📚 Year 13 WJEC Science: Quick Revision Handbook of Formulas and Theorems | Year 13 WJEC 科学：公式定理速查手册
This article provides a concise and exam-focused revision resource for Year 13 WJEC Science students, drawing together the most essential formulas, theorems and equations from physics, chemistry and biology. Each entry is presented as a bilingual English–Chinese pair, allowing you to reinforce understanding while practising scientific terminology in both languages. Use this handbook to check key relationships, confirm units and apply principles across all three disciplines during your revision sessions.
本文为 Year 13 WJEC 科学考生提供一本紧扣考点的双语速查手册，汇集了物理、化学和生物中最核心的公式、定理与方程式。每个条目均以中英文对照的形式呈现，帮助你在巩固知识的同时熟悉双语科学术语。复习期间，你可以利用本手册快速核对关键关系、确认单位并在三门学科中灵活应用原理。
1. Mechanics and Motion | 力学与运动
For uniformly accelerated motion along a straight line, the four SUVAT equations relate initial velocity u, final velocity v, acceleration a, displacement s and time t. v = u + at gives the final velocity when acceleration is constant. s = ut + ½ at² calculates displacement when initial velocity and time are known. v² = u² + 2as connects velocity and displacement without time. The average velocity form s = ½(u + v)t is useful when acceleration is uniform.
对于匀加速直线运动，四个 SUVAT 方程将初速度 u、末速度 v、加速度 a、位移 s 和时间 t 联系起来。v = u + at 给出恒定加速度下的末速度。s = ut + ½ at² 在已知初速度和时间时计算位移。v² = u² + 2as 不用时间直接关联速度和位移。平均速度形式 s = ½(u + v)t 在加速度均匀时十分有用。
Newton's second law states that the resultant force F acting on an object equals the rate of change of its momentum: F = ma for constant mass m. Momentum p is defined as p = mv. The impulse-momentum theorem links impulse FΔt to the change in momentum: FΔt = Δp. In collisions, the principle of conservation of momentum states that the total momentum of an isolated system remains constant, provided no external resultant force acts.
牛顿第二定律指出，作用在物体上的合力 F 等于其动量变化率：当质量 m 不变时，F = ma。动量 p 定义为 p = mv。冲量-动量定理将冲量 FΔt 与动量变化相联系：FΔt = Δp。碰撞过程中，动量守恒定律表明，只要没有外合力作用，孤立系统的总动量保持不变。
Work done W by a constant force is W = Fs cos θ, where θ is the angle between force and displacement. Kinetic energy Eₖ = ½ m v² and gravitational potential energy Eₚ = mgΔh. The principle of conservation of energy states that in a closed system, total energy is constant, although it may be transferred between stores. Power P is the rate of doing work, P = W/t, or for motion at constant velocity v, P = Fv.
恒力做功 W 由 W = Fs cos θ 给出，θ 是力与位移的夹角。动能 Eₖ = ½ m v²，重力势能 Eₚ = mgΔh。能量守恒定律指出，在一个封闭系统中，总能量保持不变，尽管能量可以在不同形式间转移。功率 P 是做功的速率，P = W/t，或对于以恒定速度 v 运动的情况，P = Fv。
2. Materials and Stress | 材料与应力
For a material under load, stress σ is defined as the force per unit cross-sectional area: σ = F/A. Strain ε is the extension per unit original length: ε = ΔL/L₀. The Young modulus E is the ratio of tensile stress to tensile strain within the linear elastic region: E = σ/ε. Hooke's law for a spring states F = kΔL, where k is the spring constant. The energy stored in a spring obeying Hooke's law is Eₑₗ = ½ k (ΔL)² or equivalently Eₑₗ = ½ FΔL.
