Radial Distribution Function Tutorial

Tutorial for Experiment: Radial Distribution Function

EXAMPLE: How does the most probable distance of the electron vary with the effective nuclear charge.?

EXPERIMENT: The radial distribution function, 4pr2R2, is proportional to the probability of finding the electron in a spherical shell of very small thickness dr at a distance r from the nucleus. The radial distribution function contains the radial part, R, of the atomic orbital, yn, l, ml.



The radial part of yn, l, ml and hence the radial distribution function depend on the quantum numbers n and l and the effective nuclear charge, Zeff. To observe the effect of Zeff on the radial distribution function, the values of the quantum numbers n and l must be fixed while Zeff is varied. Pick a specific atomic orbital and obtain plots of the radial distribution function versus r for various values of Zeff. The most probable distance, rmp, is the distance at which the radial distribution function has the largest value.


PROCEDURE:

  1. Click the "3d" button to select the 3d atomic orbital .



  2. And then Click the "2.0" button to set the value of Zeff. Record the most probable distance.



  3. Click the "3.0" button to reset the value of Zeff and obtain a new plot of the radial distribution function. Record the most probable distance.



  4. Click the "4.0" button to reset the value of Zeff and obtain a new plot of the radial distribution function. Record the most probable distance.



  5. Click the "5.0" button to reset the value of Zeff and obtain a new plot of the radial distribution function. Record the most probable distance.





RESULTS and OBSERVATIONS: The most probable distances taken from the four radial distribution plots for a 3d atomic orbital are listed in the table below.

Zeff Most Probable Distance (Å)
2.0 2.4
3.0 1.6
4.0 1.2
5.0 1.0


The radius, r, of the spherical shell in which there is the highest probability of finding an electron, that "occupies" a 3d atomic orbital, decreases as the effective nuclear charge "seen" by the electron increases.