# What do n, l, and m_l tell us about an orbital?

Dec 13, 2016

The quantum numbers $n , l$, and ${m}_{l}$ determine the probability pattern of an orbital.

#### Explanation:

The wave function of an orbital (its probability pattern) is determined by three quantum numbers.

The principal quantum number $n$

The principal quantum number determines the size of an orbital and its probability pattern.

$n$ can take the values 1, 2, 3, etc.

The bigger the principal quantum number the bigger the orbital. The size of an orbital is roughly proportional to the value of ${n}^{2}$.

The azimuthal quantum number, $l$

The azimuthal quantum number determines the shape of an orbital.

If $l = 0$, the orbital is an $\text{s}$ orbital.

The probability pattern has the shape of a sphere, as in the above image.

If $l = 1$, the probability pattern has roughly the shape of a dumbbell. (From WebElements)

The picture does not show the relative sizes of the orbitals, but it does show their general shapes.

The magnetic quantum number ${m}_{l}$

The magnetic orbital determines the number of orbitals of a given type and the directions they point in a magnetic field.

For a $\text{p}$ orbital, there are three possible values of ${m}_{l}$.

Thus, there are three different $\text{p}$ orbitals, and they point in three different directions in a magnetic field (along the $x , y$, and $z$ axes).

We see the ${\text{p}}_{x}$ and ${\text{p}}_{z}$ orbitals and their probability patterns in the picture above.