The gravitational attraction between electron and 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 by gravitational attraction. You will find the answer interesting.
The radius of first Bohr orbit is given by the relation:
……………(1)
Where ε0 is the absolute permittivity of free space and is given as = 8.854 × 10-12 N-1C2m-2
h is Planck’s constant and is given as 6.64 × 10-34 Js
e is charge on an electron and is equals to 1.6 × 10-19C
me is the mass of an electron, and is equals to 9.1 × 10-31 Kg
mp is the mass of proton and is equals to 1.67 × 10-27 Kg
The forces of coulomb attraction between an electron and proton is given by the relation: 
Gravitational forces of attraction between an electron and proton is given by the relation
Where G is the Gravitational constant and is equal to G = 6.67 × 10-11 N m2 Kg2
When coulomb force and Gravitational forces of attraction are equal
Or 
…………(1)
Substituting the values of equation (1) in equation (2), we get
Substituting the values, we get
On calculating, we get
∴ r1= 1.21 × 1029 m
Since Universe is 150billion light years wide, which concludes that the radius of first Bohr orbit is much greater than the size of the universe.