You are at: University of Sheffield » Chemistry » Mark Winter » Orbitron (atomic orbitals and molecular orbitals)
Chemistry books (USA)
Chemistry books (UK) WebElements Chemdex Chemputer
Introduction Wave function Electron density Dots! Radial distribution Equations

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)
  • k = a constant (value to follow)
Table of equations for the 7p orbital.
Function Equation
Radial wave function, R7px = (1/k) × 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.

Orbitron logo
Copyright Feedback The images Acknowledgments Problems? References

The Orbitron is a gallery of orbitals on the WWW

The OrbitronTM, a gallery of orbitals on the WWW, URL:
Copyright 2002-2015 Prof Mark Winter [The University of Sheffield]. All rights reserved.
Document served: Sunday 21st January, 2018