The electron cloud of a stable atom is the superposition of the electron at it's given energy level. A charge in motion produces light. If we look for the electron at one point, it's probability of being there will be the square of of the wave function. Let's say we find it here, then move over there, and find it there (lucky us!). It has moved, right? It was at one location, now it's at another, that's motion, right? So, when it moved, shouldn't it have emitted light? Did it emit light? If so, what happened to it's energy level? Did it change? What of some other atom. Surely, if we looked, we might find it's electron here or there, and since it's moving around, ought it to be emitting light, constantly?
I beleive you have already answered your own question. According to Einstein's little theory in order for an object to emit (release) energy the other side of the equal sign must also decrease. This would suggest a loss of mass or speed. Since there is no loss of mass or speed (stable atom) there will be no emission of light. Do I Pass?
