Atomic orbitals: 7p 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 (7 for the 7p orbitals)
Function | Equation |
---|---|
Radial wave function, R7px | = (1/11760√21) × ρ(6720 - 8400ρ + 3360ρ2 - 420ρ3 + 40ρ4 - ρ5) × Z3/2 × e-ρ/2 |
Angular wave function, Y7px | = √(3)x/r × (1/4π)1/2 |
Wave function, ψ7px | = R7px × Y7px |
Electron density | = ψ7px2 |
Radial distribution function | = r2R7px2 |
The corresponding radial equations for the 7py and 7pz orbitals are the same. The angular functions are the same but substitute y and z as appropriate in the formula for Y7px given above. Substitute similarly for the wave equations ψ7py and ψ7pz.
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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