📚 A-Level Physics Unit 5 January 2020 Application Question Techniques | A-Level 物理 2020年1月 Unit 5 应用题技巧
Application questions in Edexcel A-Level Physics Unit 5 (Physics from Creation to Collapse) often require you to combine conceptual understanding with multi-step calculations. They may involve nuclear decays, thermal physics, oscillations, gravitational fields, or cosmology. This article outlines practical techniques to approach these questions, drawing on the style of the January 2020 paper, helping you to secure marks for method, accuracy, and clarity.
在爱德思 A-Level 物理 Unit 5（从创生到坍缩的物理）中，应用题通常要求你把概念理解与多步计算结合起来。它们可能涉及核衰变、热力学、振动、引力场或宇宙学。本文借鉴 2020 年 1 月试卷的风格，总结出实用的解题技巧，帮助你在方法、准确性和清晰度方面拿到分数。
1. Read the Question Twice and Highlight Key Terms | 审题两遍，圈出关键词
Before writing anything, read the question carefully at least twice. Underline or highlight the command words: ‘calculate’, ‘show that’, ‘estimate’, ‘explain’. Also note the data you are given and the quantity they want you to find. In the January 2020 paper, many students lost marks by misreading whether a value was a radius or a diameter, or by confusing energy with power.
动笔之前，把题目至少仔细读两遍。在指令词下划线或高亮：’calculate’（计算）、’show that’（证明）、’estimate’（估算）、’explain’（解释）。同时留意给出的数据以及要求你求出的物理量。在 2020 年 1 月的试卷中，很多学生因为看错半径还是直径、或者把能量和功率混为一谈而丢分。
Pay attention to the number of marks available. A one‑mark question rarely requires a full derivation, while a five‑mark ‘show that’ question will expect a clear, logical sequence of steps. This helps you decide how much detail to provide.
注意题目的分数。1 分的题目通常不需要完整推导，而 5 分的’证明’题则要求清晰、有逻辑的推导步骤。这会帮你决定要写得多详细。
2. List Knowns and Unknowns in a Table | 用表格列出已知量和未知量
Create a simple table right after reading the question. Write the symbol, value, and unit for each piece of data provided. Then add the quantity you need to find with a question mark. This habit prevents you from using the wrong number later, especially when questions give extra information that is not needed.
读完题后立即画一个简单的表格。写出每个数据的符号、数值和单位，再用一个问号标出需要求出的物理量。这个习惯能避免后续用错数字，特别是当题目给出多余信息的时候。
| Symbol | Value | Unit |
| m | 0.250 | kg |
| T₁ | 300 | K |
| p | 1.0 × 10⁵ | Pa |
| V₂ | ? | m³ |
For nuclear questions, list the number of half‑lives, decay constant λ, or initial activity A₀. If the question involves two states (e.g. before and after an adiabatic change), make two columns for state 1 and state 2.
对于核物理题，列出半衰期的个数、衰变常数 λ 或初始活度 A₀。如果题目涉及两个状态（例如绝热变化前后），可为状态 1 和状态 2 分别建列。
3. Convert All Units to SI Before Starting | 先把所有单位换成国际单位制
Exam data is often given in non‑SI units: cm³, °C, minutes, g, km. Convert these immediately to m³, K, s, kg, and m. For temperature, always add 273 to Celsius values to work in kelvin. In gas law calculations, a failure to convert °C to K is one of the most common errors.
考题给出的数据往往不是国际单位：cm³、°C、分钟、g、km。要立刻把它们换成 m³、K、s、kg、m。温度要始终在摄氏值上加 273，用开尔文来计算。在气体定律计算中，忘记把 °C 换算成 K 是最常见的错误之一。
When using the ideal gas equation pV = nRT, convert volume to m³ and pressure to Pa. If the volume is given in cm³, divide by 10⁶, not 10³. Also, 1 atmosphere = 1.01 × 10⁵ Pa, so watch for atmospheres in thermal questions.
使用理想气体状态方程 pV = nRT 时，要把体积换算成 m³，压强换成 Pa。如果体积给的是 cm³，要除以 10⁶，而不是 10³。另外，1 标准大气压 = 1.01 × 10⁵ Pa，因此在热力学题中注意大气压单位。
4. Draw a Labelled Diagram or Graph | 画带标注的示意图或图像
A quick sketch can turn a confusing word problem into a clear physical situation. For thermal physics, sketch a p–V diagram and shade the area if work done is asked. For oscillations, draw a displacement‑time graph and mark the amplitude, period, and points where velocity is zero.
随手画一张简图就能把令人困惑的文字题变成清晰的物理情景。热学题，可画 p–V 图，如果要求做功，可以把面积涂上阴影。振动题，可画位移‑时间图，标出振幅、周期和速度为零的点。
In astrophysics questions, draw a rough diagram of the orbit, label the central body, the radius, and the tangential velocity vector. For red‑shift calculations, sketch the observed and rest wavelengths on a spectrum line. Diagrams make you less likely to mix up values such as perihelion and aphelion distances.
