Question

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

Answer 1

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 `"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 `"p"` orbital, there are three possible values of `m_l`.

Thus, there are three different `"p"` orbitals, and they point in three different directions in a magnetic field (along the `x, y`, and `z` axes).

We see the `"p"_x` and `"p"_z` orbitals and their probability patterns in the picture above.