Abstract- Einstein’s energy-momentum relationship, which holds in an isolated system in free space, cannot be applied to an electron in a hydrogen atom, where potential energy exists. Thus, the author has previously derived an energy-momentum relationship applicable to an electron in a hydrogen atom. It is possible, by using this relationship, to derive the relationships between the momentum of an electron, and the momentum of a photon possessed by the electron. There is a close relationship between these two physical quantities and the fine structure constant. Also, if the de Broglie relationship is applied to the energy-momentum relationship derived by the author, it is possible to derive the relationship between the wavelength of a moving electron, the wavelength of a photon possessed by the electron, and the Compton wavelength of the electron.