在天体物理题中，画一个粗略的轨道示意图，标出中心天体、轨道半径和切向速度矢量。在红移计算中，可在光谱线上标出观测波长和静止波长。图像让你不容易混淆近日点和远日点距离等数值。
5. Choose the Correct Formula Using the Data Sheet | 根据公式表选择正确的公式
The Edexcel data sheet provides all the equations you might need. However, you must decide which one applies. For example, if a question gives the activity of a sample after a certain time, and the half‑life is known, use A = A₀ e⁻λt with λ = ln 2 / T₁/₂. Do not use the number‑of‑nuclei form unless the question asks for N.
爱德思公式表提供了你可能会用到的所有方程。但是，你得自己决定用哪一个。例如，如果题目给出了样品在一定时间后的活度，且半衰期已知，则用 A = A₀ e⁻λt，其中 λ = ln 2 / T₁/₂。除非题目要求计算原子核数 N，否则不要用原子核数形式的公式。
For SHM, decide between x = A cos(ωt) and v = ±ω√(A² – x²) based on what is given. If the question mentions ‘maximum speed’, the energy approach ½ m v²ₘₐₓ = ½ k A² might be faster than differentiating. Always write down the formula you are about to use before substituting numbers – this earns method marks.
对于简谐运动，要根据已知条件在 x = A cos(ωt) 和 v = ±ω√(A² – x²) 之间做选择。如果题目提到’最大速度’，用能量法 ½ m v²ₘₐₓ = ½ k A² 可能会比求导更快。务必先写下你要使用的公式，再代入数字——这能拿到方法分。
6. Set Out Your Working Step by Step | 分步展示你的计算过程
For calculation questions, show your substitutions clearly. Write the formula, then the formula with numbers, and finally the answer. Even if your final answer is wrong, you can still gain most of the marks. For instance, when using pV = nRT to find n, write: n = pV / RT = (1.0 × 10⁵ × 2.0 × 10⁻³) / (8.31 × 300) = 0.080 mol.
对于计算题，要清楚地展示代入过程。先写公式，再写代入数值后的式子，最后写出答案。就算最终答案错了，你仍然能拿到大部分分数。例如，用 pV = nRT 求 n 时，应写成：n = pV / RT = (1.0 × 10⁵ × 2.0 × 10⁻³) / (8.31 × 300) = 0.080 mol。
Avoid performing several arithmetic steps in your head and writing only the result. The examiner cannot award marks for a mental step. In ‘show that’ questions, work to at least one more significant figure than the value you are asked to prove, then round at the end.
要避免心算好几个步骤后只写结果。考官无法给心算步骤打分。在’证明’类题目中，计算时要多用一位有效数字，最后再四舍五入到题目要求证明的数值。
7. Tackle ‘Show That’ Questions with Precision | 精确处理’证明’类题目
‘Show that’ questions are designed to test your ability to derive a given value. Start with the fundamental equation, rearrange it explicitly, and substitute the values. Use the unrounded values stored in your calculator, not intermediate rounded numbers. If you fail to reach the exact given value, check for unit errors or whether you have misread a power of ten.
‘证明’类题目旨在测试你推导给定值的能力。从基本方程出发，清晰地进行移项，再代入数值。要使用计算器中存储的未舍入值，而不是中间过程的舍入值。如果算不出题目给的精确值，检查一下单位是否错误，或者是否看错了 10 的幂次。
For example, if you are asked to show that the speed of a satellite is about 7.6 × 10³ m s⁻¹, and your calculation gives 7.3 × 10³ m s⁻¹, you may have used the altitude instead of the orbital radius from the Earth’s centre. Such questions are common in the January 2020 paper’s gravitational section.
例如，要求你证明卫星的速率约为 7.6 × 10³ m s⁻¹，而你的计算结果是 7.3 × 10³ m s⁻¹，那你可能用了轨道高度，而忘了用从地球中心起算的轨道半径。这类问题在 2020 年 1 月试卷的引力部分很常见。
8. Interpret Graphs and Extracting Gradient Data | 解读图像并提取斜率数据
Many application questions include a graph: binding energy per nucleon, radioactive decay curve, or Wien’s displacement law plot. Read the axis labels and units carefully. If you need to find the half‑life from an exponential decay graph, choose two points where the activity halves and read the time interval – do not rely on a single data point.
很多应用题会给出图像：比结合能图、放射性衰变曲线或维恩位移定律图。仔细看坐标轴标签和单位。如果需要从指数衰变图中找出半衰期，选两个活度减半的点，读它们的时间间隔——不要只依赖一个数据点。
If the question asks for the gradient, draw a large triangle on the graph and calculate Δy/Δx. Remember to convert the units of the gradient if necessary. In a pV diagram, the area under the curve represents work done, which you might estimate by counting squares.
