Electrodynamics and Relativity — David J. Griffiths
Physics · radiation-from-point-charges
Problem
In Bohr's theory of hydrogen, the electron in its ground state was supposed to travel in a circle of radius 5×10−11 m, held in orbit by the Coulomb attraction of the proton. According to classical electrodynamics, this electron should radiate, and hence spiral in to the nucleus. Show that v≪c for most of the trip (so you can use the Larmor formula), and calculate the lifespan of Bohr's atom. (Assume each revolution is essentially circular.)