How many #3d_(z^2)# orbitals have #n = 3# and #l = 2#?
1 Answer
Nov 9, 2016
You already specified an orbital, so... one...
The
#bb(n = 3)# , because the#3# in front says that. Thus, it is in the 3rd quantum level.#bb(l = 2)# , which corresponds to a#d# orbital, since the values of#l# correspond as#(0,1,2,3,4, . . . ) harr (s,p,d,f,g, . . . )# .#m_l# for this orbital is one of the values in the following set:#{-2,-1,0,+1,+2}# . It does not matter which one, but it is only one of them, since you have specified only one#d# orbital. That is,#m_l# is known, but is yours to choose, since all the#3d# orbitals in an atom are the same energy (degenerate).#m_s# requires more information to specify, but it can either be#pm"1/2"# in general. It depends on how many electrons were in that orbital to begin with, whether it's spin-up or spin-down for the electron of choice.
