Atoms - Part 6 - Orbitals
The third quantum number ml has the range -l to l. Thus for l = 0 there is only one value for ml (0). For l= 1 there can be three values for ml (-1, 0 or 1). For l = 2, ml can have five values (-2, -1, 0, 1 or 2). For l = 3, ml can have seven values (-3, -2, -1, 0, 1, 2 or 3).
Thus for the s orbital there is only one value for ml. For a p orbital there are three orientations. For a d orbital there are five orientations. For an f orbital there are seven orientations.
| orbital | s | p | d | f |
| orientations | 1 | 3 | 5 | 7 |
There is a fourth quantum number ms. This is called the spin quantum number. It can have two values, +½ and -½. This is because an electron can orient in two ways in an applied magnetic field. You might imagine two spinning electrons with the N pole upward, one spinning one way, the other spinning the opposite way. Thus an orbital specified by the first three quantum numbers can be occupied by only two electrons with ms = ½ and ms = -½.
The "location" of an electron is described in terms of the probability of finding the electron in a particular position relative to the nucleus. The shapes of orbitals are described by surfaces through regions of equal probability. The shapes most commonly used are those that include 99% probability.
An s orbital is spherical as illustrated below (Figure 15).
Figure 15.
A p orbital has two lobes separated by a nodal plane where the probability is zero. There are three orientations available for a p orbital. They are named pz, py and px. These are shown below (Figure 16).
Figure 16.
A d orbital has four lobes. The probability is zero between the lobes. There are five possible orientations. Three are shown below (Figure 17).
Figure 17.
Below are the other two possible orientations of d orbitals (Figure 18).
Figure 18.
The seven f orbitals are so complex in form that I have not tried to draw them.