The gravitational attraction between an electron and a proton in a hydrogen atom is weaker than the coulomb attraction by a factor of about 10-40. An alternative way of looking at this fact is to estimate the radius of the first Bohr orbit of a hydrogen atom if the electron and proton were bound only by gravitational attraction.© BrainMass Inc. brainmass.com October 9, 2019, 3:25 pm ad1c9bdddf
Please see the attached file.
The radius of the nth orbit of the hydrogen atom using Bohr's model ...
Derivation of the required equations included in the attachment. Easy to understand solution.