Final answer:
The electron with quantum numbers n=4, l=1, ml=0, ms=+1/2 is in a 4p atomic orbital, corresponding to the second angular momentum quantum number value, which defines the shape of the orbital (b).
Step-by-step explanation:
An electron has the quantum numbers n = 4, l = 1, ml = 0, ms = + ½. These quantum numbers correspond to an electron in a 4p atomic orbital. The principal quantum number (n) indicates the energy level and for n=4, you can have s, p, d, or f orbitals.
The angular momentum quantum number (l) defines the shape of the orbital with l=0 for s orbitals, l=1 for p orbitals, l=2 for d orbitals, and l=3 for f orbitals. Since the given question has l=1, it clearly identifies the orbital as p. The magnetic quantum number (ml) specifies the orientation of the orbital, and ml=0 matches one of the possible orientations for a p-orbital. The spin quantum number (ms) can be either +1/2 or -1/2 and does not affect the type of orbital but rather the spin orientation of the electron. Thus, the correct answer is 4p.