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

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.

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.