📚 Appendix 2: Data, Formulae and Relationships | 数据、公式与关系式
CIE A-Level Physics examinations provide a crucial reference in the form of Appendix 2: a concise compilation of experimental data, fundamental constants, conversion factors, and the essential formulae and relationships that underpin the entire syllabus. Knowing exactly what is included—and equally, what is not—gives you a huge advantage in applying these tools rapidly and correctly. This article walks you through every key element, clarifying usage and highlighting common pitfalls, so that the appendix becomes a powerful extension of your own knowledge during the exam.
CIE A-Level 物理考试会提供一份至关重要的参考资料——附录 2，它精简地汇编了实验数据、基本常数、换算因子以及支撑整个教学大纲的核心公式与关系式。准确知道附录中包含什么、不包含什么，能让你在快速、正确运用这些工具时占据巨大优势。本文将带你逐一梳理每个关键要素，阐明用途并指出常见错误，让这份附录在考试中成为你知识的强力延伸。
1. Fundamental Constants | 基本常数
gnetic waves, and in relativity. Always use this standard value unless a question specifies otherwise.
真空中光速：c = 3.00 × 10⁸ m s⁻¹。该常数出现在质能方程 E = mc²、电磁波波速公式 c = fλ 以及相对论中。除非题目另有说明，否则一律使用这个标准值。
It is the magnitude of the charge on a proton or electron and is fundamental to all current electricity, capacitance, and particle physics calculations. Remember that electron charge is –e.
基本电荷：e = 1.60 × 10⁻¹⁹ C。这是质子或电子所带电荷的绝对值，是所有电流、电容和粒子物理计算的基础。注意电子带电 –e。
The appendix also lists the reduced Planck constant h/2π for more advanced wave mechanics.
普朗克常数：h = 6.63 × 10⁻³⁴ J s。在光子能量 E = hf 和德布罗意波长 λ = h/p 中至关重要。附录还列出了约化普朗克常数 h/2π，用于更深入的波动力学。
Gravitational constant: G = 6.67 × 10⁻¹¹ N m² kg⁻². Only used in Newton' F = Gm₁m₂/r² and gravitational potential. Extremely small, reflecting how weak gravity is.
万有引力常数：G = 6.67 × 10⁻¹¹ N m² kg⁻²。仅在牛顿引力定律 F = Gm₁m₂/r² 和引力势中使用。该值极小，反映出引力非常微弱。
Avogadro constant: NA ⁻¹. Links moles to number of particles, used in ideal gas equations and radioactive decay.
阿伏伽德罗常数：NA = 6.02 × 10²³ mol⁻¹。将摩尔与粒子数联系起来，用于理想气体方程和放射性衰变。
ther constants include the Boltzmann constant k = 1.38 × 10⁻²³ J K⁻¹, electron rest mass me = 9.11 × 10⁻³¹ kg, proton rest mass mp ¹, and permeability of free space μ₀ = 4π × 10⁻⁷ H m⁻¹. Note the exact relationship c = 1/√μ₀ε₀.
其他常数包括玻尔兹曼常数 k = 1.38 × 10⁻²³ J K⁻¹、电子静止质量 me = 9.11 × 10⁻³¹ kg、质子静止质量 mp = 1.673 × 10⁻²⁷ kg、真空介电常数 ε₀ = 8.85 × 10⁻¹² F m⁻¹ 和真空磁导率 μ₀ = 4π × 10⁻⁷ H m⁻¹。请注意精确关系 c = 1/√μ₀ε₀。
2. Conversion Factors | 换算因子
ectronvolts are convenient for particle energies; convert to joules for SI calculations by multiplying by e.
附录中包含基本的单位换算。1 eV = 1.60 × 10⁻¹⁹ J。电子伏特非常便于表示粒子能量，进行国际单位制计算时只需乘以 e 即可转换为焦耳。
alent 1 u = 931.5 MeV is particularly helpful for mass defect and binding energy questions – always check whether you are given this directly or need to derive it using E = mc².
1 u（统一原子质量单位）= 1.66 × 10⁻²⁷ kg。用于表示原子核质量。其能量当量 1 u = 931.5 MeV 在处理质量亏损和结合能问题时特别有用——务必确认题目是直接给出该值，还是需要你用 E = mc² 自行推导。
ntexts. Also given are standard prefixes from pico (10⁻¹²) to tera (10¹²). Knowing these by heart saves precious time.
