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Radial Probability Distribution Curve for Hydrogen Atom

  1. Sep 10, 2011 #1
    I'm trying to plot the radial probability function for a hydrogen atom.

    I have the function itself (Psi2*4*pi*r2) my problem is that when I plot the function with angstroms on the x-axis, the y-values are larger than they should be (they look about right if I divide them by the bohr radius in angstroms).

    Here's what it should look like when plotted:
    http://hyperphysics.phy-astr.gsu.edu...ntum/hydr.html [Broken]

    I can't figure out what I'm doing wrong here!
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Sep 10, 2011 #2
    Your link doesn't work, but I suspect that your problem is units. The normalization of the radial wave function is determined by

    [tex]\int dr 4 \pi r^2 |\psi(r)|^2 = 1[/tex]

    As a consequence (4 pi r^2 psi(r)) has units of 1/(length) so that the whole expression comes out unitless. So the scale of your y axis depends on the units you choose for it.
  4. Nov 26, 2013 #3
    Can the normalized radial distribution function Rho(r) be applied, as if it were a classical statistical distribution?

    For example:
    1. Multiply Rho(r) by an arbitrary function of r, say f(r), and integrate from 0 to inf to obtain the average < f >.
    2. Derive a cumulative probability P(t) by integrating Rho(r) from 0 to t.
    3. Make a coordinate transformation r -> y, in order to obtain a new probability density Rho(y) in the variable y.
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