Question

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.

Answer 1

Let m_e and m_p be the masses of electron and proton respectively. If the electron and proton were bound only by gravitational attraction, then

According to Bohr’s quantisation conditions,angular momentum of the electron.