Enter a principal quantum number n (1 to 8) to see its subshells, the number of orbitals in each, the total of n² orbitals and the 2n² electrons the shell can hold.
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From the article Quantum Numbers n, l, m, s — Allowed Values and What Each Controls.
Question: Which of these sets are permitted?
(a) n = 2, l = 2, ml = 0, ms = +½
(b) n = 3, l = 2, ml = −3, ms = −½
(c) n = 4, l = 3, ml = +2, ms = +½
(d) n = 0, l = 0, ml = 0, ms = +½
(a) Not allowed. l must be at most n − 1 = 1; there is no 2d subshell.
(b) Not allowed. With l = 2, ml may only be −2 to +2.
(c) Allowed. n = 4 so l may be 0–3 ✓; l = 3 so ml may be −3 to +3, and +2 is inside ✓; ms = +½ ✓. An electron in a 4f orbital.
(d) Not allowed. n starts at 1; there is no shell zero.
Method: check the chain in order — n, then l against n, then ml against l, then ms. Stop at the first failure.
Worked in full in Quantum Numbers n, l, m, s — Allowed Values and What Each Controls.
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