A relativistic particle of charge Q and mass M is moving in uniform circular motion bound by a radial potential. We learned from Eq. (8.167) that the charge will lose energy to electromagnetic radiation. Assuming that this loss of energy is slow, we can describe the particle as gradually spiraling towards \(r=0\) while maintaining constant angular momentum. Apply this treatment to the ground state of the Hydrogen atom, where the atomic radius is about one Angstrom \(\left(10^{-10} \mathrm{~m}\right)\); and estimate the time it takes for the electron to crash into the nucleus. Are you surprised? Why does this not happen?