5.2. The Quantum Mechanical Model http://www.ck12.org
FIGURE 5.16
Theporbitals are dumbbell-shaped. The
image on the left shows the electron den-
sity distribution for one of the orbitals,
while the next three images shows how
theporbitals are typically drawn. The
three differentporbitals are identical in
shape, but they can be oriented along the
x,y, orzaxis.FIGURE 5.17
The fivedorbitals have more complex
shapes. Four of them have a 4-lobed
appearance with different orientations,
while thedz^2 orbital has a more complex
shape.along thez-axis, which makes a 90° angle relative to the other two orbitals. In anypsublevel, there are always three
possible orbitals, so there are also three possible values of the magnetic quantum number:ml=−1,ml= 0, andml
= +1. There is no particular relationship between the coordinates (x,y, andz) and themlvalues.
There are five differentdorbitals within eachdsublevel. The corresponding magnetic quantum numbers areml=
−2,ml=−1,ml= 0,ml= +1, andml= +2. Finally, the pattern continues with thefsublevel, which contains seven
possibleforbitals andmlvalues ranging from−3 to +3. If we only consider atoms that are in their ground state, all
of the electrons in the atoms of every known element reside in orbitals that belong to one of these four sublevels.
Spin Quantum Number
Experiments show that electrons spin on their own internal axis, much as Earth does. The spinning of a charged
particle creates a magnetic field. The orientation of that magnetic field depends upon the direction that the electron
is spinning, either clockwise or counterclockwise. Thespin quantum numberis symbolized by the letter msand
indicates the direction of electron spin.The only possible values arems= +^12 andms=−^12. Each orbital, regardless
of its shape and orientation, can hold a maximum of two electrons, and any two electrons that occupy the same
orbital must have opposite spins. Listed below (Table5.2) is a summary of the first few energy levels and sublevels
along with the number of electrons that can potentially be contained by each state.