quantum number
Summary
A quantum number is one of four values (n, l, ml, ms) that together specify an electron's state in an atom: its shell, subshell shape, orbital orientation, and spin. The most testable point is that no two electrons in an atom can have the same set of all four (Pauli exclusion principle).
Detail
Meaning: Each electron in an atom is labeled by four quantum numbers. The principal number n (1, 2, 3, …) sets the shell, which fixes the energy and size of the orbital. The angular momentum number l sets the subshell and its shape: l = 0 is s, 1 is p, 2 is d, 3 is f. The magnetic number ml sets the orbital's orientation within the subshell. The spin number ms is +½ or −½.
Equation: l = 0, 1, …, n − 1; ml = −l, …, 0, …, +l; ms = +½ or −½. Here n is the principal number, l the angular momentum number, ml the magnetic number and ms the spin number. All are dimensionless, so they have no SI unit. A subshell has 2l + 1 orbitals, and a shell holds 2n² electrons.
On the MCAT: A question gives a set such as n = 3, l = 2, ml = −2, ms = +½ and asks whether it is allowed or which subshell it describes. Other questions ask you to count orbitals or electrons in a subshell, write a configuration, or find unpaired electrons to predict paramagnetism (Hund's rule).
Common confusion: Students let l equal n, such as n = 2, l = 2. This is forbidden, because l can be at most n − 1. A 2d subshell does not exist, and the first d subshell is 3d.
Sources
- Chemistry: A Molecular Approach
- Chemistry: The Central Science
- Chemistry (Zumdahl)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.