Atomic orbitals: 5p 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 (5 for the 5p orbitals)
Function | Equation |
---|---|
Radial wave function, R5px | = (1/150√30) × ρ(120 - 90ρ + 18ρ2 - ρ3) × Z3/2 × e-ρ/2 |
Angular wave function, Y5px | = √(3)x/r × (1/4π)1/2 |
Wave function, ψ5px | = R5px × Y5px |
Electron density | = ψ5px2 |
Radial distribution function | = r2R5px2 |
The corresponding radial equations for the 5py and 5pz orbitals are the same. The angular functions are the same but substitute y and z as appropriate in the formula for Y5px given above. Substitute similarly for the wave equations ψ5py and ψ5pz.
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.
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