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Atomic orbitals: 5s 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 (5 for the 5s orbital)
Table of equations for the 5s orbital.
Function Equation
Radial wave function, R5s = (1/300√5) × (120 - 240ρ + 120ρ2 - 20ρ3 + ρ4) × Z3/2 × e-ρ/2
Angular wave function, Y5s = 1 × (1/4π)1/2
Wave function, ψ5s = R5s × Y5s
Electron density = ψ5s2
Radial distribution function = 4πr2ψ5s2
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Document served: Monday 28th September, 2020