What is the function of radial distribution

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Density function

The eigenfunctions of the H atom were obtained as exact analytical solutions of the one-particle Schrödinger equation. To represent the wave functions in polar coordinates, consider the radial part and the angular function separately. The dependence of the electron distribution in the distance from the nucleus is most obvious through the density function specified. It contains the electron density of a spherical shell with the radius. If one integrates with the radius over the entire sphere, one obtains.

The larger the principal quantum number, the further out the highest maximum of the density function lies. As the number of secondary quantum increases, the density function contracts somewhat.

The following table shows the position of the maxima and minima of in the hydrogen atom (in atomic units):

Tab. 1
  1st maximum 1. Minimum 2nd maximum 2nd minimum 3rd maximum 3rd minimum 4th maximum
  1s 1
  2s 0,76 2,0 5,24
  2p 4
  3s 0,758 1,27 4,19 4,73 13,06
  3p 3 4 12
  3d 9
  4s 0,732 1,88 4 6,61 10,65 15,52 24,62
  4p 2,808 5,52 9,59 14,48 23,58
  4d 6,78 12 21,22
  4f 16

The following figure shows as an example the radial density function for the 1s orbital of the hydrogen atom with a maximum at 1 (i.e. with Bohr's radius with).

Further functions can be found in the literature (e.g. Atkins).