📚 Year 13 Edexcel Science: Formula & Theorem Quick Reference Handbook | 爱德思13年级科学：公式定理速查手册
This revision handbook compiles essential formulas, laws, and constants across Edexcel Year 13 Physics, Chemistry and Biology. Use it as a rapid reference to reinforce key principles before your examinations.
本复习手册汇集了爱德思 Year 13 物理、化学和生物的核心公式、定律和常数，帮助您在考前快速巩固关键原理。
1. Mechanics and Materials | 力学与材料
SUVAT equations for constant linear acceleration: v = u + at, s = ut + ½at², v² = u² + 2as, s = ½(u + v)t.
匀变速直线运动的运动学方程组：v = u + at, s = ut + ½at², v² = u² + 2as, s = ½(u + v)t.
Newton’s second law: F = ma; weight W = mg.
牛顿第二定律：F = ma；重力 W = mg.
Centripetal force: F = mv²/r = mrω²; angular speed ω = 2πf = v/r.
向心力：F = mv²/r = mrω²；角速度 ω = 2πf = v/r.
Simple harmonic motion: restoring force F = -kx, acceleration a = -ω²x; period of a pendulum T = 2π√(l/g).
简谐运动：回复力 F = -kx，加速度 a = -ω²x；单摆周期 T = 2π√(l/g).
Hooke’s law: F = kx; Young modulus E = σ/ε = (F/A) / (ΔL/L₀).
胡克定律：F = kx；杨氏模量 E = σ/ε = (F/A) / (ΔL/L₀).
2. Fields (Gravitational, Electric, Magnetic) | 场（引力、电场、磁场）
Newton’s law of gravitation: F = Gm₁m₂ / r²; gravitational field strength g = F/m = GM / r².
万有引力定律：F = Gm₁m₂ / r²；引力场强 g = F/m = GM / r².
Coulomb’s law for point charges: F = kQ₁Q₂ / r², where k = 1/(4πε₀).
点电荷库仑定律：F = kQ₁Q₂ / r²，其中 k = 1/(4πε₀).
Electric field strength: E = F/q = kQ / r²; uniform electric field E = V/d.
电场强度：E = F/q = kQ / r²；匀强电场 E = V/d.
Capacitance: C = Q/V; stored energy W = ½QV = ½CV².
电容：C = Q/V；储存的能量 W = ½QV = ½CV².
Force on a moving charge in a magnetic field: F = BQv sinθ; force on a current-carrying wire: F = BIL sinθ.
运动电荷在磁场中的受力：F = BQv sinθ；通电导线受力：F = BIL sinθ.
3. Electromagnetic Induction | 电磁感应
Magnetic flux: Φ = BA cosθ.
磁通量：Φ = BA cosθ.
Faraday’s law: induced emf ε = -N ΔΦ/Δt; Lenz’s law gives the negative sign.
法拉第定律：感应电动势 ε = -N ΔΦ/Δt；负号体现了楞次定律.
Ideal transformer equation: Nₛ/Nₚ = Vₛ/Vₚ = Iₚ/Iₛ.
理想变压器方程：Nₛ/Nₚ = Vₛ/Vₚ = Iₚ/Iₛ.
RMS values for sinusoidal AC: Vᵣₘₛ = V₀/√2, Iᵣₘₛ = I₀/√2.
正弦交流电的有效值：Vᵣₘₛ = V₀/√2, Iᵣₘₛ = I₀/√2.
4. Nuclear and Particle Physics | 核与粒子物理
Exponential decay law: N = N₀ e⁻ˡᵗ, where λ is the decay constant; half‑life T½ = ln 2 / λ.
指数衰变定律：N = N₀ e⁻ˡᵗ，λ 为衰变常量；半衰期 T½ = ln 2 / λ.
Mass–energy equivalence: ΔE = Δm c²; binding energy is the energy released when nucleons bind.
质能方程：ΔE = Δm c²；结合能是核子结合时释放的能量.
Activity A = λN; units: becquerel (Bq).
活度 A = λN；单位：贝可勒尔 (Bq).
5. Thermodynamics and Ideal Gases | 热力学与理想气体
Ideal gas equation: pV = nRT, where R = 8.31 J mol⁻¹ K⁻¹.
