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There are many qualitative features to notice about these wave functions, some of
which are familiar to even beginning students of chemistry, and some of which are only
clear with our quantum mechanics background upon which now to draw. Let’s focus on
the most important:
1.
s orbitals are radially symmetric, p orbitals are axially symmetric, d orbitals have
alternating fourfold symmetry, etc.
2.
The exponential radial decay of a hydrogenic wave function depends inversely on
the principle quantum number.
3.
The orbital energy for a given atom having atomic number
Z
depends only on the
principle quantum number
n
(see eq. 1334). Thus, all wave functions having the
same principle quantum number are degenerate in energy
irrespective of whether
they are s, p, or d
, etc. Each principle quantum level has a total degeneracy of
n
2
.
(Count up the first few if you don’t see this).
4.
Because of the incorporation of the spherical harmonics in the wave functions, we
may use either complex or real forms. The complex forms are eigenfunctions of
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 Spring '08
 Staff
 Atomic orbital, wave functions, principle quantum number

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