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Atomic orbitals: 1s 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 (1 for the 1s orbital)
Table of equations for the 1s orbital.
Function Equation
Radial wave function, R1s = 2 × Z3/2 × e-ρ/2
Angular wave function, Y1s = 1 × (1/4π)1/2
Wave function, ψ1s = R1s × Y1s
= 2Z3/2e-ρ/2 × (1/4π)1/2
Electron density = ψ1s2
Radial distribution function = 4πr2ψ1s2
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Document served: Friday 27th November, 2020