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 epsi_(0)(h//2pi)^(2))/(m_(e)e^(2))`
If we consider the atom bound by the gravitational force
`=((Gm_(p)m_(e))/(r^(2)))`. Whe should replace `(e^(2))/(2pi epsi_(0))` by `(Gm_(p)m_(e))`. In that case radius of first Bohr orbit of hydrogen atom wold be given by `r_(0)=((h//2pi)^(2))/(Gm_(p)m^(2)e)` 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)` metre.
This is much greater than the estimated size of the whole universe !