Problem 13.7: Calculating <r> for the Coulomb wave functions

Start of definite integral = | End of definite integral = | Graph: rmax=

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An electron in an idealized hydrogen atom (Coulomb potential).   The probability density times r, rP(r) = R2r3, integrates over all space gives the expected value for the position of the electron, represented as <r>.  This is shown for several states plotted versus distance given in Bohr radii. You can change the start and end of the integral as well as the range plotted in the graph by changing values and clicking the "evaluate" button.

  1. There is an interesting relationship which relates this expected value of the radial position in terms of the Bohr theory.  What is that relationship in terms of a0?
  2. For a given n, how does l affect the expected value of r?