数的常见考查方式

Exam questions rarely ask for the value of a constant directly. Instead, constants are embedded in multi-step problems, and you must select the correct one and use it with the correct units.

考试很少直接考查常数的数值，而是将常数嵌入多步问题中，你需要选出正确的常数并配套正确单位使用。

Numerical substitution: You are given a formula and all other quantities; you substitute the constant and solve.

数值代入：给出公式及其他所有物理量，代入常数求解。
Unit derivation: You must derive the unit of a constant from a known equation, or check the dimensional consistency of an expression.

单位推导：要求你从已知方程推导某常数的单位，或检查表达式的量纲一致性。
Graph interpretation: For example, in the photoelectric effect, the gradient of a V_s–f graph equals h/e.

图像分析：例如在光电效应中，V_s–f 图像的斜率等于 h/e。
Order-of-magnitude estimation: You may need to estimate quantities such as the number of molecules in a room using approximate values of constants.

数量级估计：你可能需要利用常数的近似值来估算物理量，例如房间内的分子数。

A common trap is mixing powers of ten. For instance, the electron charge is 1.60 × 10⁻¹⁹ C, and the Planck constant is 6.63 × 10⁻³⁴ J s. Be careful when multiplying them in problems involving photon momentum or stopping potential.

一个常见陷阱是弄错 10 的幂次。例如，元电荷为 1.60 × 10⁻¹⁹ C，普朗克常数为 6.63 × 10⁻³⁴ J s。在涉及光子动量或截止电压的问题中将它们相乘时，务必特别小心。

11. Memory Techniques and Exam Tips | 记忆方法与考试技巧

The most effective way to remember constants is to see them in context. Every time you use a constant in a calculation, write it down with its unit and say it aloud. Repetition in context creates stronger memory traces than rote memorization alone.

记忆常数最有效的方法是在具体情境中使用它们。每次在计算中使用某个常数时，连同单位写下来并大声读出来。在情境中重复比单独死记硬背能留下更深刻的记忆痕迹。

Group constants by topic: mechanics (G), waves/photons (c, h), electricity (e, ε₀, μ₀), thermal physics (Nₐ, k), nuclear physics (u, mₑ).

按主题分组：力学（G）、波与光子（c、h）、电学（e、ε₀、μ₀）、热学（Nₐ、k）、核物理（u、mₑ）。
Know the exact relationships: c = fλ, E = hf, λ = h/p, g = GM/R², pV = NkT.

牢记精确关系式：c = fλ、E = hf、λ = h/p、g = GM/R²、pV = NkT。
Always write units in your final answer. A correct number with the wrong unit earns no marks.

最终答案一定要写单位。数字正确但单位错误是不得分的。
Check the degree of accuracy: use the constants to the same number of significant figures as the data provided in the question.

注意有效数字：常数取的有效数字位数应与题目所给数据一致。

Some students find it helpful to memorise a small card with the eight most important constants and review it before each mock exam. Write the name, symbol, value, and a typical equation for each constant.

有些学生发现，将八个最重要的常数做成小卡片，并在每次模拟考前复习，是一种有效的方法。每张卡片上写清名称、符号、数值和一个典型方程。

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Common Physical Constants and How They Are Tested | 常见物理常数及其考查方式