Take the Bohr solar system model of a hydrogen atom, with a proton at the center and an electron orbiting it. For simplicity assume that orbits are always circular (v dot a = 0) and that the proton is fixed, and starts at one Bohr radius (r_b ~ 0.05 nm) from the proton with an appropriate velocity for circular orbit (is this velocity relativistic?)

To nearest order of magnitude how long will it take before the electron reaches the proton due to classical radiation? What's the formula?

Disregard quantum mechanics (this is meant to demonstrate the need for quantum mechanics).

Hint 1

Hint 2 - if you haven't taken a course on electromagnetics

Math Difficulty Spoiler

(This is a pretty classic problem that I had in grad school. I've written up a solution, but I wont' post it just yet.)