Time and atoms

I was wondering the following: Does time effect the nucleus and Electron differently? Since Electrons travel at extreme speeds while the nucleus is almost static? How does time effect the area between the two?

Yes, there are relativistic effects that influence the energy spectrum of the electron orbits. For instance, the higher orbits in the hydrogen atom correspond to 'higher velocities' of the electron, and there is a small correction in its energy (since for high velocities you don't have simply $$\frac{1}{2}mv^2$$ as a kinetic energy term anymore. These effects can be taken care of by working with the Dirac equation, which, to some degree, you can view as the relativistic version of the Schrodinger equation. This equation also includes the spin effects that the Schrodinger equations doesn't account for (so-called spin-orbit coupling).