Studies of student understanding of simple electric dc circuits have shown that many of them find it very difficult to apply qualitative reasoning to explain the observed phenomena. It has been suggested that these difficulties may be due to their failure to construct models of microscopic processes that lead to these phenomena. Indeed, in the traditional courses, such models have generally not been emphasized. In the present study, we compared the performance of different groups of university students in answering a questionnaire designed to probe their understanding of the relationship between macroscopic phenomena of transients in a dc circuit and the microscopic processes that can explain these phenomena. One group studied from a traditional text, the second group used a recently developed text that emphasizes models of microscopic processes. We also conducted detailed interviews with some of the students. From an analysis of the performance of these two groups, and also from a comparison with a previous study on Israeli high school students, we found that most of the students whose instructional experiences included an emphasis on the development of models of microscopic processes developed a better understanding of the transient phenomena studied. They applied qualitative considerations in their analyses and were able to develop coherent models to describe their observations. Overall, they demonstrated a superior understanding of the physical phenomena.

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A novel and inexpensive device for introductory students to measure Planck’s constant using the photoelectric effect has been developed. Quasimonochromatic light illuminates the photocathode. An inexpensive voltage follower circuit with high impedance and low capacitance is used to determine the stopping potential, which is read on a standard voltmeter. The results agree to within ±5% of the currently accepted value. The experimental results are highly reproducible.

where s is the spin of the conduction electron and is the spin of the c fi i 4f electron. This interaction effectively polarizes the conduction electrons. The 4f electrons of neighboring atoms sense one another indirectly through the polarized conduction electrons. This interaction is responsible for the peculiar magnetic properties of the rare earths. These in turn give rise to anomalous behavior in many physical properties at the magnetic transition temperatures. Measurements of the transport properties and magnetization of the heavy rare earths, gadolinium through lutetium, (1-8) have shown these anomalies. The Fermi surface structure of the rare earths has been shown to be far from free-electron like. Calculations by Freeman e_t (9) for thulium, by Keeton (lO) for dysprosium, and by Loucks (11) for yttrium, a tri valent metal similar to the rare earths, show that the Fermi surfaces are extremely anisotropic. These results are reflected in the different behavior of the transport coefficients along the various crystallographic directions, as seen from single crystal studies. It is thus of particular interest to investigate the transport properties using single crystals. An extensive study of the rare earths has been carried on at the Ames Laboratory for many years. Measurements of the electrical resistivity of heavy rare earth single crystals have shown that these elements are rather poor electrical conductors. Secondly, anomalous changes in the resistivity are observed at the magnetic transition temperatures. Finally, the heavy rare earth single crystals exhibit sharp anisotropies between the basal plane and hexagonal directions. In view of this, it was of interest to investigate the related problem of thermal conduction. •The elements erbium, dysprosium, and lutetlum were chosen for this study