Volume 33, Issue 10, October 1965
 APPARATUS NOTES



Tunnel Effect Demonstrator
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Standing Waves in a Circle
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 PAPERS


Resource Letter EEC1 on the Evolution of Energy Concepts from Galileo to Helmholtz
View Description Hide DescriptionPrepared at the request of the AAPT Committee on Resource Letters; supported by a grant from the National Science Foundation.
This is one of a series of Resource Letters on different topics, intended to guide college physicists to some of the literature and other teaching aids that may help them improve course contents in specified fields of physics. No Resource Letter is meant to be exhaustive and complete; in time there may be more than one letter on some of the main subjects of interest. Comments and suggestions concerning the content and arrangement of letters as well as suggestions for future topics will be welcomed. Please send such communications to Professor Arnold Arons, Chairman, Resource Letter Committee, Department of Physics, Amherst College, Amherst, Massachusetts.
Notation: The letter E after an item number indicates elementary level, useful principally for freshman liberal arts through sophomore physics courses; the letter I indicates intermediate (junior, senior) level; and the letter A indicates advanced material principally suited for senior, graduate study. An asterisk (*) indicates items particularly recommended for introductory study.
Additional copies: Available from American Institute of Physics, 335 East 45 Street, New York, New York, 10017. When ordering, request Resource Letter EEC1 and enclose a stamped return envelope.

Mechanics Experiments using Modified PSSC Apparatus
View Description Hide DescriptionLowcost modifications we have made to standard PSSC apparatus which greatly facilitates its use by large laboratory classes are described, and an outline is given of mechanics experiments we have designed for firstyear physicsmajor students using this modified apparatus.

Quantum Scattering Theory in One Dimension
View Description Hide DescriptionA phaseshift analysis of quantum mechanical scattering problems in one dimension is developed. Many of the techniques and results of three dimensions remain even in one dimension, while the discussion is vastly simplified, and thus accessible to the student much earlier, due to the absence of special functions (in particular, Bessel and Legendre functions) with their complicated asymptotic formulas and orthogonality relations. A “partial wave” analysis leads to the familiar relation between the scattering amplitude in the partial wave and the phase shift . The optical theorem is evident as an immediate consequence of the conservation of probability. The method is applied to an analysis of the wellknown squarewell scattering resonances.

Summary of Results in the COPFIC Study
View Description Hide DescriptionA summary of replies to the communication sent by COPFIC to the chairmen of the physics departments at the undergraduate colleges is given.

Advanced Physics Laboratory Course at Cornell
View Description Hide DescriptionFor fifty years an advanced laboratory course has been one of the major course offerings of the Department of Physics at Cornell. It has been taken by all undergraduatephysics majors and by almost all physicsgraduate students, potential theorists and experimentalists alike. During this period of time, the course has gone through many changes, both in “philosophy” and in facilities. Instead of the ten or a dozen students of forty years ago, the enrollment is now over 100 and requires the teaching time of eleven staff members and a fulltime laboratory technician. The Department receives many requests for information about the course, requests for the list and description of the experiments offered, and about the general pedagogical format. Many other universities have established courses in its pattern. It is the purpose of this paper to provide a rather general description of the course, a description that might be of interest to a physics student, to a teacher, or to a person interested in the teaching of physics.

Two Quantitative Lecture Demonstrations concerning Linear Momentum
View Description Hide DescriptionTwo quantitative lecture demonstrations are described. The first uses a water jet to illustrate the relation between the reaction thrust and the time rate of change of momentum in the jet. The second demonstration uses an air trough with a conceptually simple but quantitative method for measuring the velocities of the air trough gliders. Conservation of momentum can be quantitatively verified in a variety of elastic and inelastic collisions. In both demonstrations accuracies of one or two per cent are easy to obtain.

Physics of the Mössbauer Effect
View Description Hide DescriptionThis paper considers from a simple physical point of view the Mössbauer effect, i.e., the “recoilless emission” of gamma rays from a nucleus bound in a crystal lattice. It begins with a discussion of the kinematics of gammaray emission from such a nucleus. The idealized case of a massive “lattice” characterized by a single frequency and the more realistic one and threedimensional models are treated. We point up the fact that in the Mössbauer effect the lattice as a whole (the lattice center of mass) always recoils after photon emission, so that the term “recoilless emission” is in one sense misleading. We emphasize that the essence of the Mössbauer effect is not photon emission without recoil, but rather is photon emission without transfer of energy to internal degrees of freedom of the lattice. Using the basic ideas of quantum mechanics, namely, the rules for the manipulation of probability amplitudes (the socalled “transformation theory”), we calculate the probability for recoil without excitation of internal degrees of freedom, i.e., the Mössbauer f factor, on the assumption that the individual photon emissions, and consequent lattice recoil, are instantaneous. In Appendix A we discuss this question of instantaneous emission in some detail, and show how it is not in contradiction with the fact that the nuclear transition that leads to the gammaray emission has a finite halfwidth. In Appendix B those rules of transformation theory that are used in the body of the paper are summarized.

