The value of
ℓ can = 0, 1,
... , n − 1
ℓ = 0
indicates a
spherical-
shaped s
orbital
ℓ = 1,
indicates a
dumbbell-
shaped p
orbital
ℓ = 2,
indicates a
five
orbital
orientation
d orbital
This number refers to the shape of the orbital. The number of
possible shapes is limited by the principal quantum number. The
first energy level has only one possible shape, the s orbital because
n = 1 and the limit of ℓ = (n − 1) = 0. The second has two possible
shapes, the s and p. See Figures 8a and 8b for representations of
these shapes.Magnetic
quantum
number (mℓ)
s = 1 space-
oriented
orbital
p = 3 space-
oriented
orbitals
d = 5 space-
oriented
orbitals
f = 7 space-
oriented
orbitals
The value of
m, can
equal
−ℓ,... 0...
- ℓ.
Spin
quantum
The drawings in Figure 8a show the s-orbital shape, which is a
sphere, and the p orbitals, which have dumbbell shapes with three
possible orientations on the axis shown. The number of spatial
orientations of orbitals is referred to as the magnetic quantum
number. The possible orientations are listed. Figure 8b represents
the d orbitals. Electrons are assigned one more quantum number
called the spin quantum number. This describes the spin in either of
two possible directions. Each orbital can be filled by only two
electrons with opposite spins. The main significance of electron
spin is explained by the postulate of Wolfgang Pauli. It states that in
a given atom no two electrons can have the same set of four
quantum numbers (n, ℓ, mℓ, and ms). This is referred to as the Pauli
Exclusion Principle. Therefore, each orbital in Figures 8a and 8b
can hold only two electrons.