Stability of Atom: Why Electrons Don't Emit Radiation

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Every accelerated charge particle lose its engrgy in the form of electromagnetic wave but electron of an atom moving on stationary orbit do not emit any radiation. why? And why do accelerated charge particle lose energy in the form of electromagnetic radiation? Is there any relation between frequency of such radiation and acceleration??
 
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An electron bound in an energy eigenstate is not being accelerated, at least not in the usual sense of the word. At the atomic level, quantum mechanics are important and the electron does not move around the nucleus in a circle.
 
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