附录还提供了 1 年 = 3.16 × 10⁷ s 和 1 光年 = 9.46 × 10¹⁵ m，主要用于天体物理场景。此外还列出了从皮可（10⁻¹²）到太拉（10¹²）的标准词头。熟记这些前缀能节省宝贵时间。
3. Mechanics Equations | 力学方程
as. These four equations are the backbone of kinematics. They only apply when acceleration is constant.
匀加速运动：v = u + at, s = ut + ½at², s = (u+v)t/2, v² = u² + 2as。这四个方程是运动学的基石，仅在加速度恒定时适用。
Newton' eleration. For problems involving inclined planes, remember to resolve weight components correctly.
牛顿第二定律：ΣF = ma。附录可能会将其写为合力 = 质量 × 加速度。在处理斜面问题时，切记正确分解重力分量。
rvation of momentum (total p before = total p after) is used in collisions and explosions.
动量：p = mv。冲量 = FΔt = Δp。动量守恒（碰撞前总动量 = 碰撞后总动量）用于碰撞和爆炸问题。
Work, energy, power: W = Fs cosθ, kinetic energy Ek = ½mv², gravitational potential energy Ep = mgh (near Earth's surface), power P = W/t = Fv. Efficiency = useful output / total input.
功、能、功率：W = Fs cosθ，动能 Ek = ½mv²，重力势能 Ep = mgh（近地表面），功率 P = W/t = Fv。效率 = 有用输出 / 总输入。
rce F = mv²/r = mrω². These are vital for orbits and charged particles in magnetic fields.
圆周运动：角速度 ω = 2π/T = 2πf，线速度 v = ωr，向心加速度 a = v²/r = rω²，向心力 F = mv²/r = mrω²。这些公式对轨道运动以及带电粒子在磁场中的运动至关重要。
4. Waves and Optics | 波与光学
= fλ. The relationship is fundamental for superposition, interference, and standing waves.
波速：v = fλ。对于电磁波则为 c = fλ。这是处理叠加、干涉和驻波问题的基础关系。
or small angles and coherent sources. The diffraction grating equation d sinθ = nλ is used for sharper, widely spaced maxima.
双缝干涉：λ = ax/D，其中 a 为缝间距，x 为条纹宽度，D 为缝到屏幕的距离。该公式仅对小角度和相干光源有效。衍射光栅方程 d sinθ = nλ 用于更锐利、间距更宽的最大值。
Refractive index: n = c/v = sin i / sin r (Snell' es sinθ_c = 1/n. Total internal reflection occurs when the angle of incidence exceeds θ_c.
折射率：n = c/v = sin i / sin r（斯涅尔定律）。临界角 θ_c 满足 sinθ_c = 1/n。当入射角大于 θ_c 时发生全内反射。
5. Electricity and Magnetism | 电磁学
Current and charge: ΔQ = IΔt. Electric current is the rate of flow of charge. Kirchhoff's first law (junction rule) states sum of currents entering = sum leaving.
电流与电荷：ΔQ = IΔt。电流是电荷流动的速率。基尔霍夫第一定律（节点定律）指出，流入的电流总和等于流出的电流总和。
Ohm' nal area A, and resistivity ρ: R = ρL/A. The appendix lists ρ values for common materials.
欧姆定律：V = IR。电阻取决于长度 L、横截面积 A 和电阻率 ρ：R = ρL/A。附录列出了常见材料的电阻率值。
wer in circuits: P = IV = I²R = V²/R. Electromotive force (emf) ε = W/Q. Terminal pd V = ε – Ir, where r is internal resistance.
电路功率：P = IV = I²R = V²/R。电动势 ε = W/Q。路端电压 V = ε – Ir，其中 r 为内阻。
e on a moving charge: F = BQv sinθ. On a current-carrying conductor: F = BIL sinθ. Fleming's left-hand rule determines direction.
运动电荷所受磁力：F = BQv sinθ。通电导线所受磁力：F = BIL sinθ。左手定则确定方向。
Magnetic flux Φ = BA cosθ. Faraday's law: ε = –dΦ/dt (the magnitude is |dΦ/dt|). Lenz's law gives the direction of induced emf.
磁通量 Φ = BA cosθ。法拉第定律：ε = –dΦ/dt（大小为 |dΦ/dt|）。楞次定律决定感应电动势的方向。
6. Thermal Physics | 热物理
ip for thermal energy transfer Q = mcΔθ (specific heat capacity) and Q = mL (latent heat).
