The present work devotes to the calculation of relativistic and non-relativistic electronic state and energy for atoms C, O, S, Se, Te, Sm and Pu. In comparison between the relativistic and non-relativistic electronic energy,it is concluded that if energy difference of relativistic and non-relativistic electronic energy for O atom is supposed as unit, then there will be 17.5,479,6 781 and 46 166 for S,Se,Sm and Pu ,respectively. The energy difference of relativistic and non-relativistic electronic energy for Pu is about 8.72 % of its total energy. Therefore, it is quite necessary to calculate heavy atoms using relativistic theory.