September 2026
Volume 94, Issue No. 9
The Franck–Hertz experiment: Seeing cross sections
We re-examine the classic 1914 Franck–Hertz experiment, which was crucial both for completing the old quantum theory and for providing evidence for the quantized (Bohr) structure of atoms. Our motivation is twofold: first, to revive didactic interest in the Franck–Hertz experiment, and second, to reduce the difficulty of understanding electron–atom scattering cross sections. We perform the experiment using both neon (Ne) and mercury (Hg), accounting for the differences between measurements on the two gases using semiquantitative models. The present paper goes beyond the standard analysis of current–voltage characteristics in the Franck–Hertz experiment, which is typically used to extract the excitation energies of Hg (or Ne) atoms. The diversity and richness of electron-scattering phenomena accessible with readily available equipment underscore the enduring pedagogical value of the Franck–Hertz experiment at both undergraduate and advanced levels.
EDITORIAL
In this issue: August 2026 by Geraldine L. Cochran; John Essick; Harvey Gould; Claire A. Marrache-Kikuchi; Beth Parks; Daniel Schumayer; Todd Springer; Jan Tobochnik. DOI: 10.1119/5.0349316
LETTERS TO THE EDITOR
Johannes Vermeer and The Guitar Player: Observations on the vibrating guitar string's edge by Geoffrey D. Schott. DOI: 10.1119/5.0338541
An improved version of the “extraordinary tabletop speed of light apparatus” by G. Pegna; G. Malloci. DOI: 10.1119/5.0347633
Editor's Note: An improved version of the previously published tabletop speed of light apparatus is presented, in which the amplitude modulation frequency is more than doubled, enabling a reduction in the overall size of the apparatus, while improving the precision of the measured value for c. Detailed construction instructions are provided in supplementary material.
AWARDS
2026 AAPT award citations at the summer meeting in Pasadena, California. DOI: 10.1119/5.0354335
PAPERS
A studio approach to teaching vibrations, waves, and optics by Brett J. Pearson; Bent Nielsen; Kanishka D. Wijesekara; Julia Codere; Loc Thi-Hoang Ngo; Thomas Weinacht. DOI: 10.1119/5.0299680
Editor's Note: A studio or workshop pedagogical approach makes use of integrated activities that blend together elements of lecture, lab, and recitation. This type of course delivery is becoming more popular in introductory courses; instructional resources for upper-division studio physics exist, but are scarce. In this article, the authors describe their efforts in reforming a course on vibrations, waves, and optics using worksheets that are integrated with lab. Instructors will appreciate the generous addition of 13 downloadable worksheets in the supplementary material, which can be adapted for individual readers' purposes.
A real-world application of Lagrangian mechanics: The circular restricted 3-Body Problem by Jeremy A. Riousset; Manasvi Lingam; Annelisa B. Esparza. DOI: 10.1119/5.0283816
Editor's Note: The circular restricted 3-body problem is a good approximation to orbits of planets with small moons orbiting the Sun. It is commonly taught in orbital mechanics courses, but rarely mentioned in physics courses. This paper shows that the problem serves as an excellent example of how Lagrangian techniques can simplify a solution while providing a real-world application for a classical mechanics course.
The linear stability of Lagrange points in polar coordinates by E. M. Edlund; R. M. Hayes. DOI: 10.1119/5.0299686
Editor's Note: The five Lagrange points—three of which were discovered by Euler—define special, stationary configurations of the three-body problem for which an analytic description of the system is possible. They are home to Trojan asteroids in planetary orbits and space-based observatories like the Gaia space observatory and the James Webb Space Telescope. In this article, the authors study orbits near Lagrange points using linear stability analysis. Eigenvalues reveal stable and unstable orbits, and eigenvectors provide insight into trajectories. Unlike most prior studies, the authors use polar coordinates. This reveals bean-shaped orbits that do not appear at linear order in a Cartesian coordinate system. Calculations based on JWST and Trojan asteroids connect the mathematical analysis to physical objects in our solar system. The analysis fits naturally into an advanced undergraduate mechanics or astrodynamics course and provides a case study for computational physics or mathematical methods courses. Extending the analysis to out-of-plane orbits could provide opportunities for student projects and yield further insights into orbits and maneuvers for space-based telescopes.
Prescribing natural trajectories from scale factors by S. González-Salud; G. Silva-Ortigoza. DOI: 10.1119/5.0315496
Editor's Note: Here is a new discussion of the inverse problem, ready for the classroom! The authors show how to find two-dimensional potentials that allow trajectories constant in one coordinate with motion along the other. