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Unformatted text preview: ⇥)/r3 sin2 ⇥) = sin2 cos cos 2⇥ KEY # 2, p. 3 of 5 c. Plot the orbital function using 2-dimensional polar (r, θ) coordinates, fixing φ =
0°. How does the orbital phasing appear in the function and in your plot? You
may use a computer to generate the plot.
π π π π π π θ π π π π π π The blue and red regions represent positive and negative phases, respectively. d. To what does the plot at φ = 0° correspond in Cartesian coordinates?
φ = 0 rad corresponds to the xz plane in the Cartesian coordinate system. e. Is the orbital g or u symmetric? Prove this.
Substituting (–x, –y, –z) into the Cartesian orbital function: fz(x2 y2 ) ( x, y , z ) = z (x2 y 2 )/r3 = fz(x2 y 2 ) (x, y , z ) There orbital is u symmetric. f. Using the functional form of the fz(x2–y2) orbital (in either angular spheric...
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