Radial Probability Density (Quantum Physics).

Question

I need to prepare a graph of radial probability density (RPD) from radial wave function (WF)/radius graph.

I thought the formula was RPD = WF squared x 4Pi x r squared but this does not produce the right answer.

Example for H1s (approximate figures); RPD = 0.28, r = 2 & WF = 0.25. Doesn’t compute with my formula!

Where am I going wrong?

Answer 1

It seems that you are considering the complete wave function for calculation of RPD in case of hydrogen atom. Now i would like to mention here that WF for hydrogen contains three terms, two of which give the angular dependence and the one gives the radial dependence. Now in calculating the RPD you need only that part which gives radial dependence of WF. Further this part also is dependent on n,l values and is different for different set of values. So before any calculation get some good book to see the table for R values for different set of allowed n,l values and then use formula P(r) = r^2|R|^2. I would recommend you the book by Beiser on Modern Physics.

Good Luck.