Impact of Relativity on the Theoretical Limit for the Periodic System of Elements beyond Uranium

In the periodic table of elements there cannot be elements lighter than hydrogen, but there can be elements heavier than uranium. Presently about 26 transuranic are known. When atoms’ nuclei get heavier, more protons in the nucleus mean more Coulomb force pulling the inner most electrons in, so the electrons orbiting the heavy nuclei have to go faster and faster, reaching speeds that are a substantial fraction of the speed of light. At such high speeds, the electrons become “relativistic,” and the atoms behave differently from what is expected based on their position in the periodic table. Calculations for hydrogen-like atom show that the electrons would have to travel faster than light for atoms with atomic number, which is impossible. This paper questions the validity of incorporating Einstein's relativistic mass well-known formula, to answer the long standing question of ‘Is there a maximum number of elements corresponding to a theoretical limit for the periodic system?’ We show here that Einstein's most celebrated equation holds if, and only if, the photon is conceived to be mass-ive.