How many electrons in an atom may have the following quantum numbers? (a) n = 4, ms = – ½ (b) n = 3, l = 0

 How many electrons in an atom may have the following quantum numbers?
(a) n = 4, ms = – ½ (b) n = 3, l = 0
Answer
(a) Total number of electrons in an atom for a value of n = 2n² ∴ For n = 4,
Total number of electrons = 2 (4) ² = 32
The given element has a fully filled orbital as 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰.
Hence, all the electrons are paired.
∴ Number of electrons (having n = 4 and m = - 1/2 ) = 16
(b) n = 3, l = 0 indicates that the electrons are present in the 3s orbital. Therefore, the number of electrons having n = 3 and l = 0 is 2.