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What is the maximum number of electrons in an atom that can have the following quantum numbers?
(b) n=3 and ℓ =1;
(c) n=3 and and ℓ =1 and mℓ =0;
(d) n=3 and and ℓ =1 and mℓ =-1 and ms = -1/2;
Part (a): 8 electrons;
Part (b): 6 electrons;
Part (c): 2 electrons;
Part (d): 1 electron.
For a given principal quantum number n, there are a maximum total of 2n^2 electrons. Therefore, an n = 2 shell has a maximum total of 2 (2)^2 = 8 electrons.
For a given secondary (angular momentum) quantum number ℓ, there are a maximum total of 2 (2ℓ + 1) electrons. Therefore, an ℓ = 1 subshell has a maximum total of 2 [2 (1) + 1] = 6 electrons.
A set of three quantum numbers represents a specific orbital, which contains a maximum of two electrons with opposite spins.
A set of four quantum numbers represents an electron in a specific orbital with a specific spin. The Pauli exclusion principle states that no two electrons in an atom may have the same set of four quantum numbers. Therefore, this set of quantum numbers contains a maximum of one electron.