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

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

Calculate the ratio of gravity to electrical forces for a proton and an electron separated by distance equal to the Bohr radius, ${\displaystyle a_{0}\approx 0.526\times 10^{-10}m}$ , with the electron mass ${\displaystyle \approx 9.11\times 10^{-31}kg}$, and the proton mass ${\displaystyle \approx 1.671\times 10^{-27}kg}$. 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?