材料受力时，应力 σ 定义为单位截面积上的力：σ = F/A。应变 ε 是单位原长的伸长量：ε = ΔL/L₀。杨氏模量 E 是线弹性区域内拉伸应力与拉伸应变之比：E = σ/ε。弹簧的胡克定律表述为 F = kΔL，k 是劲度系数。服从胡克定律的弹簧中储存的能量为 Eₑₗ = ½ k (ΔL)² 或等效为 Eₑₗ = ½ FΔL。
3. Waves and Optics | 波与光学
The speed v of a wave is related to its frequency f and wavelength λ by v = f λ. For a transverse wave on a string, the speed is also given by v = √T/μ, where T is the tension and μ is the mass per unit length. The refractive index n of a medium is n = c/v, with c being the speed of light in a vacuum. Snell's law describes refraction: n₁ sin θ₁ = n₂ sin θ₂, where θ₁ and θ₂ are the angles of incidence and refraction measured from the normal.
波速 v 与频率 f 和波长 λ 的关系为 v = f λ。对于弦上的横波，波速也可以用 v = √T/μ 表示，T 是张力，μ 是单位长度的质量。介质的折射率 n 为 n = c/v，c 是真空中的光速。斯涅耳定律描述折射：n₁ sin θ₁ = n₂ sin θ₂，其中 θ₁ 和 θ₂ 分别是入射角和折射角，均从法线量起。
In Young's double-slit experiment, the fringe spacing Δy on a screen at distance D from the slits with separation d is given by Δy = λD/d for small angles. For a diffraction grating with line spacing d, maxima occur when d sin θ = nλ, where n is an integer. The condition for a single slit to produce a minimum is b sin θ = mλ, with m = 1, 2, 3....
在杨氏双缝实验中，屏与缝距 D、缝间距 d 时，条纹间距 Δy 在小角度下为 Δy = λD/d。对于线间距为 d 的衍射光栅，极大值条件为 d sin θ = nλ，n 为整数。单缝产生暗纹的条件是 b sin θ = mλ，m = 1, 2, 3……
The wavelength of a photon is related to its momentum p by the de Broglie relation λ = h/p, where h is Planck's constant. Photon energy E is given by E = hf = hc/λ. The photoelectric effect is described by Eₖₘₐₓ = hf - Φ, where Φ is the work function of the metal.
光子的波长与其动量 p 的关系由德布罗意关系式 λ = h/p 给出，h 是普朗克常数。光子能量 E 由 E = hf = hc/λ 表示。光电效应方程表述为 Eₖₘₐₓ = hf - Φ，Φ 是金属的逸出功。
4. Electricity and Circuits | 电学与电路
Current I is the rate of flow of charge: I = ΔQ/Δt. Ohm's law for an ohmic conductor at constant temperature states V = IR, where V is potential difference and R is resistance. Resistance depends on the material's resistivity ρ, length L and cross-sectional area A: R = ρL/A. The power dissipated in a resistor can be written as P = IV = I²R = V²/R.
电流 I 是电荷流动的速率：I = ΔQ/Δt。欧姆定律对于恒温下的欧姆导体表述为 V = IR，V 是电势差，R 是电阻。电阻取决于材料的电阻率 ρ、长度 L 和截面积 A：R = ρL/A。电阻器上耗散的功率可写作 P = IV = I²R = V²/R。
In a series circuit the total resistance is Rₜₒₜ = R₁ + R₂ + …, while for resistors in parallel the combined resistance follows 1/Rₜₒₜ = 1/R₁ + 1/R₂ + …. The EMF ε of a source is the energy supplied per unit charge: ε = E/Q. The terminal potential difference V is related to EMF and internal resistance r by V = ε - Ir.
