弗兰克-赫兹实验理论曲线推导

Derivation oftheoretical curve of Franck-Hertz experiment

弗兰克-赫兹实验中的板极电流的理论预测模型亟待建立,现有相关理论工作侧重于对实验结果的分析和阐释,而少数理论计算模拟的工作或未展现理论曲线全貌,或运算耗时较长.本文基于两条引理和三条假设,将解析与编程结合,在1秒内给出理论曲线全貌,并分析其与实验值偏差的原因,据此引入电子运动轨迹和通过率修正,给出修正曲线全局预测,其与实验结果的符合度较高.这不但检验了玻尔理论的正确性,也表明理论成果可用于一定范围内板极电流的预测.

Theoretical prediction models for anode current of Franck-Hertz experiment need to be established urgently.Existing related theoretical works focus on the analysis and interpretation of experimental results,while a small number of theoretical calculation and simulation works either fail to predict the theoretical curve comprehensively,or take too long time.Based on two lemmas and three hypotheses,this paper provides a comprehensive prediction of the theoretical curve within 1 second,and analyzes the reasons for its deviation from experimental results.After introducing corrections of trajectory and passing rate of electrons,we obtain the modified curve,which is highly consistent with the experimental result.Our results not only verify the correctness of Bohr's theory,but also can be applied to predicting the anode current of Franck-Hertz experiment within a certain range.