James Clerk Maxwell established the equations for the dynamics of electrical and magnetic fields. In the 1890's J.J. Larmor and other physicists presented an agument that those equations implied that charged particles undergoing acceleration should emit electromagnetic radiation. The electrons and protons in atoms apparently traveling in orbits undergo acceleration in the sense that their momentua vectors are continually changing in their curved trajectories. This enigma has been troubling quantum physicists since that time.

The analysis seemed rigorous but empirically the effect was not occuring. The answer is simple.

The Larmor Effect is derived for point particles and depends upon the square of the charge. If a charge of Q is distributed over M points then the M points radiate an amount proportional to (Q/M)² for a total of Q²/M. If M goes to infinity, as it would for a spatially distributed charge no matter how small the region of distribution, then the radiation goes to zero. A spatially distributed charge does not radiate. Period.

For the detailed analysis of this topic see Quantum EM.