如果题目要求斜率，在图上画一个大三角形，计算 Δy/Δx。必要时要换算斜率的单位。在 pV 图中，曲线下的面积代表做的功，你可以通过数格子来估算。
9. Write Clear Explanations Using Physics Terminology | 用物理术语写出清晰解释
Explanation questions often worth 3–5 marks demand precise language. Instead of saying ‘the star gets brighter’, state ‘the luminosity increases because the core temperature rises, increasing the rate of nuclear fusion in the shell’. Use terms like ‘red shift’, ‘cosmic microwave background’, ‘adiabatic expansion’, or ‘damping’ appropriately.
3–5 分的解释题要求用词精准。不要说’恒星变亮了’，而要说’光度增加是因为核心温度升高，壳层中核聚变速率加快’。要恰当地使用’红移’、’宇宙微波背景’、’绝热膨胀’或’阻尼’等术语。
When explaining the shape of a binding energy per nucleon curve, link the peak (Fe‑56) to the most stable nucleus, and explain that fusion of light nuclei and fission of heavy nuclei both release energy because they move towards higher binding energy per nucleon.
解释比结合能曲线形状时，要把最高点（铁‑56）与最稳定原子核联系起来，并说明轻核聚变和重核裂变都会释放能量，因为它们都朝着比结合能增大的方向移动。
10. Time Management and Checking Answers | 时间管理与检查答案
Unit 5 application questions can be time‑consuming. Allocate roughly 1.5 minutes per mark. If you are stuck on a 2‑mark calculation after 3 minutes, move on and return later. Often a later part of the question gives a result that you need to use, so you can still attempt the rest.
Unit 5 的应用题可能很耗时。大致上按 1.5 分钟每分来分配时间。如果在某个 2 分计算上卡了 3 分钟，就先往下做，回头再来。很多时候，题目后问会给出你需要使用的某个结果，所以你仍能尝试后面的部分。
Once you finish, check that your answers have sensible units and reasonable magnitudes. The age of the Universe cannot be less than a few seconds; a star’s surface temperature cannot be 5000 K if it appears blue. Also, check that you have used the correct number of significant figures, usually the same as the least precise piece of data given.
做完后，检查你的答案是否有合理的单位和量级。宇宙年龄不可能只有几秒；一颗发出蓝光的恒星表面温度不可能是 5000 K。另外，检查有效数字的位数是否正确，一般与题目所给数据中最不精确的位数一致。
11. Common Pitfalls in Nuclear and Thermal Calculations | 核与热学计算中的常见陷阱
When using the decay equation N = N₀ e⁻λt, ensure that t and λ are in compatible time units. If the half‑life is given in days, convert it to seconds only if the time t is also in seconds. Many marks are lost due to mixing hours with seconds.
使用衰变方程 N = N₀ e⁻λt 时，要确保 t 和 λ 的时间单位一致。如果半衰期是以天为单位，只有当 t 也以秒为单位时才需要换算。混淆小时和秒是很多丢分的源头。
In thermal questions involving the first law ΔU = Q – W, pay close attention to the sign convention. Work done by the gas is positive W, so internal energy decreases. Draw an arrow diagram on your p–V sketch to remind yourself.
在涉及热力学第一定律 ΔU = Q – W 的题目中，要特别注意符号规则。气体对外做功时 W 取正，因此内能减少。在你的 p–V 草图上画一个箭头图来提醒自己。
12. Using Standard Results and Formulae for Astrophysics | 运用天体物理的标准结果和公式
For Hubble’s law v = H₀ d, remember that v is the recessional velocity and d is the proper distance. If the question asks for the age of the Universe, use t ≈ 1 / H₀, but be sure to convert H₀ from km s⁻¹ Mpc⁻¹ to s⁻¹. A typical value of 70 km s⁻¹ Mpc⁻¹ is approximately 2.3 × 10⁻¹⁸ s⁻¹.
对于哈勃定律 v = H₀ d，记住 v 是退行速度，d 是本动距离。如果题目要求宇宙年龄，使用 t ≈ 1 / H₀，但一定要把 H₀ 从 km s⁻¹ Mpc⁻¹ 换算成 s⁻¹。典型的 70 km s⁻¹ Mpc⁻¹ 大约等于 2.3 × 10⁻¹⁸ s⁻¹。
When applying the Stefan‑Boltzmann law L = 4πR²σT⁴, note that T must be in kelvin and R in metres. If a star’s radius is given in solar radii, convert using 1 R☉ = 6.96 × 10⁸ m. Check whether the question wants the luminosity in watts or in terms of solar luminosity L☉.
应用斯特藩‑玻尔兹曼定律 L = 4πR²σT⁴ 时，注意 T 要用开尔文，R 要用米。如果恒星半径以太阳半径给出，需用 1 R☉ = 6.96 × 10⁸ m 换算。看清题目要求光度以瓦特表示还是以太阳光度 L☉ 表示。
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