IB Physics: Quick Reference Table of Common Physical Constants | IB物理：常用物理常量速查表

📚 IB Physics: Quick Reference Table of Common Physical Constants | IB物理：常用物理常量速查表

The International Baccalaureate (IB) Physics syllabus provides a limited set of physical constants inside the formula booklet, but many examination questions require you to recall values quickly or identify the correct units for a given quantity. This guide presents a clear, exam-focused table of the most frequently used constants in both SL and HL courses, with tips for precision and unit conversion.

IB物理课程在公式手册中提供了有限的物理常量表，但许多考试题目要求你快速回忆常量数值，或根据给定的物理量选择正确的单位。本指南以考试为中心，汇总了SL和HL阶段最常用的物理常量，并附有精度提示和单位换算技巧。

1. Fundamental Constants | 基本物理常量

These constants appear across almost every topic in IB Physics, from mechanics to quantum theory. The speed of light \(c\) and the gravitational constant \(G\) are central to both classical and modern physics. In IB data booklet, \(c = 3.00 \times 10^8\ \text{m s}^{-1}\) and \(G = 6.67 \times 10^{-11}\ \text{N m}^2 \text{kg}^{-2}\) are given to three significant figures.

这些常量几乎出现在IB物理的所有章节中，从力学到量子理论。光速\(c\)和万有引力常量\(G\)是经典物理和现代物理的核心。在IB数据手册中，\(c = 3.00 \times 10^8\ \text{m s}^{-1}\)，\(G = 6.67 \times 10^{-11}\ \text{N m}^2 \text{kg}^{-2}\)，均保留三位有效数字。

Speed of light in vacuum: \(c = 3.00 \times 10^8\ \text{m s}^{-1}\)
Vacuum permittivity: \(\varepsilon_0 = 8.85 \times 10^{-12}\ \text{C}^2 \text{N}^{-1} \text{m}^{-2}\)
Vacuum permeability: \(\mu_0 = 4\pi \times 10^{-7}\ \text{T m A}^{-1} = 1.26 \times 10^{-6}\ \text{T m A}^{-1}\)

When solving problems involving electromagnetic waves, remember that \(c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}\). This relation is not always explicitly printed on the data booklet, so understanding the connection saves time.

在解决电磁波相关问题时，记住 \(c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}\)。这个关系不一定在数据手册中明确列出，理解这一联系可以节省时间。

2. Gravitational and Astronomical Constants | 引力与天文常量

Gravitation appears in Topic 6 (Circular Motion and Gravitation) and is extended in HL fields. The astronomical unit (AU) and the parsec are often tested in astrophysics options.

引力在Topic 6（圆周运动与万有引力）中出现，并在HL的场论中进一步延伸。天文单位（AU）和秒差距（parsec）常在天体物理选修部分考查。

Gravitational constant: \(G = 6.67 \times 10^{-11}\ \text{N m}^2 \text{kg}^{-2}\)
Acceleration due to gravity at Earth’s surface: \(g = 9.81\ \text{m s}^{-2}\)
Mass of Earth: \(M_{\text{Earth}} = 5.97 \times 10^{24}\ \text{kg}\)
Radius of Earth: \(R_{\text{Earth}} = 6.37 \times 10^6\ \text{m}\)
Mass of the Sun: \(M_{\text{Sun}} = 1.99 \times 10^{30}\ \text{kg}\)
1 AU: \(1.496 \times 10^{11}\ \text{m}\)
1 parsec: \(3.09 \times 10^{16}\ \text{m}\)

For orbital mechanics problems, combine \(F = \frac{GMm}{r^2}\) with \(F = \frac{mv^2}{r}\) to derive expressions for orbital speed and period. You can use the Earth’s radius to convert between altitude and orbital radius.

对于轨道力学问题，结合 \(F = \frac{GMm}{r^2}\) 和 \(F = \frac{mv^2}{r}\) 可推导出轨道速度和周期的表达式。使用地球半径可在高度和轨道半径之间进行换算。

3. Thermal and Statistical Constants | 热学与统计物理常量

Thermal physics in IB requires the Boltzmann constant and the universal gas constant for calculations involving kinetic theory and ideal gases. The value of \(k_B\) connects the average kinetic energy of particles to absolute temperature.

IB热学中，涉及分子动理论和理想气体的计算需要玻尔兹曼常量 \(k_B\) 和普适气体常量 \(R\)。\(k_B\) 将粒子的平均动能与绝对温度联系起来。

Boltzmann constant: \(k_B = 1.38 \times 10^{-23}\ \text{J K}^{-1}\)
Universal gas constant: \(R = 8.31\ \text{J K}^{-1} \text{mol}^{-1}\)
Avogadro constant: \(N_A = 6.02 \times 10^{23}\ \text{mol}^{-1}\)
Standard atmospheric pressure: \(1\ \text{atm} = 1.013 \times 10^5\ \text{Pa}\)
Absolute zero: \(0\ \text{K} = -273.15\ ^{\circ}\text{C}\)

The ideal gas equation can be written in two equivalent forms: \(pV = nRT\) and \(pV = N k_B T\). In the second form, \(N\) is the total number of molecules. To convert between them, use \(R = N_A k_B\).

