The values of Quantum numbers for the 5th electron of boron and last entering electron of potassium?

Elements on the second row of the periodic table occupy #n = 2# orbitals, and boron has three valence electrons, occupying #2s# and #2p# orbital(s). Potassium on the other hand, is on the fourth row (occupies only an #s# orbital with #n = 4#) and has one valence electron.

Boron only has 5 electrons, so two of them go into the #1s#, two into the #2s#, and one into a #2p# orbital.

#underbrace(ul(uarr color(white)(darr))" "ul(color(white)(uarr darr))" "ul(color(white)(uarr darr)))_(2p)#

#underbrace(ul(uarr darr))_(2s)#

#" "#
#" "#
#" "#
#" "#
#" "#
#" "#

#underbrace(ul(uarr darr))_(1s)#

• Any #color(blue)(2)p# orbital has #color(blue)(n = 2)# (given in the name).
• All #p# atomic orbitals have angular momenta of #color(blue)(l = 1)#, seeing as #l = 0, color(blue)(1), 2, 3 harr s, color(blue)(p), d, f#.
• The z-projection of the angular momentum can only take on values #{-l, -l+1, . . . , l-1, l}#, so #color(blue)(m_l = {-1,0,+1})# are your options.
• The electron can be spin up or down, and being a fermion, it is a spin-half particle. So we have #color(blue)(m_s = +1/2)# (by convention).

When you figure out how to define the #4s# orbital of potassium, you should say what you think the quantum numbers are for the unpaired electron...