Atomic orbitals: 4s 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 (4 for the 4s orbital)
Table of equations for the 4s orbital.
Function Equation
Radial wave function, R4s = (1/96) × (24 - 36ρ + 12ρ2 - ρ3) × Z3/2 × e-ρ/2
Angular wave function, Y4s = 1 × (1/4π)1/2
Wave function, ψ4s = R4s × Y4s
Electron density = ψ4s2
Radial distribution function = 4πr2ψ4s2
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.