Which statement correctly describes the four quantum numbers (n, l, ml, ms) and their possible values?

• A. n = 1, 2, 3, ...; l = 0 for s, 1 for p, 2 for d, 3 for f; ml = -l, ..., +l; ms = +1/2 or -1/2.
• B. n = 0, 1, 2, ...; l = 0, 1, 2, ...; ml = -l, ..., +l; ms = +1/2 or -1/2.
• C. n = 1, 2, 3, ...; l = 0 or 1 or 2 only; ml = -l to +l; ms = ±1/2.
• D. n = 1, 2, 3, ...; l can be any integer; ml any integer; ms = ±1/2.

Answer: (A)

The four quantum numbers describe an electron’s state: n sets the energy level, l is the orbital angular momentum, ml is the orientation of that angular momentum, and ms is the spin. n can be any positive integer starting at 1. For a given n, l can be 0 up to n−1, with the common subshell mapping l = 0 for s, 1 for p, 2 for d, and 3 for f. For each l, ml can take integer values from −l to +l, giving the different magnetic orientations. The spin quantum number ms can only be +1/2 or −1/2.

So the statement that lists n = 1, 2, 3, ...; l = 0 for s, 1 for p, 2 for d, 3 for f; ml = −l, ..., +l; ms = ±1/2 correctly captures these allowed values and the subshell mapping. The other choices fail because they allow n = 0, omit the n−1 limit on l, omit the s/p/d/f correspondence, or let l and ml take arbitrary integers that aren’t restricted by n.