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.

Radius of the first Bohr orbit is given by the relation, Where, ∈0= Permittivity of free space h= Planck’s constant = 6.63 × 10−34Js me= Mass of an electron = 9.1 × 10−31kg e= Charge of an electron = 1.9 × 10−19C mp= Mass of a proton = 1.67 × 10−27kg r= Distance between the electron and the proton Coulomb attraction between an electron and a proton is given as: Gravitational force of attraction between an electron and a proton is given as: Where, G = Gravitational constant = 6.67 × 10−11N m2/kg2 If the electrostatic (Coulomb) force and the gravitational force between an electron and a proton are equal, then we can write: ∴FG=FC Putting the value of equation (4) in equation (1), we get: It is known that the universe is 156 billion light years wide or 1.5 × 1027m wide. Hence, we can conclude that the radius of the first Bohr orbit is much greater than the estimated size of the whole universe. read less