The Bohr radius was derived using the non-relativistic de Broglie approximation, not the relativistic de Broglie equation. In this work, we will derive a relativistic Bohr radius from both the relativistic de Broglie approximation and relativistic kinetic energy. The Bohr model of the hydrogen atom has since been replaced by modern quantum mechanics and the Schrodinger equation. It is well known that the Schrodinger equation confirms the first Bohr radius as the most probable radius, but the Schrodinger equation itself is non-relativistic. The Dirac equation can likely be used, but there seem to be very few publications on the relativistically corrected Bohr radius. This is something we will discuss.
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