Atomic orbitals: 4p equations
The symbols used in the following are:
- r = radius expressed in atomic units (1 Bohr radius = 52.9 pm)
- π = 3.14159 approximately
- e = 2.71828 approximately
- Z = effective nuclear charge for that orbital in that atom.
- ρ = 2Zr/n where n is the principal quantum number (4 for the 4p orbitals)
The corresponding radial equations for the 4py and 4pz orbitals are the same. The angular functions are the same but substitute y and z as appropriate in the formula for Y4px given above. Substitute similarly for the wave equations ψ4py and ψ4pz.
For s-orbitals the radial distribution function is given by 4πr2ψ2, but for non-spherical orbitals (where the orbital angular momentum quantum number l > 0) the expression is as above. See D.F. Shriver and P.W. Atkins, Inorganic Chemistry, 3rd edition, Oxford, 1999, page 15.