串联电路的总电阻为 Rₜₒₜ = R₁ + R₂ + …，并联电阻的组合满足 1/Rₜₒₜ = 1/R₁ + 1/R₂ + …。电源的电动势 ε 是每单位电荷提供的能量：ε = E/Q。路端电压 V 与电动势和内阻 r 的关系为 V = ε - Ir。
For a capacitor of capacitance C, the charge stored is Q = CV. The energy stored in a charged capacitor is E = ½ CV² = ½ QV = ½ Q²/C constant for an RC circuit is τ = RC; during discharge, the voltage decays as V = V₀ e⁻ᵗ/ᴿᶜ and the current as I = I₀ e⁻ᵗ/ᴿᶜ.
电容量为 C 的电容器，储存的电荷为 Q = CV。已充电电容器中储存的能量为 E = ½ CV² = ½ QV = ½ Q²/C。RC 电路的时间常数 τ = RC；放电时，电压按 V = V₀ e⁻ᵗ/ᴿᶜ 衰减，电流按 I = I₀ e⁻ᵗ/ᴿᶜ 衰减。
5. Fields and Modern Physics | 场与现代物理
Newton's law of gravitation gives the force between two point masses m₁ and m₂ separated by distance r: F = G m₁m₂/r², where G is the gravitational constant. The gravitational field strength g at a distance r from a mass M is g = GM/r². In a uniform electric field, the force on a charge q is F = qE and the field strength between parallel plates is E = V/d.
牛顿万有引力定律给出两个相距 r 的质点 m₁ 和 m₂ 之间的力：F = G m₁m₂/r²，G 为万有引力常数。距离质量 M 球心 r 处的重力场强度 g 为 g = GM/r²。在匀强电场中，电荷 q 所受的力为 F = qE，平行板间的场强为 E = V/d。
Coulomb's law for the force between two point charges is F = kQ₁Q₂/r², where k = 1/(4πε₀) in a vacuum. The electric potential V near a point charge Q is V = kQ/r. The force on a charge q moving with velocity v in a magnetic field B is given by the Lorentz force: F = qvB sin θ, where θ is the angle between v and B.
库仑定律描述两点电荷间的力：F = kQ₁Q₂/r²，真空中 k = 1/(4πε₀)。点电荷 Q 附近的电势 V 为 V = kQ/r。电荷 q 以速度 v 在磁场 B 中运动时所受的力由洛伦兹力给出：F = qvB sin θ，θ 是 v 与 B 的夹角。
In nuclear physics, the radius of a nucleus is given approximately by R = R₀ A¹/³ ere A is the nucleon number and R₀ ≈ 1.2 fm. Radioactive decay follows the exponential law N = N₀ e⁻λᵗ, where λ is the decay constant. The activity A is A = λN. The half-life t½ is related to λ by t½ = ln 2 / λ. Einstein's mass-energy relation is E = mc².
在核物理中，原子核半径近似为 R = R₀ A¹/³，A 为核子数，R₀ ≈ 1.2 fm。放射性衰变遵循指数规律 N = N₀ e⁻λᵗ，λ 为衰变常数。活度 A 为 A = λN。半衰期 t½ 与 λ 的关系为 t½ = ln 2 / λ。爱因斯坦的质能关系式为 E = mc²。
6. Amount of Substance and Stoichiometry | 物质的量与化学计量
f particles N = n Nₐ, where Nₐ is the Avogadro constant. For gases, the ideal gas equation pV = nRT 8.31 J mol⁻¹ K⁻¹. At room temperature and pressure (RTP), the molar volume of an ideal gas is approximately 24.0 dm³ mol⁻¹.
摩尔将粒子数与质量联系起来：物质的量 n = 质量 m / 摩尔质量 M。粒子数 N = n Nₐ，Nₐ 为阿伏伽德罗常数。对于气体，理想气体状态方程 pV = nRT 将压强 p、体积 V、物质的量 n 和热力学温度 T 联系起来，R = 8.31 J mol⁻¹ K⁻¹。在室温常压下，理想气体的摩尔体积约为 24.0 dm³ mol⁻¹。
Concentration c of a solution is c = n / V, usually expressed in mol dm⁻³. In a titration, the amount of solute in one solution is determined using nₐ / n₆ = νₐ / ν₆ tom economy = (molar mass of desired product / sum of molar masses of all products) × 100.
