What is a quantum number set for Arsenic?

1 Answer
Dec 31, 2017

From the Pauli Exclusion Principle, arsenic can have up to #33# simultaneous sets of quantum numbers, and it's up to you which one you point your finger to... Which of the #33# electrons?

Well, I don't know, let's say we pick a #4s# electron for no reason other than it's there. Then for that electron...

  • It must be on the energy level given by #n = 4#.
  • #s# orbitals, spherically shaped, have zero angular momentum, so #l = 0#.
  • There can only be one #4s# orbital in existence. For #l = 0#, #m_l# is limited in range to only the set #{0}#. Each value of #m_l# corresponds to one orbital, and so there is only one.
  • Every electron can have either spin-up #1//2# or spin-down #1//2# for the value of #m_s#. Since this orbital is filled already, there is not just one choice.

Thus, one has two options for a #4s# electron.

#(n,l,m_l,m_s) = (4,0,0,+1/2)#

#(n,l,m_l,m_s) = (4,0,0,-1/2)#

Maybe you can brainstorm the other #31# on your own time.