Atomic orbitals: 3p 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 (3 for the 3p orbitals)
Function | Equation |
---|---|
Radial wave function, R3px | = (1/9√6) × ρ(4 - ρ) × Z3/2 × e-ρ/2 |
Angular wave function, Y3px | = √(3)x/r × (1/4π)1/2 |
Wave function, ψ3px | = R3px × Y3px |
Electron density | = ψ3px2 |
Radial distribution function | = r2R3px2 |
The radial equation for the 3px, 3py, and 3pz orbitals is the same in each case. The angular functions are the same but substitute y and z as appropriate in the formula for Y3px given above. Substitute similarly for the wave equations ψ3py and ψ3pz.
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.
The OrbitronTM, a gallery of orbitals on the WWW: https://winter.group.shef.ac.uk/orbitron/
Copyright 2002-2023 Prof. Mark Winter [The University of Sheffield]. All rights reserved.