# Does the angular momentum quantum number #l# designate the shape of the orbital?

##### 1 Answer

Basically yes. The **angular momentum quantum number** **magnetic quantum number**

But for the most part you can say that

If we take the

(Ignore the "

Looks like a

The **orbital angular momentum** in the ** don't** need to use on a General Chemistry test):

#color(blue)(hatL_z)Y_l^(m_l)(theta,phi) = color(blue)(m_lℏ)Y_l^m(theta,phi)#

What you should notice here is that *operator* for the z-direction, **corresponds to**

If

- The
#-1# refers to the lower cone on the above image. - The
#0# refers to a dot at the origin in the above image. It is also where the node is. - The
#+1# refers to the upper cone in the above image.

This tells us that **vector projection** of

Therefore, what you should notice is that **unique**, **orthogonal** (perpendicular) **orientations** there are for any orbital in that sublevel.

(The orthogonality is not crucial knowledge for General Chemistry, but it matters because a quantum mechanics postulate states that any orbital must be orthogonal to every other orbital in its sublevel.)

*Ultimately, since there are three values for* *there are three* *orbitals:* *and*