Question #d02f6

1 Answer
Stefan V.
Oct 7, 2017

Here's what I got.

Explanation:

For starters, you know that the energy shell in which an electron is located inside an atom is given by the principal quantum number, #n#.

In your case, you have

#n = 4#

Now, the energy subshell in which an electron is located is given by the angular momentum quantum number, #l#.

The #d# subshell, which is the subshell that contains the #d# orbitals, is given by

#l = 2#

The orientation of an orbital located in a given subshell #l# is given by the magnetic quantum number, #m_l#.

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

The #d# subshell contains a total of #5# orbitals, each described by a different value of the magnetic quantum number

#m_l = {-2, 1, 0, +1, + 2}#

Finally, the spin quantum number, #m_s#, tells you the spin of an electron inside an orbital.

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

You can now write the quantum number sets that can describe an electron located in the #"4th"# energy shell, in the #4d# subshell.

I'll give you several examples to go by

  • #n = 4, l= 2, m_l = -2, m_s = +1/2#
  • #n = 4, l= 2, m_l = -2, m_s = -1/2#
  • #n = 4, l= 2, m_l = 0, m_s = -1/2#
  • #n = 4, l= 2, m_l = +1, m_s = +1/2#
  • #n = 4, l= 2, m_l = +2, m_s = -1/2#
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