The Frank-Hertz experiment is important for verifying the quantization of electron energy and is aclassie in recent physics experiments, However, the experimental results are generally limited by the experimental conditions and data processing methods. In this paper, Matlab soltware is used to calculate the first excitation potential of monatomie gas argon by segmented linear interpolation , three times Hermite inte rpolation and three times spline interpolation and ploting the curve of eight sets of measured data, and it is found that the curve fitted by three times spline interpolation is smoother and the consisency of the results is belter. Meanwhile ,the first exeitation potential of the gas argon is obtained by the quantum mechanics-based first nature prineiple caleulation, and compared with the experimental results, it is found that compared with the Perdew-Burke-Erzerhof( PBE ) generalized funetion, the first excitation potential calculated by using theHeyd-Seuseria-Emzerhof( HSE06 ) generalized function has a better agreement with the experimental value ,and the introduction of spin-orbit coupling leads to the cleavage of the energy level but does not change theexeitation potential significantly.