# Atomic orbitals: 6*s* 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*= 2*Zr*/*n*where*n*is the principal quantum number (6 for the 6*s*orbital)

Function | Equation |
---|---|

Radial wave function, R_{6s} |
= (1/2160√6) × (720 - 1800ρ + 1200ρ^{2} - 300ρ^{3} + 30ρ^{4} - ρ^{5}) × Z^{3/2} × e^{-ρ/2} |

Angular wave function, Y_{6s} |
= 1 × (1/4π)^{1/2} |

Wave function, ψ_{6s} |
= R_{6s} × Y_{6s} |

Electron density | = ψ_{6s}^{2} |

Radial distribution function | = 4πr^{2}ψ_{6s}^{2} |

The Orbitron

^{TM}, 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.