Physics equations/18-Electric charge and field/A:ElectricFieldGravityCompare

This is a good warmup activity before a lab:

Consider the electric and gravitational fields for the electron in the hydrogen atom at Earth's surface

$F_{G}=G{\frac {mM}{r^{2}}}\,$ , where $G\approx 6.674\times 10^{-11}\ m^{3}\ kg^{-1}\ s^{-2}$

Calculate the ratio of gravity to electrical forces for a proton and an electron separated by distance equal to the Bohr radius, $a_{0}\approx 0.526\times 10^{-10}m$ , with the electron mass $\approx 9.11\times 10^{-31}kg$, and the proton mass $\approx 1.671\times 10^{-27}kg$. The ratio F/F_G is about 2x10³⁹, a large large number.

1. Perform this calculation.
2. What does this say about the importance of Earth's gravity in calculating electron energy levels?