question_answer 12)

The gravitational attraction between electron and proton in a hydrogen atom is weaker than the coulomb attraction by a factor of about . 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:

If electron and proton were bound by gravitational attraction, then          ?(1) Also, according to Bohr's condition, Squaring both sides,                                                   ?(2) Dividing eqn. (2) by (1), or For 1st orbit, n = 1, Also, and   It is astonishing this value of r is much greater than the size of universe.