Year 13 SQA Science: Formula & Theorem Quick-Reference Handbook | Year 13 SQA 科学：公式定理速查手册

📚 Year 13 SQA Science: Formula & Theorem Quick-Reference Handbook | Year 13 SQA 科学：公式定理速查手册

This quick-reference handbook collects the most frequently needed formulae and key theorems across Physics, Chemistry and Biology for Year 13 SQA Science. Each entry is presented with a brief explanation in English immediately followed by its Chinese equivalent, helping you to locate, recall and apply the correct relationship in exam conditions.

本速查手册汇集了 Year 13 SQA 科学课程中物理、化学和生物最常用的公式与核心定理。每个条目均先给出英文简要说明并紧接中文配对解释，方便你在考试中快速定位、回忆并正确运用相应的关系式。

1. Mechanics and Motion | 力学与运动

Newton’s second law states that the net force acting on an object equals the product of its mass and acceleration: F = ma. This vector equation is the foundation of linear dynamics.

牛顿第二定律指出，物体所受合力等于其质量与加速度的乘积：F = ma。这一矢量方程是线性动力学的基础。

F = ma

The equations of motion for constant acceleration in a straight line are: v = u + at, s = ut + ½at², v² = u² + 2as, where u is initial velocity, v final velocity, a acceleration, t time and s displacement.

匀加速直线运动的运动学方程为：v = u + at、s = ut + ½at²、v² = u² + 2as，其中 u 为初速度，v 为末速度，a 为加速度，t 为时间，s 为位移。

v = u + at   s = ut + ½at²   v² = u² + 2as

Momentum p is defined as mass × velocity: p = mv. In an isolated system, total momentum is conserved during collisions and explosions.

动量 p 定义为质量与速度的乘积：p = mv。在孤立系统中，碰撞和爆炸前后总动量守恒。

p = mv

Kinetic energy Eₖ and work done W are scalar quantities: Eₖ = ½mv², W = Fd cos θ, where θ is the angle between force and displacement. The work–energy theorem links work done to the change in kinetic energy.

动能 Eₖ 和做功 W 是标量：Eₖ = ½mv²，W = Fd cos θ，其中 θ 为力与位移的夹角。功能定理将外力做功与动能变化联系起来。

Eₖ = ½mv²   W = Fd cos θ

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2. Electricity and Circuits | 电学与电路

Ohm’s law relates voltage V, current I and resistance R: V = IR. For components that obey Ohm’s law, resistance is constant at constant temperature.

欧姆定律给出电压 V、电流 I 和电阻 R 的关系：V = IR。对于满足欧姆定律的元件，在恒温下电阻为常数。

V = IR

Electrical power P can be calculated using P = IV = I²R = V²/R. These expressions help determine energy transformation in resistive loads.

电功率 P 可通过 P = IV = I²R = V²/R 计算，用于确定电阻性负载中的能量转换速率。

P = IV = I²R = V²/R

Resistance of a uniform conductor is given by R = ρL/A, where ρ is resistivity, L is length and A is cross-sectional area. Resistors in series add directly, while for parallel resistors the reciprocal sum is used: 1/Rₜ = 1/R₁ + 1/R₂ + …

均匀导体的电阻由 R = ρL/A 给出，ρ 为电阻率，L 为长度，A 为截面积。串联电阻直接相加，并联电阻则采用倒数求和：1/Rₜ = 1/R₁ + 1/R₂ + …

R = ρL/A   1/Rₜ = 1/R₁ + 1/R₂

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3. Thermal Physics | 热物理

The heat energy required to change an object’s temperature is Q = mcΔθ, where m is mass, c is specific heat capacity and Δθ is the temperature change (in K or °C).

改变物体温度所需热量为 Q = mcΔθ，m 为质量，c 为比热容，Δθ 为温度变化（开尔文或摄氏度）。

Q = mcΔθ

For an ideal gas, the equation of state is pV = nRT, where p is pressure, V is volume, n is amount of substance, R is the molar gas constant and T is thermodynamic temperature.

理想气体状态方程为 pV = nRT，p 为压强，V 为体积，n 为物质的量，R 为摩尔气体常数，T 为热力学温度。

pV = nRT

The average translational kinetic energy of a gas molecule is directly proportional to the absolute temperature: Eₖ,avg = (3/2)kT, where k is the Boltzmann constant. This links microscopic motion to macroscopic temperature.