理想气体方程有两种等价形式：\(pV = nRT\) 和 \(pV = N k_B T\)。在第二种形式中，\(N\) 是分子总数。两者之间通过 \(R = N_A k_B\) 换算。

4. Electromagnetic Constants | 电磁学常量

Electromagnetic constants are essential for Topic 5 (Electricity and Magnetism) and Topic 11 (Electromagnetic Induction). The elementary charge \(e\) appears wherever charge quantization matters.

电磁常量对于Topic 5（电与磁）和Topic 11（电磁感应）至关重要。基本电荷 \(e\) 出现在任何涉及电荷量子化的场合。

Elementary charge: \(e = 1.60 \times 10^{-19}\ \text{C}\)
Electron mass: \(m_e = 9.11 \times 10^{-31}\ \text{kg}\)
Proton mass: \(m_p = 1.67 \times 10^{-27}\ \text{kg}\)
Electron rest energy: \(m_e c^2 = 0.511\ \text{MeV}\)
Coulomb’s law constant: \(k = \frac{1}{4\pi \varepsilon_0} = 8.99 \times 10^9\ \text{N m}^2 \text{C}^{-2}\)

For electric field and potential calculations, remember that \(E = \frac{kQ}{r^2}\) for a point charge. The sign of the charge determines the direction of the field but not the magnitude in the formula.

在电场和电势计算中，点电荷的场强公式为 \(E = \frac{kQ}{r^2}\)。电荷的正负决定场强方向，但公式中不体现方向。

5. Quantum and Atomic Constants | 量子与原子物理常量

Quantum physics is a major part of IB Physics HL and also appears in the core syllabus for photoelectric effect and energy levels. Planck’s constant is perhaps the most recognisable symbol in this section.

量子物理是IB物理HL的重要组成部分，在核心内容中也涉及光电效应和能级。普朗克常量 \(h\) 是这一部分最有代表性的符号。

Planck constant: \(h = 6.63 \times 10^{-34}\ \text{J s}\)
Reduced Planck constant: \(\hbar = \frac{h}{2\pi} = 1.05 \times 10^{-34}\ \text{J s}\)
Rydberg constant: \(R_H = 1.10 \times 10^7\ \text{m}^{-1}\)
Bohr radius: \(a_0 = 5.29 \times 10^{-11}\ \text{m}\)
Fine structure constant: \(\alpha = \frac{e^2}{4\pi \varepsilon_0 \hbar c} \approx \frac{1}{137}\)

When applying the photoelectric effect equation \(E_{\text{photon}} = \phi + K_{\text{max}}\), use \(E = hf\). If the problem gives wavelength instead of frequency, convert with \(c = f\lambda\). The cutoff wavelength corresponds to \(E_{\text{photon}} = \phi\).

应用光电效应方程 \(E_{\text{photon}} = \phi + K_{\text{max}}\) 时，使用 \(E = hf\)。如果题目给出波长而不是频率，则用 \(c = f\lambda\) 换算。截止波长对应 \(E_{\text{photon}} = \phi\)。

6. Nuclear Physics Constants | 核物理常量

Nuclear physics questions in IB often require mass-energy equivalence and binding energy calculations. The atomic mass unit is used across Topic 7 and the HL option on particle physics.

IB核物理题目常常涉及质能方程和结合能计算。原子质量单位在Topic 7和HL粒子物理选修中广泛使用。

Atomic mass unit: \(1\ \text{u} = 1.66 \times 10^{-27}\ \text{kg} = 931.5\ \text{MeV/c}^2\)
Neutron mass: \(m_n = 1.67 \times 10^{-27}\ \text{kg}\)
Proton mass (in u): \(m_p = 1.0073\ \text{u}\)
Electron mass (in u): \(m_e = 0.000549\ \text{u}\)

To calculate binding energy, use \(E = \Delta m c^2\). The mass defect \(\Delta m\) is the difference between the total mass of individual nucleons and the mass of the nucleus. Expressing \(\Delta m\) in u and multiplying by 931.5 MeV/u gives binding energy directly.

计算结合能时使用 \(E = \Delta m c^2\)。质量亏损 \(\Delta m\) 是单个核子总质量与原子核质量之差。用u表示 \(\Delta m\) 并乘以 931.5 MeV/u，可直接得到结合能。

7. Wave and Sound Constants | 波与声学常量

Wave phenomena require few universal constants, but the speed of sound in air is a commonly used value in experiments and exam problems. The refractive index of a vacuum is defined as exactly 1, which helps simplify Snell’s law calculations.

