negative first guess other than the exact solution w i l l lead to successive approximations moving away from the true solution (4). If eq 1is instead rewritten as
then MSA will work, but very slowly. With the first guess of 0.0162, MSA with eq 4 will take over 400 iterations to converge to the correct solution. Moreover, it is unlikely that most students would realize in advance that eq 4 is preferable to eq 3 when using MSA. The graphical approach is also useful with equations of the following form, which arises in monoprotic acid-base equilibrium problems.
One approach is to convert eq 6 to a quadratic equation, but this must be handled with care due to numerical precision considerations in the quadratic formula (5, 6). Another approach is to use MSA, stopping the iterations according to the "5% rule" (7,8) or an ionization ratio (9). If the graphical approach is used, there is no need to wony about numerical precision in the quadratic formula or rules for stopping the MSA iteration process. Another point to consider when solving mathematical equations is the possibility of multiple solutions, some of which may not be physically sensible. How does the student using MSA know-thereis only one physically sensible solution to the equation given? Agraphical representation of the equation will easily conv*e the skeptical student that only one such solution exists because the curve will cross the x axis only once over the range of physically sensible x values. Finally, we are not advocating the eradication of the quadratic formula or MSA as methods for equation solving. The MSAapproachis an important concept, useful for solving mmplex, multivariable problems beyond the scope of the graphical methods presented here. However, depending on the course and student background, the graphical approach provides a simple alternative or supplement to MSA.
Wave Functions for Hydrogen Atomic Orbitals Using Mathcad Dean E. Turner Murray State University Murray, KY 42071
Several notes have appeared recently in this Journal showing how Mathcad can be applied to problems in chemical education (10, 111, including one by Rioux that implemented a Taylor series expansion for radial wave functions for the hydrogen atom (12). A similar application using Theorist by Prescience on the Macintosh has also been described (13). Reading Rioux's paper, I was inspired to use Mathcad to derive exact wave functions for hydrogen and to prepare a doeument that plots them. The user need only enter the desired quantum numbers to see vari-
ous graphs describing orbitals up to 4p, making it useful for classroom demonstrations or students' exploration Times for recalculationand replotting vary from 1-2 min using a 33-MHz 80386-DX computer with no coprocessor. Most of this time is required to prepare a three-dimensional plot of electron density. (Much less time is needed if the radial function alone is desired.) The complete document appears in Figures 1and 2 on the following pages. I can offer my personal testimony to the power and ease of using Mathcad. Although I had not studied quantum mechanics since my undergraduate days about 15 years ago, I was able to develop this document in a single weekend while also taking care of young children. I believe that programs like Mathcad make it possible to reasonably ask a typical undergraduate to perform tasks like this that have heretofore been too difiicult. The program's symbolic processor does calculus and algebra, and its array and graphics tools perform calculations and display the results. Thus, students should be able to apply the principles they have learned even to mathematically complex pmblems.
Interfacing Atomic Absorption Instruments to a PC for Student Laboratories John M. ~okosa' and Keith M. Dery GMI Engineering and Management Institute Flint, MI 48504
Several models of Perkin-Elmer atomic absorption (AA) instruments were designed to be interfaced with the Perkin-Elmer 3600 data station, a computer used with PE instruments since the late 1970's. Because we wanted to use the PE-5000 (both airlacetylene flame and graphite furnace modes) for a new course in environmental chemistry, we also needed a suitable computer interface for the AA, in order to handle several laboratories of 20 plus students. An easy to use program incorporating data collection, analysis, and graphics was the basic need for the students. Unfortunately, the PE-3600 software and Perkin-Elmer's recently introduced Wata Management S o h a r e " for the PC (functionally identical to the 3600 software)were more demanding than required for student use.2 Experimental Examination of the microprocessor documentation lead to the realization that the PE-5000 communicates bidirectionally with an external computer usiw ASCII codes. allowing not only downloading if raw data, but also full Antrol of the instrument. We therefore decided to write a program for two-way communication with the instrument in Basic (Microsoft QuickBasic 4.5) computer lanrmaw. Basic was chosen because it is an easy m&hiie language to understand, program in, and change - by. anyone . familiar with a microcomputer.
- -
'~uthorto whom correspondence should be addressed. 2Availablefrom Pehin-Elmer Corporation, Norwalk, CT. (Continued on nertpage)
Volume 70 Number 7 July 1993
A185
