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Problem 13.5: Determine most-probable values for Coulomb wave functions

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The probability density, P(r) = R2(r)r2,  for an electron in an idealized hydrogen atom (Coulomb potential) for several states is shown as plotted versus distance given in Bohr radii.

  1. For which state(s) do(es) the most-probable value(s) of the electron's position agree with the Bohr model?
  2. For 1s, 2p, and 3d what is the relationship between the most-probable value and the Bohr radius?
  3. Rank the states by the electron's most-probable position (least first).
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