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2023-02-27

How many electrons in an atom may have the following quantum numbers? (a) n = 4, m=-1/2
(b) n = 3, l = 0

Nathan Franco

The given element has a fully filled orbital as
1s^22s^22p^63s^23p^64s^23d^10
1s22s22p63s23p64s23d10 1s^{ 2} 2s^{ 2} 2p^{ 6} 3s^{ 2} 3p^{ 6} 4s^{ 2} 3d^{ 10} Hence, all the electrons are paired.
Since there are a total of 32 electrons, there must be 16 orbitals, each of which contains two electrons with m values of -12 and 12. Therefore, there are 16 electrons with the quantum numbers n = 4 and m = 12, and the expression (b) n = 3 and l = 0 denotes the presence of the electrons in the 3s orbital. As a result, there are 2 electrons with n = 3 and l = 0.

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