基于Python的弗兰克–赫兹实验汞原子高激发态的比例计算

Python-Based Calculation of the Proportions of Mercury Atoms in Highly Excited States in the Franck-Hertz Experiment

摘要: 弗兰克–赫兹实验是验证原子能级量子化的经典实验，在大学物理实验教学中具有重要地位。传统教学多聚焦于第一激发电位的测量，其验证性特征明显但探究性不足。本文提出一种融合物理建模与计算思维的实验数据分析新方法：首先利用低温条件下的U-I特性曲线，通过Python编程反演热阴极电子速率分布函数；进而基于该模型分析高温下的复杂U-I曲线，定量计算不同激发态汞原子的数量比例。该方法将经典验证性实验拓展为综合性研究项目，不仅深化了实验物理内涵，还有效培养了学生的计算物理思维和数据处理能力，为大学物理实验教学改革提供了新思路。

Abstract: The Franck-Hertz experiment is a classic experiment for verifying the quantization of atomic energy levels and holds an important position in university physics experimental teaching. Traditional teaching mainly focuses on measuring the first excitation potential, which has obvious verification characteristics but lacks exploratory nature. This paper proposes a new experimental data analysis method that integrates physical modeling and computational thinking: first, the electron velocity distribution function of the thermionic cathode is derived through inversion using Python programming with the U-I characteristic curves under low-temperature conditions; then, based on this model, the complex U-I curves under high-temperature conditions are analyzed to quantitatively calculate the proportions of mercury atoms in different excited states. This method extends the classic verification experiment into a comprehensive research project, which not only deepens the understanding of experimental physics but also effectively cultivates students’ computational physics thinking and data processing capabilities, providing new insights for university physics experimental teaching reform.