Q 12.12 The gravitational attraction between electron and proton in a hydrogen atom is weaker than the coulomb attraction by a factor of about . 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 by gravitational attraction. You will find the answer interesting.
As per the bohrs model
(i)
If the proton and the electron were bound only by the gravity the gravitational force between them will provide the centripetal force required for circular motion
(ii)
From equation (i) and (ii) we can calculate that the radius of the ground state (for n=1) will be
The above value is larger in order than the diameter of the observable universe. This shows how very weak the gravitational forces of attraction are as compared to electrostatic forces.