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What is meant by "the energy of an electron is quantized"?
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this is a difficult concept to explain, in general, it means the amount cannot be any arbitrary amount and that it can only be a multiple of some minimum nonzero amount.
Another way to say it is that the energy comes in packets.
Well, sure. That's a very basic explanation that doesn't really explain mathematics behind it.
If they're looking for the total explanation I'd suggest Google or chemistry/physics books.
The energy is quantized in certain circumstances, such as in or from atomic shells, but can be continuous, such as for free electrons.
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