What are the quantum numbers for the 9th electron in flourine?

1 Answer
Nov 22, 2017

Answer:

#n = 2, l =1, m_l = 0, m_s = -1/2#

Explanation:

You know that fluorine has an atomic number equal to #9#, which means that the #"9th"# electron in an atom of fluorine is the last one added when "constructing" the neutral atom of fluorine.

Fluorine is located in period #2# of the Periodic Table, which implies that the #"9th"# electron in fluorine is located on the second energy level.

Consequently, you can say that this electron will have a principal quantum number, #n#, which describes the energy level on which an electron is located in an atom, equal to

#n = 2#

Now, fluorine is located in group #17# of the Periodic Table, which means that fluorine is part of the #p# block.

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This implies that the angular momentum quantum number, #l#, which describes the energy subshell in which the electron is located, will be equal to

#l = 1#

This is the case because you have

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

and so on. Next, for the #p# subshell, the magnetic quantum number, #m_l#, which tells you the orientation of the orbital in which the electron is located, will be equal to

#m_l = {-1, 0, +1}#

By convention, you have

  • #m_l = -1 -># describes the #p_y# orbital #-># corresponds to groups #13# and #16#
  • #m_l = color(white)(-)0 -># describes the #p_z# orbital corresponds to groups #14# and #17#
  • #m_l = +1 -># descrbes the #p_x# orbital corresponds to groups #15# and #18#

Since the #"9th"# electron corresponds to group #17#, you can say that it will have

#m_l = 0#

This electron will be added to the #2p_z# orbital, which is the #p_z# orbital located on the second energy level.

Finally, the spin quantum number, #m_s#, which tells you the spin of the electron, can take two possible values

#m_s = {+1/2, - 1/2}#

Now, the #"9th"# electron will have

#m_s = -1/2#

because, by convention, electrons added to a half-filled orbital are assigned spin-down. The #p_z# orbital is half-filled because of Pauli's Exclusion Principle, which states that all three #p# orbitals must be half-filled before any of them can be filled completely.

You can thus say that the full quantum number set that describes the #"9th"# electron in an atom of fluorine will be

#n = 2, l =1, m_l = 0, m_s = -1/2#

The electron is located on the second energy level, in the #2p# subshell, in the #2p_z# orbital, and has spin-down