Study of diffraction and wave properties of the electron using a graphite crystal: A scientific study and digital simulation

Abstract

This study investigates the phenomenon of electron diffraction through a graphite crystal in order to verify the wave nature of electrons and examine the relationship between electron wavelength and crystal structure. The study combines theoretical analysis, practical experimentation, and numerical simulation. De Broglie's hypothesis and Bragg’s law were used to interpret the formation of diffraction rings and to estimate the interplanar spacings of the crustal. The experiment was conducted using an electron diffraction tube containing a graphite crystal and fluorescent screen. Anode voltages ranging from 1kv to 5 kv were applied, and the radii of the two diffraction rings formed around the central bright spot were measured. The results showed that the radii of the diffraction rings decreased as the anode voltage increased, whereas the electron wavelength increased when the voltage decreased, in agreement with the de Broglie relation. The graphical analysis also revealed an approximately direct relationship between the radii of the diffraction rings and the electron wavelength, as well as a linear relationship between the ring radii and the reciprocal square root of the anode voltage. A numerical simulation model was also developed using python and Matlab and the Numpy, Mat lab, and Scipy libraries to represent the variation in the electron wavelength and the diffraction ring patterns at different voltages. The simulation showed the formation of circular and concentric rings. It also demonstrated that reducing the applied voltage increases both the electron wavelength and the ring radii, which agrees with the practical results and theoretical predictions. Based on the slopes of the graphical relationships, the interplanar spacings of the graphite crystal were estimated to be approximately 216.6 pm and 162.5 pm using one method, and 199 pm and 157.5 pm using another method. The study demonstrates that electron diffraction through graphite confirms the wave nature of electrons and that numerical simulation patterns and representing the relationship between voltage, wavelength, and ring radius. The results also highlight the importance of integrating practical experimentation simulation in the study of crystal structures and quantum mechanical phenomena.