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.

Explanation

The radius of the first Bohr orbit of a hydrogen atom is `r_0=(4pi in_0(h//2pi)^2)/(m_e e^2)`
If we consider the atom bound by the gravitational force=`((Gm_(p) m_e)/(r^2))`, we should replace `(e^2)/(4pi in_0)` by `(Gm_(p) m_(e))`. In that case, radius of first Bohr orbit of hydrogen atom would be given by `r_0=((h//2pi)^2)/(Gm_(p) m_e^2)` Putting the standard values, we get `r_0=((6.6xx10^(-34)//2pi)^2)/(6.67xx10^(-11)xx1.67xx10^(-27)xx(9.1xx10^(-31))^2)=1.2xx10^(29) meter`. This is much greater than the estimated size of the whole universe!