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 Click here to return to the Physics Archives

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