WJEC物理 电阻率 电动势 光电效应 半衰期
WJEC 的 A-Level 物理把电学与光学放在 AS 第二单元（Electricity and Light，2420U2），把原子核放在 A2 第三单元（Oscillations and Nuclei，1420U3）。两块内容看上去隔着一整年，其实共用同一套工具：电荷守恒、能量转换与指数关系。下面按 WJEC specification 的条目顺序，把电学、光子与核衰变里最容易丢分的十二个环节拆开讲，每节给一个公式、一组典型数值和一个学生常犯的错误。文中的物理常量取自 WJEC 官网公布的数据表，考试时以卷首数据表为准。
电学光学与核物理分在两个单元里
AS 第二单元 Electricity and Light 占整个 A level 的 20%，内容从导电机制、电阻、直流电路一路排到波的性质、折射、光子与激光。核衰变与核能归在 A2 第三单元 Oscillations and Nuclei，和简谐振动、热物理同卷。复习顺序因此不能按课本页码走：电路的电流电压测量与光学的光子能量考在同一份卷子上，核衰变却要和振动图像一起练。WJEC 官网的单元编号是 2420U1 到 1420U5，AS 两个单元各 100 UMS。很多学生以为核物理是最后一章，留到考前两周再看，实际上它和 Unit 3 的振动题共享指数与图像这两项技能，放一起练更省时间。
Electricity and Light sits in AS Unit 2 (2420U2) and carries 20 per cent of the full A level, while the nuclei material belongs to A2 Unit 3 (1420U3) and shares a paper with oscillations and thermal physics. Revision order therefore matters more than page order, because circuit measurements and photon energies appear on one paper while decay curves sit beside vibration graphs; the WJEC specification lists five units numbered 2420U1 to 1420U5, with each AS unit worth 100 UMS.
电阻率 ρL/A 与金属的温度系数
电阻率公式写成 R = ρL/A 时，A 是导线的横截面积，不是直径。WJEC 的实验题常给一段金属丝的长度与直径，要求先算 A、再求 ρ、最后和公布值比较。铜在室温下 ρ 约 1.7 × 10^-8 Ω m，长 1.00 m、直径 0.50 mm 的铜丝截面是 1.96 × 10^-7 m^2，电阻只有 0.087 Ω。这么小的电阻用普通万用表直接量，接触电阻能吃掉一半读数，所以标准做法是长导线配伏安法。常见的错误是把直径当半径代进去，结果差四倍。金属的 ρ 随温度升高而增大，半导体相反，题目给温度系数时正负号就按这条判断。
The relation R = ρL/A uses cross-sectional area, not diameter, and WJEC practical questions usually give the length and diameter of a wire and expect the area first, then the resistivity, then a comparison with a published value. Copper near room temperature sits at about 1.7 × 10^-8 ohm metres, so a metre of 0.50 mm wire comes out near 0.087 ohm, far too small for a bench multimeter to read without contact resistance dominating; that is why the standard experiment uses a long wire with a voltmeter and an ammeter. Entering the diameter as a radius is the slip that shifts the answer by a factor of four.
电动势 内阻 与 端电压
电池的电动势 ε 是单位电荷通过电池时获得的能量，它和内阻 r 一起决定路端电压。闭合电路里 ε = I(R + r)，端电压 V = ε - Ir，电流越大端电压掉得越多。WJEC 的数据处理题喜欢给一组 V 与 I 的读数让画图：截距是 ε，斜率是 -r。一节 1.50 V 的干电池内阻 0.50 Ω，接 2.5 Ω 外电阻，电流 0.50 A，端电压只剩 1.25 V，输出效率约 83%。很多学生以为电动势就是开路时电压表的读数，实际上电压表本身有内阻，读数略小于 ε。阅卷时看到只写 V = IR 而不提 r 的答案，后半段的分数通常拿不到。
Terminal voltage falls as current rises, and on a graph of V against I the intercept gives the e.m.f. while the gradient gives the internal resistance with a negative sign. A 1.50 V cell with 0.50 ohm of internal resistance driving 0.50 A therefore delivers only 1.25 V across a 2.5 ohm load, an efficiency near 83 per cent. Applying V = IR to the whole circuit without separating r from R loses the later marks, and reading the open-circuit voltmeter value as the e.m.f. is the related trap, since the meter's own resistance keeps that reading slightly low.
