The scattering of electron by a photon is a well-known reaction in physics. In this study, the change in the electron’s energy after the scattering is taken into account. The previous works are searched. In order to take into account this change in the electron’s energy in the equation of motion of the electron, the Dirac equation is used with the virial theorem. The scattered electron kinetic energy which is given to the electron by the loss in photon’s energy is related to the potential energy of the electron by the virial theorem which states that the potential energy is two times of the kinetic energy in minus sign. A first time application of the virial theorem on a scattered electron by a photon is included to the Dirac equation.