波动现象需要的通用常量不多，但空气中的声速是实验和考试题目中常用的值。真空折射率精确定义为1，这简化了斯涅耳定律的计算。

Speed of sound in air (at 20 °C): \(v = 343\ \text{m s}^{-1}\)
Speed of sound in air (at 0 °C): \(v = 331\ \text{m s}^{-1}\)
Refractive index of vacuum: \(n = 1\)
Refractive index of water: \(n \approx 1.33\)
Refractive index of glass: \(n \approx 1.50\)

For standing waves in pipes and strings, use \(v = f\lambda\). In a closed pipe, the fundamental wavelength is \(4L\); in an open pipe, it is \(2L\). Always check the boundary conditions before applying harmonics.

对于管和弦中的驻波，使用 \(v = f\lambda\)。闭管基波波长为 \(4L\)，开管基波波长为 \(2L\)。应用谐波公式前先检查边界条件。

8. Particle Physics Masses | 粒子物理质量常量

The IB particle physics option requires knowledge of the masses of common particles, usually expressed in \(\text{MeV/c}^2\). These values help identify particles and compare their masses in decay reactions.

IB粒子物理选修要求掌握常见粒子的质量，通常以 \(\text{MeV/c}^2\) 为单位。这些值有助于识别粒子并比较衰变反应中的质量。

Electron: \(m_e = 0.511\ \text{MeV/c}^2\)
Muon: \(m_\mu = 105.7\ \text{MeV/c}^2\)
Tau: \(m_\tau = 1777\ \text{MeV/c}^2\)
Pion (charged): \(m_{\pi^\pm} = 139.6\ \text{MeV/c}^2\)
Neutron: \(m_n = 939.6\ \text{MeV/c}^2\)
Proton: \(m_p = 938.3\ \text{MeV/c}^2\)

In particle reactions, energy and momentum are conserved, and masses are used to calculate the \(Q\)-value of the reaction. If the total final mass exceeds the initial mass, energy is absorbed from the environment.

在粒子反应中，能量和动量守恒，质量用于计算反应的 \(Q\) 值。如果末态总质量大于初态总质量，则系统从环境中吸收能量。

9. Unit Conversions and Prefixes | 单位换算与词头

IB Physics requires fluency in SI prefixes. A single calculation can mix metres with kilometres, or joules with electronvolts. Keeping a mental table of prefixes prevents careless errors.

IB物理要求熟练使用SI词头。一个计算中可能同时出现米和千米、焦耳和电子伏特。熟记词头表可避免因单位换算而产生的粗心错误。

Prefix	Symbol	Factor
giga	G	10⁹
mega	M	10⁶
kilo	k	10³
centi	c	10⁻²
milli	m	10⁻³
micro	μ	10⁻⁶
nano	n	10⁻⁹
pico	p	10⁻¹²

Common conversions include \(1\ \text{eV} = 1.60 \times 10^{-19}\ \text{J}\) and \(1\ \text{keV} = 10^3\ \text{eV}\). For energy problems in quantum physics, convert wavelength to energy using \(E = \frac{hc}{\lambda}\) and check that the final unit is consistent with the problem’s requirement.

常见换算包括 \(1\ \text{eV} = 1.60 \times 10^{-19}\ \text{J}\) 和 \(1\ \text{keV} = 10^3\ \text{eV}\)。在量子物理的能量计算中，使用 \(E = \frac{hc}{\lambda}\) 将波长转换为能量，并检查最终单位是否与题意一致。

10. Exam Tips for Using Constants | 常量使用应试技巧

Exam success depends on knowing which constant to use and in which form. The IB data booklet provides many values, but you need to know their exact location and understand alternative forms.

考试成功的关键在于知道使用哪个常量以及使用哪种形式。IB数据手册提供了许多数值，但你需要知道它们的确切位置并理解替代形式。

Always write the constant you use before substituting numbers.
Use the same significant figures as the given data in the question.
When solving problems step by step, keep intermediate values in your calculator rather than rounding early.
For multi-part questions, pay attention to whether the question asks for the value of \(g\) or the gravitational constant \(G\).
Remember that \(c\) appears in wave, electromagnetic, and nuclear equations—check the context before writing \(c = 3 \times 10^8\) m/s.

Practising with past paper questions will help you identify which constants appear most frequently. Create your own flash cards for constants that you tend to forget, especially combinations like \(hc = 1240\ \text{eV nm}\).

通过练习历年真题，你可以识别出哪些常量出现频率最高。为容易忘记的常量制作自己的闪卡，特别是像 \(hc = 1240\ \text{eV·nm}\) 这样的组合常量。

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IB Physics: Quick Reference Table of Common Physical Constants | IB物理：常用物理常量速查表