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# Atomic orbitals: 6p 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 (6 for the 6p orbitals)
Table of equations for the 6p orbital.
Function Equation
Radial wave function, R6px = (1/432√210) × ρ(840 - 840ρ + 252ρ2 - 28ρ3 + ρ4) × Z3/2 × e-ρ/2
Angular wave function, Y6px = √(3)x/r × (1/4π)1/2
Wave function, ψ6px = R6px × Y6px
Electron density = ψ6px2
Radial distribution function = r2R6px2

The corresponding radial equations for the 6py and 6pz orbitals are the same. The angular functions are the same but substitute y and z as appropriate in the formula for Y6px given above. Substitute similarly for the wave equations ψ6py and ψ6pz.

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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 The Orbitron is a gallery of orbitals on the WWW The OrbitronTM, a gallery of orbitals on the WWW, URL: http://winter.group.shef.ac.uk/orbitron/ Copyright 2002-2015 Prof Mark Winter [The University of Sheffield]. All rights reserved. Document served: Sunday 25th February, 2018