Obtain an expression for the frequency of radiation emitted when a hydrogen atom de-excites from level n to level (n–1). For large n,show that this frequency equals the lassical frequency of revolution of the electron in the orbit.

Explanation

The first orbit Bohr’s model has a radius `a_0` given by `a_0 = (4 pi epsilon_0 (h//2pi)^2)/(m_e e^2)`. If we consider the atom bound by the gravitational force `(Gm_pm_e//r^2).` We should replace `(e^2/4 pi epsilon_0)` by `Gm_p m_e`. That is, the radius of the first Bohr orbit is given by `a_0^G = ((h//2pi)^2)/(Gm_p m_e^2) ~= 1.2 xx 10^(29) m`.
This is much greater than the estimated size of the whole universe!.