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I'm just looking for clarification - is the number of electrons that can occupy a given orbital equal to the number of possible values of m times 2?
Only 2 electrons can occupy a single orbital, one electron will be spinning up while the other spins down.
Yeah it will never be more than two electrons in a single orbital, it will just start to fill another.
To find the total number of electrons in a subshell, l, you multiply the total number of mls by 2. If you need to find the total number of electrons in a shell, n, you can easily use the formula 2n2. And Chiara is correct that the total number of electrons in an orbital, ml, is always 2. Be careful of the terminology that questions use, because it will change your answer.
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