理想气体状态方程：pV = nRT，其中 R = 8.31 J mol⁻¹ K⁻¹.
Mean kinetic energy of a gas molecule: Ek = ³⁄₂ kT, where k = 1.38 × 10⁻²³ J K⁻¹.
气体分子的平均动能：Ek = ³⁄₂ kT，波尔兹曼常量 k = 1.38 × 10⁻²³ J K⁻¹.
First law of thermodynamics: ΔU = Q + W (work done on the system is positive).
热力学第一定律：ΔU = Q + W（外界对系统做功W取正）.
Specific heat capacity: Q = mcΔθ; specific latent heat: Q = mL.
比热容：Q = mcΔθ；比潜热：Q = mL.
6. Organic Chemistry: Key Reaction Mechanisms | 有机化学：关键反应机理
Electrophilic addition of HBr to alkenes: proceeds via a carbocation intermediate; major product follows Markovnikov’s rule.
烯烃与HBr的亲电加成：经由碳正离子中间体；主产物遵循马氏规则.
Nucleophilic substitution (SN2) of primary haloalkanes with aqueous NaOH: RCH₂Br + OH⁻ → RCH₂OH + Br⁻.
伯卤代烷与NaOH水溶液的亲核取代(SN2)：RCH₂Br + OH⁻ → RCH₂OH + Br⁻.
Elimination (E2) of haloalkanes with ethanolic KOH: forms alkenes, e.g. C₂H₅Br + KOH → C₂H₄ + KBr + H₂O.
卤代烷与KOH乙醇溶液的消除(E2)：生成烯烃，如 C₂H₅Br + KOH → C₂H₄ + KBr + H₂O.
Oxidation of alcohols: primary alcohol → aldehyde → carboxylic acid; secondary alcohol → ketone.
醇的氧化：伯醇 → 醛 → 羧酸；仲醇 → 酮.
Polymerisation: addition polymers (e.g. polyethene) and condensation polymers (e.g. polyester, polyamide) form with repeating units.
聚合反应：加聚反应（如聚乙烯）和缩聚反应（如聚酯、聚酰胺）生成重复单元.
7. Physical Chemistry Equations | 物理化学方程式
Rate equation: rate = k [A]ᵐ [B]ⁿ, determined only by experiment.
速率方程：rate = k [A]ᵐ [B]ⁿ，只能由实验确定.
Arrhenius equation: k = A e⁻ᴱᵃ/ᴿᵀ or in linear form ln k = -Ea/RT + ln A.
阿伦尼乌斯方程：k = A e⁻ᴱᵃ/ᴿᵀ 或线性式 ln k = -Ea/RT + ln A.
Equilibrium constant (homogeneous): Kc = [products]/[reactants]; Kp = p(products)/p(reactants).
平衡常数（均相）：Kc = [产物]/[反应物]；Kp = p(产物)/p(反应物).
pH definition: pH = –log[H⁺]; ionic product of water Kw = [H⁺][OH⁻] = 1.0×10⁻¹⁴ at 298 K.
pH定义：pH = –log[H⁺]；水的离子积 Kw = [H⁺][OH⁻] = 1.0×10⁻¹⁴ (298 K).
Gibbs free energy: ΔG = ΔH – TΔS; related to cell potential by ΔG = –nFE.
吉布斯自由能：ΔG = ΔH – TΔS；与电池电动势的关系 ΔG = –nFE.
Nernst equation (simplified for 298 K): E = E° – (0.0592/n) log Q.
能斯特方程 (298 K简化)：E = E° – (0.0592/n) log Q.
8. Inorganic Chemistry & Periodicity | 无机化学与周期性
Born–Haber cycle energy balance: ΔHf = ΔHₐₜ + IE + EA + LE (atomisation, ionisation, electron affinity, lattice energy).
波恩–哈伯循环能量平衡：ΔHf = ΔHₐₜ + IE + EA + LE（原子化焓、电离能、电子亲和能、晶格能）.
Lattice energy is directly proportional to the product of ionic charges and inversely proportional to ionic radius: LE ∝ (Q⁺Q⁻) / (r⁺ + r⁻).
晶格能与离子电荷乘积成正比，与离子半径之和成反比：LE ∝ (Q⁺Q⁻) / (r⁺ + r⁻).
Transition metal complexes: co‑ordination number and ligand exchange affect colour and geometry.
过渡金属配合物：配位数和配体交换影响颜色和空间构型.
Manganate(VII) titration: MnO₄⁻ + 5Fe²⁺ + 8H⁺ → Mn²⁺ + 5Fe³⁺ + 4H₂O; 1:5 mole ratio.
高锰酸钾滴定：MnO₄⁻ + 5Fe²⁺ + 8H⁺ → Mn²⁺ + 5Fe³⁺ + 4H₂O；物质的量之比1:5.
9. Analytical Techniques | 分析技术
Infrared spectroscopy: wavenumber ν̃ = 1/λ; characteristic absorption bands identify functional groups (O–H ~3200–3600 cm⁻¹, C=O ~1700 cm⁻¹).
红外光谱：波数 ν̃ = 1/λ；特征吸收峰识别官能团（O–H ~3200–3600 cm⁻¹，C=O ~1700 cm⁻¹）.
Mass spectrometry: molecular ion peak gives Mᣵ; fragmentation pattern helps determine structure.
质谱：分子离子峰给出 Mᣵ；碎片峰帮助推断结构.
1H NMR: chemical shift δ (ppm); integration trace gives proton ratios; splitting follows the n+1 rule.
核磁共振氢谱：化学位移 δ (ppm)；积分曲线给出氢原子数比；裂分遵循 n+1 规则.
Chromatography: retention factor Rf = distance moved by spot / distance moved by solvent.
色谱：比移值 Rf = 溶质移动距离 / 溶剂前沿移动距离.
10. Genetics and Evolution | 遗传与进化
Hardy–Weinberg principle: p + q = 1 and p² + 2pq + q² = 1, where p and q are allele frequencies.
哈代–温伯格平衡：p + q = 1 且 p² + 2pq + q² = 1，p、q为等位基因频率.
Chi‑squared test for genetics: χ² = Σ (O – E)² / E; compare to critical value at degrees of freedom n – 1.
遗传学卡方检验：χ² = Σ (O – E)² / E；与自由度为 n−1 的临界值比较.
Monohybrid cross phenotypic ratio for heterozygous parents: 3 : 1; dihybrid (independent assortment): 9 : 3 : 3 : 1.
杂合亲本单基因杂交表型比：3 : 1；双基因独立分配表型比：9 : 3 : 3 : 1.
Natural selection: allele frequencies change when phenotypes confer differential reproductive success.
自然选择：当表型带来不同繁殖成功率时，等位基因频率发生改变.
11. Statistical Tests and Formulas in Biology | 生物统计检验与公式
Mean (x̄) and standard deviation (s) for a sample: s = √[Σ(x – x̄)² / (n – 1)].
样本均值 (x̄) 和标准差 (s)：s = √[Σ(x – x̄)² / (n – 1)].
Standard error of the mean: SE = s / √n.
均值标准误差：SE = s / √n.
Student’s t‑test (unpaired, equal variance assumed): t = (x̄₁ – x̄₂) / √(s₁²/n₁ + s₂²/n₂).
学生 t 检验（非配对，假设方差相等）：t = (x̄₁ – x̄₂) / √(s₁²/n₁ + s₂²/n₂).
Simpson’s index of diversity: D = 1 – Σ (n/N)², where n is the number of individuals of one species and N is total individuals.
辛普森多样性指数：D = 1 – Σ (n/N)²，n 为某物种个体数，N 为总个体数.
Lincoln index (mark–release–recapture): N = (M × C) / R, where M = number initially marked, C = total caught in second sample, R = number of marked recaptures.
林肯指数（标记重捕法）：N = (M × C) / R，M 为初标数量，C 为第二次捕获总数，R 为重捕标记数.
12. Core Constants and Unit Conversions | 核心常数与单位换算
Avogadro constant NA = 6.02 × 10²³ mol⁻¹; molar gas constant R = 8.31 J mol⁻¹ K⁻¹.
阿伏伽德罗常数
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