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The answer lies in the understanding of the quantum model of the atom which is by far the most accurate to date. The classical model of the electron orbiting around the nucleus like the Earth does around the sun is an incorrect view. You can read about this at How Stuff Works or this question has been asked before.

 

http://www.scienceforums.net/forums/showthread.php?t=10263

http://science.howstuffworks.com/atom8.htm

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As mezarashi points out, the orbits are not planetary in nature. But you have an electrostatic force of attraction between the two, and the Heisenberg Uncertainty Principle precludes the electron from being bound to a region the size of a nucleus.

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