Assume that structure of hydrogen atom is gov- erned by classical mechanics. An electron is circulating around a proton and it is radiating energy at a rate given `(dE)/(dt) = (e^(2)a^(2))/(6pic^(3)in_(0))` where a is the acceleration of the electron.
Assume that speed of the electron is `v (gt gt c)`.
(a) Estimate the fraction of kinetic energy lost by the electron per revolution in terms of v. Make suitable assumptions.
(b) Is the energy loss per revolution large? Is it safe to assume that orbit is circular during a small time interval?

Answer

(a) `(8pi)/(3)((v)/(c))^(3)` , (b) No, Yes