Tube Method for Measuring the Velocity of Sound in Gases
View Description Hide DescriptionA technique for measuring the velocity of sound in gases confined in tubes is described. The basic apparatus first proposed by F. A. Angona [J. Acoust. Soc. Am. 25, No. 6, 1111–15 (1953)] mainly for measurement of tube attenuation coefficients was adapted for this purpose. The method involves locating two positions of identical phase along a free progressive wave. Such a wave is made possible by an absorbing termination. The value obtained for the velocity of sound in high purity nitrogen gas at 21.1 C (70 F) and atmospheric pressure is 349.78 m/sec as compared to a calculated value of 349.80 m/sec.

SingleConcept Films in Physics
View Description Hide DescriptionShort films are described which are designed to be used within a teacher's lecture, having application at various levels of instruction. The importance of the teachers' guide is stressed. Commercial distribution of the series is on a nonexclusive basis. New projectors and film formats are described. An annual competition is proposed for short 8mm films made by physics teachers for use in their own classes.

Experiments with a Thermoelectric Heat Pump
View Description Hide DescriptionA teaching experiment based on a commercial thermoelectric heat pump which utilizes semiconductor materials is described. The measurements made yield the figure of merit for the thermocouple as well as its coefficient of performance as a pump.

Differentiating Orthogonal Unit Vectors with respect to Curvilinear Coordinates
View Description Hide DescriptionThe identity is used to obtain a simple heuristic derivation and also an exact derivation for derivatives of unit vectors in dimensions. Only an expression for is obtained by this method, but may be expressed in terms of and thus in terms of the unit vectors .

Determination of Radii of Curvature of Spherical Surfaces using Newton's Rings
View Description Hide DescriptionNewton's rings formed by an air film bounded by spherical surfaces are discussed. Thephysical and mathematical limitations involved in determining the radii of curvature of thebounding spherical surfaces are pointed out.

Correction to the Rydberg Constant for Finite Nuclear Mass
View Description Hide DescriptionIf the problem of the hydrogenlike atom is done with the assumption that the nucleus is at rest, the resulting energy levels are proportional to the Rydberg constant for infinite mass. It is traditional to obtain the Rydberg constant for finite mass of the nucleus by a simple substitution of the reduced mass of the system for the electron mass in the expression for the Rydberg constant for infinite nuclear mass. Realization that such a substitution (which is drawn from classical mechanics) does not give a correct transformation to the centerofmass coordinate system in the case of charged particles, leads one to significant corrections for the Rydberg constants of finite nuclear masses. The corrections are drawn from classical, nonrelativistic physics. Also, an interesting conjecture about the energy levels of hydrogenlike atoms, under the assumptions of Bohr theory and classical physics, is obtained.

The Synchrodropper—A Versatile Tool
View Description Hide DescriptionA usefully stable synchronous water dropper having many uses in demonstration and laboratory work is described. A tuned leaf spring is driven by ordinary 60cps alternating current power and arranged to dispense serially drops of constant size. By observing these drops with an electronic flash or synchronous motor driven stroboscope during either their free fall or collision, demonstration experiments and measurements can be made. A design for producing uniform drops with a minimum of “jitter” and operating difficulty is given together with appropriate methods for assuring reliable performance.

Rate of SurfaceStrain Tensor
View Description Hide DescriptionAlthough some work exists relating to the kinematics of fluid surfaces, no development parallel to that for linear and volume elements exists. It is shown, in this paper, that a rate of surfacestrain tensor can be defined that has the same relationship to rate of surface extension that the rate of strain tensor has to rate of linear extension. Under some circumstances, this new tensor and a more useful form of the surface transport theorem derived from it, provide an improvement in the physical interpretation of equations of fluid motion. Practical applications have been found in the field of nonNewtonian flow, and hopefully will be found in other fields such as the theory of surface waves and meteorology.

The Weight of Mass
View Description Hide DescriptionIt is argued that insistence on the use of the word “mass,” where one would ordinarily say “weight” is nothing but pedantry, and imposes a needless “weight,” i.e., burden, on students. Evidence is invoked from laws that the word “weight” expresses the notion of the measure of an object, which is supposed to be the peculiar meaning of “mass,” and has done so for a long time. Finally, an example shows how dropping this distinction (which, it is maintained, is nothing but a distinction without a difference) helps to clear up certain objections which have been proposed about the development of Newton's laws.

Temperature and Pressure Dependence of the Viscosity of Gases
View Description Hide DescriptionThis paper describes a method for making absolute measurements of the viscosity of gases, using timed flow through a capillary. Air, nitrogen, carbon dioxide, argon, helium, and hydrogen were studied at temperatures between 77° and 295°K. Nitrogen was also measured at pressures from 15 to 130 cm of mercury. Accuracy of 2% or 3% is obtained with relatively simple apparatus. The experiment is suitable for an undergraduate laboratory.
