azimuthal quantum number

Meaning: The azimuthal quantum number l tells you which subshell an electron occupies within shell n, and so the shape of its orbital. l = 0 is s (spherical), l = 1 is p (dumbbell), l = 2 is d, and l = 3 is f. The number of angular nodes in the orbital equals l. In atoms with more than one electron, energy depends on both n and l, so within a shell the energy rises in the order s < p < d < f.

Equation: l = 0, 1, 2, …, n − 1, and ml = −l, …, 0, …, +l, so a subshell holds 2l + 1 orbitals. Here n is the principal quantum number and ml is the magnetic quantum number. All three are dimensionless integers. The orbital angular momentum has magnitude L = √(l(l + 1)) ħ, where L is in J·s and ħ = h/2π is in J·s.

On the MCAT: A question may give a set of quantum numbers and ask whether it is allowed, or name the subshell it describes. For example, (3, 1, 0, +½) is a 3p electron. You may also be asked to count orbitals or electrons in a subshell. A p subshell has 3 orbitals and holds 6 electrons.

Common confusion: Students mix up l, ml, and ms. l sets shape, ml sets orientation in space, and ms sets spin. Because l must be less than n, subshells such as 1p, 2d, and 3f cannot exist. Do not confuse l with n, which sets the shell and the overall size.