WJEC物理 电路 光电效应 核衰变 半衰期
2| 3|WJEC A-Level Physics Unit 3 和 Unit 4 涵盖了电学、光学与原子核物理三大核心模块。这些内容不仅是考试的必考点，也是理解现代物理学的基础。本文将系统梳理电路分析、光电效应以及核衰变的核心概念与解题技巧，帮助你在考前快速回顾重点。WJEC A-Level Physics Units 3 and 4 cover three core modules: electricity, light, and nuclear physics. These topics are not only essential for your exams but also form the foundation of modern physics. This article systematically reviews the key concepts and problem-solving techniques for circuit analysis, the photoelectric effect, and nuclear decay to help you revise efficiently before the exam.
4| 5|一、电学 Electricity
6| 7|电流与电荷 Current and Charge
8| 9|电流定义为电荷的流动速率，公式 I = ΔQ / Δt。在 WJEC 考试中，你需要熟练运用 Q = It 来计算电路中通过某一截面的总电荷量。记住，金属导体中的载流子是电子，每个电子携带的电荷量为 e = 1.6 × 10⁻¹⁹ C。Current is defined as the rate of flow of charge, given by I = ΔQ / Δt. In WJEC exams, you need to confidently use Q = It to calculate the total charge passing through a cross-section of a circuit. Remember that charge carriers in metal conductors are electrons, each carrying a charge of e = 1.6 × 10⁻¹⁹ C.
10| 11|欧姆定律与电阻 Ohm's Law and Resistance
12| 13|欧姆定律表明，在一定温度下，导体两端的电压与通过它的电流成正比：V = IR。电阻的定义式 R = V / I 适用于所有元件，但只有欧姆导体才满足 I-V 特性曲线为过原点的直线。对于非欧姆元件（如二极管、灯丝），I-V 曲线会弯曲，此时只能使用 R = V / I 计算特定工作点下的电阻。Ohm's Law states that at constant temperature, the voltage across a conductor is proportional to the current through it: V = IR. While the definition R = V / I applies to all components, only ohmic conductors produce a straight-line I-V characteristic passing through the origin. For non-ohmic components such as diodes and filament lamps, the I-V curve is nonlinear, so you can only calculate resistance at a specific operating point using R = V / I.
14| 15|电阻率 Resistivity
16| 17|电阻率 ρ 是材料的固有属性，反映材料阻碍电流的能力。公式 R = ρL / A 告诉我们，导体的电阻与长度 L 成正比，与横截面积 A 成反比。WJEC 常考的实验题包括测量导线的电阻率----你需要用千分尺测量直径、用米尺测量长度、用伏安法测量电阻。Resistivity ρ is an intrinsic material property that quantifies how strongly a material opposes current flow. The formula R = ρL / A tells us that resistance is proportional to length L and inversely proportional to cross-sectional area A. A common WJEC practical exam question involves measuring the resistivity of a wire: you need a micrometer to measure diameter, a metre rule for length, and a voltmeter-ammeter setup for resistance.
18| 19|基尔霍夫定律 Kirchhoff's Laws
20| 21|基尔霍夫第一定律（电流定律 KCL）：流入电路中任一点的电流之和等于流出该点的电流之和，本质是电荷守恒。基尔霍夫第二定律（电压定律 KVL）：闭合回路中，电动势的代数和等于各元件两端电压的代数和，本质是能量守恒。串联电路中电流处处相等，总电阻为各电阻之和；并联电路中各支路电压相等，总电阻的倒数为各电阻倒数之和。Kirchhoff's First Law (KCL): the sum of currents entering any junction equals the sum leaving it -- this is charge conservation. Kirchhoff's Second Law (KVL): the algebraic sum of EMFs around any closed loop equals the sum of potential differences, reflecting energy conservation. In series circuits, current is the same everywhere and total resistance is the sum of individual resistances. In parallel circuits, voltage across each branch is identical, and the reciprocal of total resistance equals the sum of reciprocals.
