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A semi-relativistic total energy of the hydrogen-like ions is presented. The established expression taking only into account the dependence of the mass electron on the speed could be considered as a first correction of the Bohr's semi-classical formula. Comparison with relativistic total energy expression obtained from the Dirac's relativistic wave equation is made. In addition, the present relativistic theory of the hydrogen-like ions is extended to the helium isoelectronic series. It is shown that, for the ground state of two electron systems, the relativistic screening constant σ^rel decreases when increasing the nuclear charge up to Z = 5. Beyond, σ^rel increases when increasing Z and, the plot σ^rel = f (Z) is like a valley of stability where the bottom is occupied by the B^3+-helium-like ion. As a result, only He, Li^+, Be^2+ and B^3+ exist in the natural matter in low temperature. All the other helium-like positive-ions, such as C^4+, N^5+, O^6+, F^7+, Ne^8+, …, can only exist in hot laboratory and astrophysical plasmas. , number=1, journal=Journal of Atomic and Molecular Sciences, year=2012, month=Mar., pages=23–40