What is a combination of four quantum numbers that could be assigned to an electron occupying a 5p orbital?

1 Answer
Nov 11, 2015

Here's what I got.


As you know, you need four quantum numbers to describe the exact location of an electron in a atom and its spin.


The principal quantum number, #n#, describes the energy level on which the electron resides. In your case, an electron that can occupy a 5p-orbital will have its principal quantum number equal to #5#

#n = 5 -># the electron is located on the fifth energy level

The angular momentum quantum number, #l#, describes the subshell in which the energy can be found. For the fifth energy level, #l# can take values in the range

#l = 0, 1, 2, 3, 4#

Now, as its name suggests, a 5p-orbital will be located in a p-subshell, which is characterized by #l=1#.

#l = 1 -># the electron is located in the 5p-subshell

The magnetic quantum number, #m_l#, tells you the exact orbital in which the electron can be found. A p-subshell can have three orbitals, regardless of energy level.

This means that you have three possibilities here, since the exact orbital is not specified by the problem

#m_l = {-1, 0, 1} -># the electron can reside in any of the three 5p-orbitals

Finally, the spin quantum number, #m_s#, which describes the spin of the electron, can only have two possible values, #+1/2# for spin-up and #-1/2# for spin-down.

This means that an electron residing in a 5p-orbital can have

#m_s = {+1/2, -1/2} -># either spin-up or spin-down

So, one set of quantum numbers that can describe an electron located in a 5p-orbital is

#n=5, l=1, m_l = -1, m_s = +1/2#

This electron is located on the fifth energy level, in the 5p-subshell, in the #5p_x# orbital, and has spin-up.

There are a total of six sets of quantum numbers that can be used here.