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4-D Spheres
Name: Unknown
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: Around 1993
Question:
I was wondering if electron orbitals are really 4 dimensional (or
higher) spheres because d and p orbitals look similar to pictures I have seen
of 3-D projections of 4-D spheres. Any comments?
Replies:
Well, there might be something to your observation, but I have
never heard of this before. The equations describing p-orbitals, though, are
really pretty simple - basically the wave function amplitude is proportional
to x *f(r) (or y, or z) where r = sqrt(x^2 + y^2 + z^2) and f(r) is something
like an exponential e^(-a*r), although it has oscillations or higher n values.
The pictures normally shown are surfaces of constant amplitude; so solutions
of an equation of the form x * f(r) = constant. Since f(r) has spherical
symmetry, (it depends only on distance r from the nucleus) the angular
dependence of the surface is due to the factor x - the surface pokes out along
the x-axis, and comes in to the origin when it meets the x=0 plane.! Also, d-
orbitals are kind of similar, but instead of x have a factor x^2 - y^2, or
z^2, or xy, etc, so their extensions tend to be narrower (due to the higher
power) and more complicated.
A. Smith
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Update: June 2012
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