Quantum Numbers
Chem12A, Organic Chemistry I
Quantum numbers work like addresses for electrons in an atom. To narrow down your intended
recipient, you would write the state city street street number to tell the post office
where to go. Quantum numbers work the same way: energy level type of orbital
orientation of orbital orientation of electron. Every electron in an atom will have a unique
set of quantum numbers in the form [n, l, ml, ms].
Principal Quantum Number (n = 1, 2, 3, 4, …∞)
The principal quantum number, n, defines the energy level or shell
of the electron. It is the first quantum number that must be
determined, as it defines the available values for all other quantum
numbers. Think of Bohr’s model for the atom; n defines the ring on
which the electron resides.
The value of n tells you how many levels away from the nucleus the electron is. The valence shell
of an atom is the highest occupied shell and is mathematically equivalent to the period of the
element (i.e., H is in period 1, so the valence shell for H is n = 1).
Azimuthal (Angular Momentum) Quantum Number (l = 0, 1, 2, …(n-1) )
The azimuthal, or angular momentum, quantum number, l, defines the type or shape of the
orbital where the electron most probably resides. It is the second quantum number to be
determined as its value relies only on n (i.e., if n = 2, then l = 0 or 1 since n – 1 = 1). Each type of
orbital has a unique number of nodes (e.g., where the wave changes phases) which is
mathematically equivalent to l.
If l = 0, the electron is in an s-orbital that has 0 nodes.
If l = 1, the electron is in a p-orbital that has 1 node.
If l = 2, the electron is in a d-orbital that has 2 nodes.
If l = 3, the electron is in an f-orbital that has 3 nodes.
s-orbital
p-orbital
d-orbital
f-orbital
