IOSR Journal of Applied Physics (IOSR-JAP) e-ISSN: 2278-4861.Volume 11, Issue 3 Ser. II (May. – June. 2019), PP 25-29 www.iosrjournals.org DOI: 10.9790/4861-1103022529 www.iosrjournals.org 25 | Page The Impact of the Electric susceptibility on Electron Effective Mass Elmardi.A. M. Ali 1 , M. H. M. Hilo 2 , KH. M. Haroun 3 , Lutfi Mohammed Abdalgadir 4 , Mubarak Dirar Abdallah 5 1 (Department of Physics, College of Science and Arts-Alrass/Qassim University, Saudi Arabia) 2,5 (Department ofPhysics, College of Science / Sudan University of Science & Technology, Sudan) 3 (Department ofPhysics, College of Radiobiological and Imaging science / Al Zaiem Al Azhari University, Sudan 4 (Department ofPhysics, College of of Science & Humanities-Hurymilla / ShaqraUniversity, Saudi Arabia) Corresponding Author:- Elmardi.A. M. Ali Abstract: The electron effective mass directly depends on the electric field where the electron presented in it. In this study the electron effective mass was studied by derivation (mathematically) for the equations of motion(velocity and acceleration).Considering that the electron presented in an electric field, an equation for electron effective mass was found. When neglecting the electric field, the effective mass is equal to the ordinary mass. --------------------------------------------------------------------------------------------------------------------------------------- Date of Submission: 13-05-2019 Date of acceptance: 30-05-2019 --------------------------------------------------------------------------------------------------------------------------------------- I. Introduction In solid state physics, a particle's effective mass (often denoted m*) is the mass that it seems to have when responding to forces[1], or the mass that it seems to have when interacting with other identical particles in a thermal distribution. One of the results from the band theory of solids is that the movement of particles in a periodic potential[2], over long distances larger than the lattice spacing, can be very different from their motion in a vacuum. The effective mass is a quantity that is used to simplify band structures by modeling the behavior of a free particle with that mass [3]. For some purposes and some materials, the effective mass can be considered to be a simple constant of a material [4]. In general, however, the value of effective mass depends on the purpose for which it is used, and can vary depending on a number of factors. For electrons or electron holes in a solid, the effective mass is usually stated in units of the rest mass of an electron, me (9.11×10 −31 kg)[5]. In these units it is usually in the range 0.01 to 10, but can also be lower or higher-for example, reaching 1,000 in exotic heavy fermion materials, or anywhere from zero to infinity (depending on definition) in graphene. As it simplifies the more general band theory [6], the electronic effective mass can be seen as an important basic parameter that influences measurable properties of a solid, including everything from the efficiency of a solar cell to the speed of an integrated circuit [7]. II. The Effective Quantum Model In this model the electrons or particles are need to be free. Thus the energy expression can be given by [8]: E= ℏ 2 k 2 2m ∗ = ℏ 2 k ∗ 2 2m (1) The effect of the field is embedded in the mass for the second term, while it is embedded in the wave number in the third term. Thus m ∗ m =  k k ∗  2 (2) The wave number is given for vacuum by: k= 2π λ = 2πf λf = ω c (3) While for any medium it is given by: k ∗ = 2π λ = 2πf λf = ω v = ωμ o ε o μ r ε r k ∗ = μ o 1+ χ m ε o 1+ χ e  (4) Where χ m is magnetic susceptibility and χ e is electric susceptibility Where the magnetic and electric susceptibility are given by [9]: