A possible set of values for the four quantum numbers for the highest-energy electron in V4+ (Z = 23) is:

Question

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To determine the four quantum numbers for the highest-energy electron in V4+ (Z = 23), we first establish the electron configuration.
- Vanadium has 23 electrons in its neutral state. In V4+, four electrons are removed, giving 19 electrons total.
- The typical ground-state configuration for V4+ ends with a single electron in the 3d subshell, i.e., [Ar] 3d1. This means the highest-energy (outermost) electron resides in a 3d orbital with principal quantum number n = 3 and azimuthal quantum number l = 2.
Now, evaluate each option:
Option 1: n = 4, l = 2, ml = –2, ms = –1/2
- This would place the electron in the 4d subshell (n = 4, l = 2). Since the highest-energy electron is in the 3d shell (n = 3) for V4+ with configuration 3d1, this option places the electron in a higher principal quantum number than correct. It also conflicts with the actual valence shell for the highest-energy electron in this ion.
Option 2: n = 3, l = 0, ml = 0, ms = –1/2
- Here l = 0 corresponds to an s orbital (3s), not a d orbital. The highest-energy electron in V4+ occupies a d orbital (3d), so this option is inconsistent with the correct orbital type.
Option 3: n = 3, l = 1, ml = 0, ms = +1/2
- This describes a 3p electron (l = 1). But the outermost electron for V4+ is in 3d (l = 2), not 3p, making this option incorrect.
Option 4: n = 3, l = 2, ml = +1, ms = +1/2
- This exactly places the electron in the 3d subshell (n = 3, l = 2) with a permissible magnetic quantum number ml = +1 from the set {–2, –1, 0, +1, +2}, and an up-spin (ms = +1/2). Since there is a single 3d electron in V4+, this combination is consistent with the highest-energy electron being in a 3d orbital with a valid ml and ms.
Option 5: n = 4, l = 0, ml = 0, ms = –1/2
- This would correspond to a 4s electron. In V4+, the valence is 3d, not 4s, so this does not describe the highest-energy electron.
In summary, options 1, 2, 3, and 5 misplace either the principal quantum number, the subshell type, or both, relative to the known ground-state configuration of V4+ (3d1). Only option 4 correctly identifies the electron as residing in the 3d subshell with valid ml and ms values for the highest-energy electron in this ion.

A possible set of values for the four quantum numbers for the highest-energy electron in V4+ (Z = 23) is:

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