Explicit expressions for hydrogenic orbitals are given in Tables 10.1 and 9.3. (a) Verify both that the

Question:

Explicit expressions for hydrogenic orbitals are given in Tables 10.1 and 9.3.
(a) Verify both that the 3px orbital is normalized (to I) and that 3px and 3dxy are mutually orthogonal.
(b) Determine the positions of both the radial nodes and nodal planes of the 35, 3px' and 3dxy orbitals.
(c) Determine the mean radius of the 35 orbital.
(d) Draw a graph of the radial function for the three orbitals(of part
(b) And discuss the significance of the graphs for interpreting the properties of many-electron atoms.
(e) Create both xy-plane polar plots and boundary surface plots for these orbitals. Construct the boundary plots so that the distance from the origin to the surface is the absolute value of the angular part of the wave function. Compare the 5, p, and d boundary surface plots with that of an [-orbital; e.g. Ψ= x (5z2 - r2) cc sin θ (5 cos2 θ-l) cos Φ. Distribution
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