温标换算：T/K = θ/°C + 273.15。绝对零度为 0 K。附录包括热量传递的关系式 Q = mcΔθ（比热容）和 Q = mL（潜热）。
⁻¹ is the molar gas constant. Alternatively, pV = NkT, where N is the number of molecules.
理想气体方程：pV = nRT，其中 n 为物质的量，R = 8.31 J K⁻¹ mol⁻¹ 为摩尔气体常数。也可以写作 pV = NkT，其中 N 为分子数。
Kinetic theory: p = ⅓ρ⟨c²⟩, where ⟨c²⟩ is the mean square speed. Average translational kinetic energy of a molecule = ³⁄₂ kT.
气体动理论：p = ⅓ρ⟨c²⟩，其中 ⟨c²⟩ 为方均速率。分子的平均平动动能 = ³⁄₂ kT。
First law of thermodynamics: ΔU = Q + W (or ΔU = Q – W depending on sign convention—the CIE appendix consistently uses ΔU = Q + W with work done ON the system as positive).
热力学第一定律：ΔU = Q + W（或 ΔU = Q – W，取决于符号约定——CIE 附录统一使用 ΔU = Q + W，以对系统做功为正值）。
7. Nuclear and Particle Physics | 核与粒子物理
tive decay: Activity A = λN. Decay constant λ = ln2 / t₁/₂. Exponential decay law N = N₀ e–λt, A = A₀ e–λt. Half-life t₁/₂ is the time for half the nuclei to decay.
放射性衰变：活度 A = λN。衰变常数 λ = ln2 / t₁/₂。指数衰变律 N = N₀ e–λt，A = A₀ e–λt。半衰期 t₁/₂ 是半数原子核发生衰变所需的时间。
tion properties are described, with fundamental equations like α: ⁴₂He, β⁻: n → p + e⁻ + ν̄ (antineutrino), β⁺: p → n + e⁺ + ν.
质能等价：E = mc²。平均结合能 =（总结合能）/（质量数）。附录描述了 α、β、γ 辐射的特性，并给出基本方程，如 α：⁴₂He，β⁻：n → p + e⁻ + ν̄（反中微子），β⁺：p → n + e⁺ + ν。
Particle classification: hadrons, baryons, mesons, leptons. Conservation laws: charge, baryon number, lepton number, strangeness (in strong interactions). Quark compositions of protons (uud) and neutrons (udd) are listed.
粒子分类：强子、重子、介子、轻子。守恒定律：电荷数、重子数、轻子数、奇异数（在强相互作用中）。附录列出了质子（uud）和中子（udd）的夸克组成。
8. Capacitance and Electronics | 电容与电子学
capacitor, C = εA/d, where ε = εᵣε₀. Energy stored in a capacitor: W = ½QV = ½CV² = ½Q²/C.
电容定义：C = Q/V。平行板电容器的电容 C = εA/d，其中 ε = εᵣε₀。电容器储存的能量：W = ½QV = ½CV² = ½Q²/C。
Discharging a capacitor: Q = Q₀ e–t/RC, I = I₀ e–t/RC, V = V₀ e–t/RC. Time constant τ = RC. Half-life = RC ln2.
电容器放电：Q = Q₀ e–t/RC，I = I₀ e–t/RC，V = V₀ e–t/RC。时间常数 τ = RC。半衰期 = RC ln2。
Operational amplifiers: The appendix provides gain formulae for inverting (–Rf/Rᵢ) and non-inverting (1 + Rf/Rᵢ) configurations. Slew rate and CMRR are also defined.
运算放大器：附录提供了反相（–Rf/Rᵢ）和同相（1 + Rf/Rᵢ）组态的增益公式。还定义了转换速率和共模抑制比（CMRR）。
9. Gravitational and Electric Fields | 引力与电场
ional field strength: g = F/m. For a point mass, g = GM/r². Gravitational potential: φ_g = –GM/r. Work done in moving a mass m in a gravitational field is mΔφ_g.
引力场强度：g = F/m。对于点质量，g = GM/r²。引力势：φ_g = –GM/r。在引力场中移动质量 m 所做的功为 mΔφ_g。
= V/d. Electric potential: Vₑ = Q/(4πε₀r). Force on a charge in an electric field: F = QE.