22| 23|电动势与内阻 EMF and Internal Resistance
24| 25|电动势 ε 是电源将单位正电荷从负极搬运到正极所做的功。实际电源都有内阻 r，端电压 V = ε − Ir。WJEC 经典实验：通过改变外电路负载电阻 R，测量 V 和 I，绘制 V-I 图。图像的 y 截距为 ε，斜率的绝对值为内阻 r。Electromotive force ε is the work done per unit charge to move positive charge from the negative to the positive terminal. Real power sources have internal resistance r, so terminal voltage V = ε − Ir. The classic WJEC experiment: vary the external load R, measure V and I, and plot a V-I graph. The y-intercept gives ε, and the absolute slope gives internal resistance r.
26| 27|电功率与能量 Electrical Power and Energy
28| 29|电功率 P = VI = I²R = V²/R。对于电池供电电路，总功率 εI 的一部分消耗在内阻上 (I²r)，剩余的输出给外电路。焦耳定律 Q = I²Rt 描述了电流热效应。在 WJEC 计算题中，注意区分"电源输出的功率"和"负载消耗的功率"。Electrical power P = VI = I²R = V²/R. For a battery-powered circuit, total power εI is partly dissipated in the internal resistance (I²r), with the remainder delivered to the external circuit. Joule's Law Q = I²Rt describes the heating effect. In WJEC calculations, carefully distinguish between "power delivered by the source" and "power dissipated by the load."
30| 31|二、光学 Light
32| 33|光子的能量 Photon Energy
34| 35|爱因斯坦提出光是由光子组成的，每个光子的能量 E = hf = hc / λ，其中 h = 6.63 × 10⁻³⁴ J·s 为普朗克常数。这一公式是 WJEC 光学计算的基石----频率越高（波长越短），光子能量越大。紫外线光子比可见光光子能量更高，这就是为什么紫外线能引发光电效应而红光不能。Einstein proposed that light consists of photons, each carrying energy E = hf = hc / λ, where h = 6.63 × 10⁻³⁴ J·s is Planck's constant. This formula is the cornerstone of WJEC optics calculations: higher frequency (shorter wavelength) means higher photon energy. UV photons carry more energy than visible photons, which is why ultraviolet light can trigger the photoelectric effect while red light cannot.
36| 37|光电效应 The Photoelectric Effect
38| 39|当光照射金属表面时，电子从金属表面逸出的现象称为光电效应。关键方程是爱因斯坦光电方程：hf = φ + KE_max。其中 φ 是金属的逸出功（work function），KE_max 是逸出电子的最大动能。三个重要实验结论：(1) 只有频率高于阈频 f₀ = φ / h 的光才能产生光电效应；(2) 增大光强会增加光电子数量但不改变最大动能；(3) 光电子的最大动能与光强无关，只取决于入射光的频率。When light shines on a metal surface, electrons are emitted -- this is the photoelectric effect. The key equation is Einstein's photoelectric equation: hf = φ + KE_max, where φ is the work function and KE_max is the maximum kinetic energy of emitted electrons. Three crucial experimental findings: (1) only light with frequency above the threshold f₀ = φ / h can cause emission; (2) increasing intensity increases the number of photoelectrons but not their maximum kinetic energy; (3) KE_max depends only on the frequency of incident light, not on its intensity.
40| 41|光电效应实验与 Stopping Potential
42| 43|WJEC 实验题常要求绘制 KE_max 对频率 f 的图像。图像为一条直线，斜率等于普朗克常数 h，x 截距为阈频 f₀，y 截距的负值为逸出功 φ。stopping potential V_s 是使光电流降为零所需的反向电压：eV_s = KE_max = hf − φ。WJEC exam questions frequently ask you to plot KE_max against frequency f. The graph is a straight line whose gradient equals Planck's constant h, the x-intercept is threshold frequency f₀, and the negative y-intercept equals the work function φ. The stopping potential V_s is the reverse voltage needed to reduce the photocurrent to zero: eV_s = KE_max = hf − φ.
