Radial Probability Distribution Curve for Hydrogen Atom

[Jimmy25]

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

I can't figure out what I'm doing wrong here!

 

[The_Duck]

Your link doesn't work, but I suspect that your problem is units. The normalization of the radial wave function is determined by

$$\int dr 4 \pi r^2 |\psi(r)|^2 = 1$$

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.

 

[Mandragonia]

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.