电场强度：E = F/Q。对于点电荷，E = Q/(4πε₀r²)。平行板间的匀强电场：E = V/d。电势：Vₑ = Q/(4πε₀r)。电荷在电场中所受的力：F = QE。
Similarities between gravitational and electric fields: both follow inverse-square laws, both have potentials that are inversely proportional to distance, and both obey superposition principles.
引力场和电场的相似之处：两者都遵循平方反比律，势能都与距离成反比，且都遵循叠加原理。
10. Quantum and Photoelectric Effect | 量子与光电效应
Photon energy: E = hf. Einstein's photoelectric equation: hf = ϕ + KE_max, where ϕ on and KE_max is the maximum kinetic energy of emitted electrons. The stopping potential Vs is related by KE_max = eV_s.
光子能量：E = hf。爱因斯坦光电方程：hf = ϕ + KE_max，其中 ϕ 为逸出功，KE_max 为出射电子的最大动能。遏止电势 Vs 满足 KE_max = eV_s。
ential difference V gains kinetic energy eV = ½mv², enabling estimation of its wavelength.
德布罗意波长：λ = h/p = h/(mv)。这体现了波粒二象性。电子经电势差 V 加速后获得动能 eV = ½mv²，由此可估算其波长。
Energy levels in atoms: ΔE = E₂ – E₁ = hf. The appendix may include spectral series and the hydrogen energy level formula En = –13.6 eV / n².
原子能级：ΔE = E₂ – E₁ = hf。附录可能包含光谱线系以及氢原子能级公式 En = –13.6 eV / n²。
11. Mathematics for Physics | 物理数学
. Trigonometry ratios sinθ = opposite/hypotenuse, cosθ = adjacent/hypotenuse, tanθ = opposite/adjacent. Sine rule and cosine rule are also given.
附录提供了物理中会用到的数学关系式：圆面积 = πr²，球表面积 = 4πr²，球体积 = ⁴⁄₃πr³。三角函数比值 sinθ = 对边/斜边，cosθ = 邻边/斜边，tanθ = 对边/邻边。另外还给出正弦定理和余弦定理。
Small-angle approximations: for θ in radians (or very small), sinθ ≈ θ, cosθ ≈ 1 – θ²/2, tanθ ≈ θ. These are used in pendulum motion and single-slit diffraction.
小角度近似：当 θ 以弧度为单位（或非常小）时，sinθ ≈ θ，cosθ ≈ 1 – θ²/2，tanθ ≈ θ。这些近似用于单摆运动和单缝衍射。
ful when linearising data for graphical analysis, such as in radioactive decay or capacitor discharge.
对数关系：若 y = kxⁿ，则 log y = log k + n log x。这在将数据线性化以用于图像分析时非常有用，例如放射性衰变或电容器放电。
r (cross) product definitions are given, useful in work (F·s) and magnetic force (qv × B).
矢量：分解为分量，通过平行四边形法或分量法进行加法运算。标量积（点积）和矢量积（叉积）的定义在附录中给出，常用于功（F·s）和磁力（qv × B）。
12. Key Relationships Summary | 关系式总结
nθ factor when field and direction are not perpendicular. Similarly, E = ½QV, ½CV², and ½Q²/C all represent stored energy in a capacitor and are algebraically equivalent.
附录的结构让相互关联的物理量集中出现，帮助你发现规律。例如 F = BIL 和 F = BQv 在磁场与方向不垂直时都包含 sinθ 因子。同样，E = ½QV、½CV² 和 ½Q²/C 都表示电容器储存的能量，在代数上等价。
ance, g = GM/r² gives units of N/kg, which is equivalent to m s⁻², confirming its nature as acceleration.
务必核对附录中给出的每个物理量的单位。如果你推导出的表达式单位不匹配，说明存在错误。例如，g = GM/r² 的单位是 N/kg，等同于 m s⁻²，证实了它的加速度本质。
and then λ = h/mv. Practise such multi-step applications until they become second nature.
许多关系式可以联合使用。粒子被电势 V 加速后获得的动能为 KE = eV = ½mv²，由此可求出 v 再代入 λ = h/mv。此类多步骤应用要反复练习，直到游刃有余。
Finally, remember the appendix is a tool, not a substitute for understanding. The exam tests your ability to select and manipulate the right equations under time pressure. Regular, active recall of these formulae in problem-solving is the surest path to success.
最后，记住附录只是一种工具，不能替代理解。考试考查的是你在时间压力下正确选择和灵活运用公式的能力。在解题过程中定期主动回想这些公式，是通往成功最可靠的途径。
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