Question

physical chemistry problems using excel:

#1 Use Excel (or another graphing program) to plot the 2s and 2p radial wavefunctions (R). Determine where the nodes in these functions occur. Plot the square of the radial wavefunctions (R^2) for the 2s and 2p orbitals of a hydrogen atom. By differentiation, determine where the maxima in square of the radial wavefunction (R^2) occur for these orbitals. Physically, what do the maxima of R^2 represent?

#2 Use Excel to plot the 2s and 2p radial distribution functions. What are the most probable radii that a 2s and 2p electron will be found? Why are these values different than that calculated in 1?

Answer 1

The respective equations of the three orbitals are:

And their respective curves are:

• A node is a point where the electron density is zero. Putting the above-mentioned equations equal to zero, we find that 1s and 2p become zero only at infinity, and, therefore, don’t have any radial node. Whereas 2s orbital becomes zero at r = 2a/z, which is one point of the radial node.
• Given are the curves for the square of the radial functions:

• Once we square and differentiate the above equations and put them to zero, we’ll find that the maxima of the 2s curve r= 4A/z and R= 2A/z. Similarly, the root for 2p orbital comes at r= 2A/z.

• physically these points represent the maximum probability of finding an electron in that region.

• most probable radii are the expectation values fo these radii.