A simple concise relativistic modification of the standard Bohr model for hydrogen-like atoms with circular orbits is presented. As the derivation requires basic knowledge of classical and relativistic mechanics, it can be taught in standard courses in modern physics and introductory quantum mechanics. In addition, it can be shown in a class that one straightforward prediction of this relativistic version of Bohr's model is the impossibility of finding atoms in nature with atomic number larger than a critical value. (Contains 1 figure and 1 footnote.)