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

1 Answer
Dec 13, 2016

Answer:

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.

fc.deltasd.bc.ca

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.

p orbitals
(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.