Final answer:
The correct answer represents one electron and is (4,0,1/2, 0), with the option C being correct assuming no spin orientation preference.Valence electrons of Mn in its ground state occupy the 4s subshell, with quantum numbers represented by (4, 0, 0, +1/2) or (4, 0, 0, -1/2).
Step-by-step explanation:
The valence electron in the ground state of Mn (manganese) has the quantum numbers that represent its energy level (n), angular momentum (l), magnetic (ml), and spin (ms) states. Using the rules of quantum mechanics, the valence electron of Mn in its ground state is in the 4s subshell, as Mn has an [Ar] 3d5 4s2 electron configuration and the 4s electrons are the last to fill and therefore are the valence electrons.
As such, the principal quantum number (n) for the valence electron is 4. For an s orbital, the angular momentum quantum number (l) is 0. The magnetic quantum number (ml) which can range from -l to +l, for an s orbital where l is 0, ml is also 0. Lastly, the spin quantum number (ms) can be either +1/2 or -1/2. Without any specific information to favor one or the other, we could have either spin state for the valence electron.
In summary, two possible sets of quantum numbers for one of Mn's valence electrons could be (4, 0, 0, +1/2) or (4, 0, 0, -1/2), corresponding to both possible spin states of the 4s electron. Therefore, the correct answer from the given options would be C) 4,0,1/2, 0 for one electron, with the understanding that the spin could also be -1/2 for the other electron in the 4s subshell.