Very Small Physics 3

The founders of quantum mechanics largely ignored relativity when they first applied quantum theory to chemistry:

"The general theory of quantum mechanics is now almost complete... they give rise to difficulties only when high-speed particles are involved, and are therefore of no importance in the consideration of atomic and molecular structure and ordinary chemical reactions." - Paul Dirac, 1929

Treat an atom as a two-body problem with one electron and a central nucleus with a charge ZZ and a mass much greater than the electron.

Was Dirac correct? At what element in the periodic table would relativistic effects become important for an electron in a ground state?

Note: Significant errors start to appear between classical and relativistic dynamics when the Lorentz factor γ=11v2/c21.05\gamma = \frac{1}{\sqrt{1-v^2/c^2}} \geq 1.05. It may be useful to perform this calculation in atomic units, where ,e,me,\hbar, e, m_e, and 4πϵ04 \pi \epsilon_0 are defined as 1.1. In these units, the speed of light is c=137c = 137.

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