串联 并联 与 基尔霍夫两条定律
串联电路电流处处相同，电压按电阻分配；并联电路电压相同，电流按电导分配。6 Ω 与 3 Ω 并联得 2 Ω，再串 4 Ω 就是 6 Ω，总电流由 ε 除以 6 Ω 得到。基尔霍夫第一定律说节点电流代数和为零，第二定律说闭合回路的电动势之和等于电压降之和，写方程前先定绕行方向、再统一符号。学生最常把三个电阻的并联公式记错，两个电阻的乘积除以和还记得，三个就开始连乘。分压器接上负载后输出会跌落，这是电位器实验里被忽略最多的一点。
Series elements share a current while parallel branches share a voltage, so 6 ohm and 3 ohm in parallel give 2 ohm and then add 4 ohm in series for 6 ohm overall. Kirchhoff's first law is charge conservation at a junction and the second is energy around a loop; fixing a direction before assigning signs prevents most algebra errors. Three-resistor networks are where the reciprocal formula breaks down in students' working, and a loaded potential divider is the case that goes untested.
漂移速度 I = nAve 与 载流子数密度
电流的微观表达式 I = nAve 里，n 是单位体积的自由电子数，v 是漂移速度，e 是 1.60 × 10^-19 C。铜的 n 约 8.5 × 10^28 m^-3，1 mm^2 的导线通 1 A 电流，漂移速度只有 7 × 10^-5 m/s，比蜗牛慢得多。这说明灯泡一亮不是电子从开关跑到灯丝，而是电场以接近光速在导线里建立起来。很多学生以为电子以光速运动，其实传到的是信号，不是载流子。题目给 n 与 A 求 v 时，把 mm^2 换成 m^2 这一步少乘 10^-6 是最常见的量级错误。
The microscopic form I = nAve links current to carrier density, area and drift speed; copper holds about 8.5 × 10^28 electrons per cubic metre, so one amp through a square millimetre moves them at roughly 7 × 10^-5 m/s. A lamp lights instantly because the field is set up along the wire at close to light speed, not because electrons sprint from the switch. Losing the conversion from square millimetres to square metres is where the order of magnitude disappears.
光电效应 hf = φ + Ek
光电效应方程 hf = φ + Ek(max) 把入射光频率、逸出功和最大初动能绑在一起，与光强无关。低于阈频的光无论照多久都不出电子；高于阈频时，光强只改变单位时间的电子数。6.63 × 10^-34 J s 乘频率得到单个光子能量，钠的逸出功约 2.3 eV，对应阈频 5.5 × 10^14 Hz，落在黄绿光。截止电压 V 满足 eV = Ek(max)，测出 V 就能反推 φ，这是实验题的固定套路。常见的错误是把光强当成能量决定因素，把光电流大小和最大初动能混为一谈。
Einstein's photoelectric equation ties frequency, work function and maximum kinetic energy together and leaves intensity out of the energy balance. Below the threshold frequency no emission occurs however long the light shines, while above it intensity only changes the number of electrons per second; for sodium the work function near 2.3 eV puts the threshold in the yellow-green at about 5.5 × 10^14 Hz. Measuring the stopping potential gives the maximum kinetic energy directly, and confusing that potential with the photocurrent is the error that costs explanation marks.
光子能量 hc/λ 与 能级跃迁
能级跃迁放出的光子能量等于两能级之差，写成 hc/λ = E2 - E1，波长越短能量越大。氢原子基态比电离限低 13.6 eV，从 n = 3 跳到 n = 2 发出 656 nm 的红光，从 n = 2 跳到 n = 1 是 122 nm 的紫外。计算时先把 eV 换成 J，再代 hc = 1.99 × 10^-25 J m，否则量级会全错。吸收谱线与发射谱线位置相同、强度分布不同，问到太阳光谱的暗线时要答到外层原子吸收特定波长。很多学生以为能级越高谱线越密，实际上能级间隔随 n 增大而变小，越靠上越挤。
A transition releases a photon whose energy equals the gap between the levels, so hc/λ = E2 - E1 and shorter wavelengths carry more energy. In hydrogen the ground state lies 13.6 eV below the ionisation limit, the 3 to 2 jump produces the 656 nm red line and the 2 to 1 jump the 122 nm ultraviolet one. Converting electronvolts to joules before substituting hc = 1.99 × 10^-25 J m keeps the answer in the right decade, and the dark lines in the solar spectrum come from absorption by cooler outer atoms rather than from missing emissions.
双缝干涉 λ = ax/D 与 单缝衍射
双缝条纹间距公式 λ = ax/D 里，a 是缝间距，x 是相邻亮纹间距，D 是缝到屏的距离。把 D 拉大一倍，条纹间距也大一倍，这是学生用激光做干涉实验时最直观的一次验证。单缝衍射的中央亮纹宽度约 2λD/b，b 是缝宽，缝越窄中央越宽也越亮。白光入射时中央是白色、两侧成彩色，因为紫光偏折角度小。两个缝相干要求频率相同、相位差恒定，同一束激光分出来就自动满足。常见的错误是量条纹时从第一条亮纹量到第五条，却按四条间距算，结果差 25%。
Fringe spacing follows λ = ax/D, so doubling the screen distance doubles the separation, which is the quickest check available with a laser in the lab. Single-slit diffraction widens the central maximum as the slit narrows, its width being roughly 2λD/b, and white light gives a white centre with coloured edges because violet bends least. Coherence needs a constant phase difference at the two slits, and a single split laser beam supplies it automatically; counting four intervals as five when reading fringes is a 25 per cent error that shows up in mark schemes every year.
