What are m and s for a #3p# electron?

1 Answer
Jan 6, 2015

Could you be referring to the quantum numbers #m_l# and #m_s#, corresponding maybe to the electrons in a 3p-orbital?

Let's assume you are talking about chlorine, which has an electron configuration

#"Cl": ["Ne"]3s^(2)3p^5#

and you want to determine the magnetic quantum number, #m_l#, and the spin quantum number, #m_s#, for the unpaired electron sitting in a 3p-orbital.

Since you are dealing with a 3p-orbital, your principal and angular momentum quantum numbers will be #n=3# and #l=1#.

The magnetic quantum number can only take integer values ranging from #-l# to #+l#, so you have three possible values for #m_l#:

#m_l =-1#, #m_l = 0#, and #m_l = +1#,

each corresponding to one of the three 3p-orbitals #3p_x#, #3p_y#, and #3p_z#. Let's ssume that

#"Cl": ["Ne"]3s^(2)3p_x^(2)3p_y^(2)3p_z^(1)#

In this case, the unpaired electron can be found in the #3p_z# orbital, which corresponds to #m_l = +1#.

Since the spin quantum number can only be #-1/2# or #+1/2#, and since no electrons are already present to influence the spin, let's assume your electron has a positive spin, #+1/2#.

So, the quantum numbers that describe chlorine' unpaired electron are:

#n=3#
#l=1#
#m_l = +1#
#m_s = +1/2#