Which of the following set of quantum numbers describe an electron? Which is/are not?
Elaborate your answer why.

(a) n = 3, l = 2, ml = −3, ms = −1⁄2
(b) n = 0, l = 0, ml = 0, ms = +1⁄2
(c) n = 4, l = 2, ml = −1, ms = 0
(d) n = 3, l = 1, ml = −1, ms = +1⁄2
(e) n = 4, l = −3, ml = −1, ms = +1
(f) none

Note that the first number is the principal quantum number (n); the second number is the angular momentum quantum number (l); the third number is the magnetic quantum number (ml); the last number is the spin quantum number (ms).

Keep in mind that the possible values for each quantum number are as follows:

n = 1, 2, 3, ...
l = 0 to (n - 1)
ml = -l to l
ms = +1/2, -1/2

> In (a), the value of ml must be -2, -1, 0, 1, or 2 because the value of l is 2. Since the value of ml here is -3, it does not describe an electron.

> In (b), the value of n must be a positive integer. Since the value of n here is 0, it does not describe an electron.

> In (c), the value of ms must be +1/2 or -1/2. Since the value of ms here is 0, it does not describe an electron.

> In (e), the value of ms must be +1/2 or -1/2. Since the value of ms here is +1, it does not describe an electron.

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