44| 45|波粒二象性 Wave-Particle Duality
光电效应证明了光的粒子性（光子），而干涉和衍射实验证明了光的波动性。德布罗意进一步提出物质波假说：任何运动粒子都具有波动性，其波长 λ = h / p = h / mv。电子衍射实验（Davisson and Germer）证实了这一假说。在 WJEC 考试中，你需要能够解释哪些现象支持波动模型、哪些支持粒子模型。The photoelectric effect demonstrates the particle nature of light (photons), while interference and diffraction demonstrate its wave nature. De Broglie extended this with his matter-wave hypothesis: any moving particle has wave properties with wavelength λ = h / p = h / mv. Electron diffraction experiments by Davisson and Germer confirmed this. In WJEC exams, you need to explain which phenomena support the wave model and which support the particle model.
48| 49|原子光谱与能级 Atomic Spectra and Energy Levels
50| 51|原子中的电子只能处于特定能级。当电子从高能级 E₂ 跃迁到低能级 E₁ 时，会发射光子，能量 hf = E₂ − E₁。发射光谱由一系列离散的亮线组成，每条线对应一个特定的电子跃迁。吸收光谱则是在连续光谱背景上出现暗线。氢原子光谱的巴尔末系是最经典的 WJEC 考点。Electrons in atoms occupy discrete energy levels. When an electron transitions from a higher level E₂ to a lower level E₁, a photon is emitted with energy hf = E₂ − E₁. Emission spectra consist of discrete bright lines, each corresponding to a specific electron transition. Absorption spectra show dark lines against a continuous background. The Balmer series of the hydrogen spectrum is the most classic WJEC exam topic.
52| 53|三、原子核物理 Nuclei
54| 55|原子核的结构 Nuclear Structure
56| 57|原子核由质子和中子（统称核子）组成。原子序数 Z 表示质子数，质量数 A 表示核子总数，中子数 N = A − Z。核力是短程强相互作用力，作用范围约 10⁻¹⁵ m，克服了质子间的库仑斥力将核子束缚在一起。The nucleus consists of protons and neutrons, collectively called nucleons. Atomic number Z is the number of protons, mass number A is the total number of nucleons, and neutron number N = A − Z. The strong nuclear force is a short-range interaction (~10⁻¹⁵ m) that overcomes Coulomb repulsion between protons to bind nucleons together.
58| 59|放射性衰变 Radioactive Decay
60| 61|不稳定的原子核会自发衰变，释放辐射。三种主要衰变类型：(1) α衰变：释放氦核 ⁴₂He，质量数减4，原子序数减2；(2) β⁻衰变：中子转变为质子，释放电子和反中微子，原子序数加1，质量数不变；(3) γ衰变：原子核从激发态回到基态，释放高能光子，不改变质量数和原子序数。Unstable nuclei decay spontaneously, emitting radiation. Three main types: (1) Alpha decay: emission of a helium nucleus ⁴₂He, mass number decreases by 4 and atomic number decreases by 2. (2) Beta-minus decay: a neutron converts to a proton, emitting an electron and antineutrino, atomic number increases by 1, mass number unchanged. (3) Gamma decay: the nucleus drops from an excited state to the ground state, emitting a high-energy photon with no change in A or Z.
62| 63|衰变规律与半衰期 Decay Law and Half-Life
64| 65|放射性衰变服从指数衰减规律：N = N₀e^(−λt)，其中 λ 为衰变常数。活度 A = λN，表示每秒衰变次数，单位为贝克勒尔 Bq。半衰期 T₁/₂ = ln2 / λ，是放射性核素数目减半所需的时间。WJEC 常考的半衰期计算包括：从 N₀ 求剩余量、从活度求时间、碳-14 定年法。Radioactive decay follows an exponential law: N = N₀e^(−λt), where λ is the decay constant. Activity A = λN gives the number of decays per second, measured in becquerels (Bq). Half-life T₁/₂ = ln2 / λ is the time for half the radioactive nuclei to decay. Common WJEC half-life calculations include finding remaining quantity from N₀, determining time from activity, and carbon-14 dating.
