Within the Density Functional Theory a new model of exchange potential containing corrective terms for self interaction and long range behavior is proposed . This potential model contains three constants: alpha , beta and gamma. The first two are determined through experimental data while the third is calculated by means of a polynomial function of six degrees depending on the total number of electrons. When this potential is introduced in the effective potential and Kohn-Sham equations are solved by iterations, calculated total energies and eigen values reproduce with high accuracy the experimental values. Total electronic densities obtained with this scheme are employed to find numerically the point where the derivatives of the kinetic energy respect to the total electronic density equal either the exchange correlation potential or half the effective Kohn-Sham potential. Solutions of this equality come as a singular point in the radial mesh and are correlated with atomic and covalent radius