溶液的浓度 c 为 c = n / V，通常以 mol dm⁻³ 表示。在滴定中，一种溶液中溶质的物质的量通过 nₐ / n₆ = νₐ / ν₆ 确定，其中 ν 为化学计量系数。产率百分数 = (实际产量 / 理论产量) × 100。原子利用率 = (目标产物的摩尔质量 / 所有产物摩尔质量之和) × 100。
7. Thermodynamics and Energetics | 热力学与能量学
The enthalpy change ΔH for a reaction at constant pressure is the heat transferred. Using calorimetry, q = mcΔT, where m is mass, c specific heat capacity and ΔT temperature change. Hess's law allows enthalpy changes to be combined: ΔHₚₐₜₕ₁ = ΔHₚₐₜₕ₂ for a cycle. Standard enthalpy of formation ΔH⦵ₓ and combustion ΔH⦵ₓ are key data. Bond enthalpy calculations use ΔH ≈ Σ(bond energies broken) - Σ(bond energies made).
在恒压条件下，反应的焓变 ΔH 等于传递的热量。使用量热法时，q = mcΔT，m 为质量，c 为比热容，ΔT 为温度变化。盖斯定律允许组合焓变：对于一个循环，ΔHₚₐₜₕ₁ = ΔHₚₐₜₕ₂。标准生成焓 ΔH⦵ₓ 和标准燃烧焓 ΔH⦵ₓ 是关键数据。键焓计算利用 ΔH ≈ Σ(断裂键能) - Σ(形成键能)。
The Gibbs free energy change determines reaction feasibility: ΔG = ΔH - TΔS, where ΔS is entropy change. A reaction is feasible when ΔG < 0. The relation ΔG = -RT ln K links equilibrium constant K to free energy, allowing the calculation of equilibrium position from thermodynamic data.
吉布斯自由能变决定反应的可行性：ΔG = ΔH - TΔS，ΔS 为熵变。当 ΔG < 0 时反应可行。关系式 ΔG = -RT ln K 将平衡常数 K 与自由能联系起来，从而可由热力学数据计算平衡位置。
8. Kinetics and Equilibrium | 动力学与平衡
The rate of a reaction is often given by the rate equation: rate = k[A]ᵐ[B]ⁿ, where m and n are orders with respect to reactants A and B. The overall order is m + n. The Arrhenius equation relates rate constant k to temperature T and activation energy Eₐ: ln k = ln A - Eₐ/(RT) or in exponential form k = A e⁻ᴱᵃ/ᴿᵀ, where A is the pre-exponential factor.
反应速率常由速率方程给出：rate = k[A]ᵐ[B]ⁿ，m 和 n 分别为对反应物 A 和 B 的级数，总反应级数为 m + n。阿伦尼乌斯方程将速率常数 k 与温度 T 和活化能 Eₐ 关联：ln k = ln A - Eₐ/(RT)，指数形式为 k = A e⁻ᴱᵃ/ᴿᵀ，A 为指前因子。
For a reversible reaction aA + bB ⇌ cC + dD at equilibrium, the equilibrium constant Kc (in terms of concentration) is Kc = ([C]ᶜ[D]ᵈ) / ([A]ᵃ[B]ᵇ) The ion product of water Kₕ = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴ mol² dm⁻⁶ at 298 K. pH is defined as pH = -log₁₀[H⁺]; for strong acids, [H⁺] ≈ [acid].
对于可逆反应 aA + bB ⇌ cC + dD 在平衡时，浓度平衡常数 Kc 为 Kc = ([C]ᶜ[D]ᵈ) / ([A]ᵃ[B]ᵇ)。对于气体，Kp 使用分压。水的离子积 Kₕ = [H⁺][OH⁻] =
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