📚 A-Level Physics: Formula Derivations in Unit 5 January 2021 Paper | A-Level 物理：2021年1月Unit 5试卷公式推导
The January 2021 Unit 5 paper for A-Level Physics (IAL Physics Unit 5: Physics from Creation to Collapse) challenges students to derive and apply fundamental formulas across topics such as nuclear decay, oscillations, thermal physics, gravitational fields, and cosmology. Mastering these derivations not only reinforces conceptual understanding but also prepares you for the analytical demands of the exam. In this article, we will walk through the key derivations that frequently appear in this paper, complete with step-by-step explanations in both English and Chinese.
2021年1月的A-Level物理Unit 5试卷（IAL物理第五单元：从创世到坍缩）要求学生推导并应用核衰变、振动、热物理、引力场和宇宙学等主题的基本公式。掌握这些推导不仅能加深概念理解，还能帮助你应对考试的分析性要求。本文将带您逐步回顾该试卷中常考的关键公式推导，并提供中英双语的分步解释。
1. Radioactive Decay Law | 放射性衰变定律推导
to the current number of undecayed nuclei N. This gives the differential equation: dN/dt = –λ N, where λ is the decay constant (probability of decay per unit time).
放射性衰变的随机性意味着单位时间内发生衰变的原子核数与当前未衰变核的数量N成正比。由此得到微分方程：dN/dt = –λ N，其中λ为衰变常数（单位时间内每个核的衰变概率）。
Separate the variables: (1/N) dN = –λ dt. Integrate both sides: ∫ (1/N) d
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