The four quantum numbers for an atom refer to the state of the valence or outermost electron.
The four numbers are:
#n# is the distance of the electron from the nucleus, and can be #1, 2, 3, 4# etc,
#l# is the shape of the orbital of the electron, from #0# to #n-1#
#m_l# is the orientation of the orbital, ranging from #-l# to #+l#, and
#m_s# is the spin property of the electron, either #+1/2# or #-1/2#
For a potassium atom, the electron configuration is #1s^2 2s^2 2p^6 3s^2 3p^6 4s^1#, which means that #n = 4#.
It also means that, since the outermost electron is in an #s# orbital, #l = 0#.
#m_l# can range from #-l# to #+l#, but if #l = 0# because it is an #s# orbital, then #m_l# must be #0#, too.
#m_s# can be either #+1/2# or #-1/2#, depending on the spin of the electron, it doesn't particularly matter in this case.
Therefore, the full set of quantum numbers for a #K# atom is #4, 0, 0, +-1/2#
