Chemistry 3730 assignment 8

Due: Friday, Oct. 31, 10:00 a.m.

Use the following table of hydrogenic wavefunctions to answer the questions:

1. Calculate in the 2s and 3s states. Combining these results with the 1s result computed in class ( ), comment on the results with respect to a simple shell model of the atom.

   Maple hint: You will have to use assume(a0>0);

2. 1. Work out the normalized 3s and radial probability distributions.
   2. Sketch these distributions.
   3. Radial nodes are points where the radial probability distribution is zero. Locate the radial nodes of the 3s state.

      Maple hint: Use solve() to find the nodes. Maple may report redundant solutions (i.e. it may print out the same root more than once).

   4. Compute the probability that the electron will be found between the last node and infinity in the 3s state. Report your answer to four significant figures.

      Hint: If you have a normalized r.d.f., you do not need to use the full wavefunction.