Question #64fc6

1 Answer
Jun 12, 2017

Answer:

#"3 e"^(-)#

Explanation:

The idea here is that each individual orbital can hold a maximum of #2# electrons, one having spin-up, or #m_2 = +1/2#, and the other having spin-down, or #m_s = -1/2#.

This implies that in order to figure out how many electrons that are located in the #2p# subshell can have #m_2 = -1/2#, you must determine how many orbitals are present in this subshell.

As you know, the number of orbitals present in a given subshell #l# is given by the number of values that the magnetic quantum number, #m_l#, can take.

#m_l = {-l, -(l-1), ..., -1, 0, 1, ..., (l-1), l}#

In your case, you are dealing with a #p# subshell, so you should know that #l=1# since you have

  • #l = 0-># the s subshell
  • #l=1 -># the p subshell
  • #l=2 -># the d subshell

and so on. This means that any #p# subshell, including the #2p# subshell, which is simply the #p# subshell located on the second energy level, will have

#m_l = (-1,0,1}#

So, three values for #m_l# give you #3# orbitals for any #p# subshell.

Now, you know that you get a maximum of #2# electrons per orbital, but that only #1# electron can have #m_2 = -1/2# in an orbital--the other electron located in the same orbital must have #m_2 = +1/2#.

This means that you have

#3 color(red)(cancel(color(black)("2p orbitals"))) * ("1 e"^(-)color(white)(.)"with m"_s = -1/2)/(1color(red)(cancel(color(black)("2p orbital")))) = "3 e"^(-)# #"with m"_s = -1/2#