核素符号 强相互作用的短程性 与 稳定性
核素把核子数 A 写在左上、质子数 Z 写在左下，同位素 Z 相同而 A 不同。α 衰变让 A 减 4、Z 减 2，β 负衰变让 Z 加 1 而 A 不变，γ 只带走能量。强相互作用把核子绑在一起，作用距离约 1 fm，超出几个 fm 就迅速消失，所以重核里质子间的库仑斥力迟早占上风。中子过多的核走 β 负衰变，质子过多的走 β 正衰变或电子俘获。很多学生以为核力随距离增大而平稳减小，实际它是短程吸引加更短程的排斥芯，核密度基本恒定正是这个平衡的结果。
Nuclide notation puts the nucleon number top left and the proton number bottom left, and each decay mode follows from conservation of both: alpha removes four nucleons and two protons, beta minus raises Z by one, gamma carries energy alone. The strong force acts over about a femtometre and falls away sharply beyond that, which is why Coulomb repulsion eventually wins in heavy nuclei. Neutron-rich nuclides decay by beta minus emission and proton-rich ones by beta plus or electron capture, while the near-constant density of nuclei follows from short-range attraction balanced by an even shorter-range repulsive core.
指数衰变 A = λN 与 半衰期
放射性衰变服从 A = λN 与 N = N0 e^(-λt)，半衰期 T½ = ln2/λ，λ 越大衰变越快。半衰期是统计规律，样品越小涨落越明显，单个核何时衰变无法预测。碳 14 的半衰期约 5730 年，用它测年代靠的是活度比，不是数剩下的原子个数。碘 131 半衰期 8.0 天，三个半衰期后活度剩 12.5%，临床给药量就是这么估的。题目常给活度随时间的数据让作半对数图，斜率等于 -λ。常见的错误是把半衰期说成一半原子同时衰变所需的时间，这样写会被判概念错误。
Activity and population are linked by A = λN and the population falls as N = N0 e^(-λt), giving a half-life of ln 2 over λ; a semi-log plot of activity against time is therefore a straight line of gradient -λ. Half-life is a statistical statement, so small samples fluctuate and no individual nucleus has a scheduled decay time. Carbon-14 dating works on the activity ratio rather than on counting remaining atoms, and iodine-131 with its 8.0 day half-life falls to 12.5 per cent after three half-lives, which is how clinical doses are estimated.
质量亏损 与 1 u 对应的能量
核反应的质量亏损 Δm 乘 c^2 得到释放的能量，1 u 对应约 931 MeV，所以 1 g 质量完全转化相当于 9 × 10^13 J。氘核的结合能 2.2 MeV，比结合能曲线在铁 56 附近最高，重核裂变与轻核聚变都朝这个方向走。算结合能要先查各核素质量，用质子数乘氢原子质量加中子质量再减去核质量，查表值若是原子质量还要扣掉电子。质量亏损只占母核质量的千分之几，有效位不够就会算成零。很多学生以为质量在反应中消失了，其实它转化成了光子与动能。
Binding energy comes from the mass defect through E = mc^2, and the useful conversion is that one atomic mass unit corresponds to about 931 MeV, so a gram of mass fully converted would release close to 9 × 10^13 J. Binding energy per nucleon peaks near iron-56, which is why fission of heavy nuclei and fusion of light ones both release energy. Subtracting nuclear mass from the sum of proton and neutron masses needs care when the table lists atomic masses, because the electrons have to be accounted for.
单位换算 eV 与 J 以及有效数字
1.60 × 10^-19 C 的电荷过 1 V 电势差得 1 eV，等于 1.60 × 10^-19 J，这个换算在电学、光子与核物理三块内容里反复出现。把 2.5 MeV 换成 J 是 2.5 × 10^6 乘 1.60 × 10^-19 得 4.0 × 10^-13 J，卷面写成标准形式比写 4.0e-13 稳。WJEC 的计算题一般给两到三位有效数字的输入，答案保留同样位数即可，多写不扣分但容易暴露中间步骤的取整问题。单位漏写在 A2 卷上会单独扣分，MeV 与 eV 混用是最常见的一种。很多学生以为单位不影响得分，阅卷时每个物理量后面缺单位都要另算一次。
One electronvolt is the energy gained by an electron across one volt, namely 1.60 × 10^-19 J, and that conversion reappears in circuit, photon and nuclear questions alike. Turning 2.5 MeV into joules means multiplying 2.5 × 10^6 by 1.60 × 10^-19 to get 4.0 × 10^-13 J, and the answer should match the two or three significant figures supplied in the data. Missing units are marked separately on the A2 papers, and mixing MeV with eV is the slip that most often survives into the final line.
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