66| 67|核反应与质能方程 Nuclear Reactions and Mass-Energy
68| 69|爱因斯坦质能方程 E = mc² 是核物理的核心。在核反应中，反应前后的质量差 Δm 转化为能量释放：ΔE = Δm c²。核裂变（如铀-235）和核聚变（如氢同位素）都通过质量亏损释放巨大能量。WJEC 计算题要求你用原子质量单位 u 进行计算，记住 1u = 931.5 MeV。Einstein's mass-energy equation E = mc² is central to nuclear physics. In nuclear reactions, the mass difference Δm before and after the reaction is converted to released energy: ΔE = Δm c². Nuclear fission (e.g., uranium-235) and fusion (e.g., hydrogen isotopes) both release enormous energy through mass defect. WJEC calculations require working in atomic mass units u, and you must remember that 1u = 931.5 MeV.
70| 71|辐射的穿透能力与防护 Penetration and Shielding
72| 73|α粒子穿透力最弱，一张纸即可阻挡，但在空气中的电离能力最强。β粒子穿透力中等，几毫米铝板可阻挡。γ射线穿透力最强，需要几厘米铅板或厚混凝土才能有效衰减。WJEC 常考辐射在电场和磁场中的偏转：α带正电，偏转方向遵循左手定则；β⁻带负电，偏转方向与α相反；γ不带电，不发生偏转。Alpha particles have the weakest penetration -- a sheet of paper stops them -- but the strongest ionising power in air. Beta particles have moderate penetration, stopped by a few millimetres of aluminium. Gamma rays have the strongest penetration, requiring several centimetres of lead or thick concrete for effective shielding. WJEC frequently tests deflection in electric and magnetic fields: alpha particles are positively charged and deflect according to Fleming's left-hand rule; beta-minus particles are negatively charged and deflect in the opposite direction; gamma rays carry no charge and do not deflect.
74| 75|四、WJEC 计算题技巧 WJEC Calculation Tips
76| 77|电路题 Circuit Problems: 先判断串并联关系，画等效电路图。对于复杂电路，用基尔霍夫定律列方程。注意电源内阻 r 不可忽略时，端电压低于电动势。实用技巧：用 V = ε − Ir 代入外电路方程，消去 V 解出 I。Start by identifying series and parallel relationships and draw an equivalent circuit diagram. For complex circuits, apply Kirchhoff's laws to set up equations. When internal resistance r is significant, terminal voltage drops below EMF. Pro tip: substitute V = ε − Ir into the external circuit equation, eliminate V, and solve for I.
78| 79|光电效应题 Photoelectric Problems: 确认入射光频率是否大于阈频。用 hf = φ + KE_max 列方程，注意单位统一：eV 与 J 的换算 1 eV = 1.6 × 10⁻¹⁹ J。stopping potential 题直接用 eV_s = hf − φ。Confirm that the incident frequency exceeds the threshold. Apply hf = φ + KE_max and watch your units: 1 eV = 1.6 × 10⁻¹⁹ J. For stopping potential problems, use eV_s = hf − φ directly.
80| 81|衰变与半衰期题 Decay and Half-Life Problems: 记住三种方法：(1) 直接使用半衰期次数：N = N₀ / 2^n，其中 n = t / T₁/₂；(2) 指数公式 N = N₀e^(−λt)；(3) 活度比例 A / A₀ = N / N₀ = e^(−λt)。碳定年法中用 ¹⁴C 的活度比推算年代，T₁/₂ = 5730 年。Remember three approaches: (1) direct half-life counting: N = N₀ / 2^n, where n = t / T₁/₂; (2) exponential formula N = N₀e^(−λt); (3) activity ratio A / A₀ = N / N₀ = e^(−λt). For carbon dating, use the ¹⁴C activity ratio with T₁/₂ = 5730 years.
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