气体分子的平均平动动能与绝对温度成正比：Eₖ,avg = (3/2)kT，k 为玻尔兹曼常数，将微观运动与宏观温度联系起来。

Eₖ,avg = (3/2)kT

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4. Waves and Optics | 波与光学

The wave equation relates speed v, frequency f and wavelength λ: v = fλ. It applies to all travelling waves, including sound and electromagnetic radiation.

波动方程关联波速 v、频率 f 与波长 λ：v = fλ，适用于所有行波，包括声波与电磁辐射。

v = fλ

Snell’s law governs refraction at a boundary: n₁ sin θ₁ = n₂ sin θ₂, where n is the refractive index and θ is the angle to the normal. Total internal reflection occurs when the angle of incidence exceeds the critical angle.

斯涅尔定律描述界面折射：n₁ sin θ₁ = n₂ sin θ₂，n 为折射率，θ 为与法线的夹角。当入射角大于临界角时发生全内反射。

n₁ sin θ₁ = n₂ sin θ₂

The lens formula is 1/f = 1/u + 1/v, with sign conventions. Magnification m is v/u (image height/object height). For a double-slit, constructive interference satisfies d sin θ = nλ.

透镜公式为 1/f = 1/u + 1/v（需遵守符号规则）。放大率 m = v/u（像高/物高）。双缝干涉的加强条件为 d sin θ = nλ。

1/f = 1/u + 1/v   d sin θ = nλ

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5. Quantum and Nuclear Physics | 量子与核物理

The energy of a photon is E = hf = hc/λ, where h is Planck’s constant. This quantisation explains the photoelectric effect, where the maximum kinetic energy of emitted electrons is Eₖ = hf – ϕ, with work function ϕ.

光子的能量为 E = hf = hc/λ，h 为普朗克常数。这种量子化解释了光电效应：逸出电子的最大动能 Eₖ = hf – ϕ，ϕ 为逸出功。

E = hf   Eₖ = hf – ϕ

The de Broglie wavelength of a particle with momentum p is λ = h/p, demonstrating wave–particle duality. It applies to electrons and other massive particles.

动量为 p 的粒子的德布罗意波长为 λ = h/p，体现了波粒二象性，适用于电子等实物粒子。

λ = h/p

Radioactive decay obeys A = λN, where A is activity, λ is the decay constant and N is the number of undecayed nuclei. The half-life T₁/₂ = ln2/λ. Mass–energy equivalence is E = mc², and in nuclear reactions ΔE = Δm c².

放射性衰变遵循 A = λN，A 为活度，λ 为衰变常数，N 为未衰变核数。半衰期 T₁/₂ = ln2/λ。质能方程为 E = mc²，核反应中 ΔE = Δm c²。

A = λN   T₁/₂ = ln2/λ   E = mc²

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6. Chemical Kinetics | 化学动力学

The rate equation for a reaction aA + bB → products often takes the form: rate = k[A]ᵐ[B]ⁿ, where m and n are reaction orders and k is the rate constant. The overall order is m+n.

反应 aA + bB → 产物 的速率方程通常为：rate = k[A]ᵐ[B]ⁿ，m 和 n 为反应级数，k 为速率常数，总反应级数为 m+n。

rate = k[A]ᵐ[B]ⁿ

The Arrhenius equation connects the rate constant to temperature: ln k = ln A – Eₐ/(RT). A plot of ln k against 1/T gives a straight line with gradient –Eₐ/R, enabling activation energy to be determined.

阿伦尼乌斯方程将速率常数与温度关联起来：ln k = ln A – Eₐ/(RT)。以 ln k 对 1/T 作图得到一条直线，斜率为 –Eₐ/R，可由此求得活化能。

ln k = ln A – Eₐ/(RT)

For first-order reactions, the integrated rate law is ln[A]ₜ = ln[A]₀ – kt, showing an exponential decay of reactant concentration. The half-life t₁/₂ = ln2/k is independent of initial concentration.

对于一级反应，积分速率定律为 ln[A]ₜ = ln[A]₀ – kt，体现反应物浓度呈指数衰减。其半衰期 t₁/₂ = ln2/k 与初始浓度无关。

ln[A]ₜ = ln[A]₀ – kt   t₁/₂ = ln2/k

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7. Equilibrium and Thermodynamics | 平衡与热力学

The equilibrium constant K for a general reaction aA + bB ⇌ cC + dD is expressed as K = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ, using equilibrium concentrations. Solids and pure liquids are omitted from the expression.

一般反应 aA + bB ⇌ cC + dD 的平衡常数表达为 K = [C]ᶜ[D]ᵈ / [A]ᵃ

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