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We have learned from the subject of quantum mechanics that energy exists in discrete packages called quanta. You cannot have a half a quantum of energy, the universe is not constucted that way. The farther an electron is from the nucleus, the more potential energy it has (in the same way that an elevated object has gravitational potential energy) and that energy comes in specific quanta. Therefore, electrons can only have specific orbital distances. Any other distance would require a fraction of a quantum of energy, which is not allowed.

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