Electromagnetic radiation is emitted by accelerating charges. The rate at which energy is emitted from a charge q with acceleration a is given by:
dE/dt = q2a2/6Πε0c3
where c is the speed of light. This equation, known as the Larmor formula, is a good approximation for charges moving at speeds which are small compared to c.
[A] Use the Larmor formula to calculate the classical expectation of the power emitted by a hydrogen atom in its ground state. For this purpose, consider the hydrogen atom to be composed of an electron orbiting a proton with a radius of 0.0529 nm with a kinetic energy of 13.6 eV.
[B] Qualitatively, what will happen to the orbit?
[C] What does your result tell you about the (classical) stability of hydrogen? How long would you expect hydrogen to survive under these conditions?