An early (non-quantum) model of the hydrogen atom had a point-like electron undergoing uniform circular motion around a fixed proton at radius r = 5*10^11 m. The problem with this model is that the electron would radiate away all of its energy due to its centripetal acceleration v^2/r, and get sucked into the proton. (Luckily for us, this serious deficiency is fixed by quantum mechanics.)
Estimate (only to an order of magnitude) how long it would take for the atom to collapse - that is, how long does it take the initial kinetic energy of the electron ½ mev2 to be radiated away? You can assume that the power radiated is constant.
P=(q^2)*(a^2)/(6*pi*e*c^3) is the power radiated by a charge q moving with acceleration a.
F = q^2 / 4*pi*e*c^3 is Coulomb's Law, or the attractive force between the proton and electron.
q = 1.6 * 10^-19 C
e = 8.85 * 10^-12 F/m (permittivity of free space)
me = 9.11 * 10^-31 kg (electron mass)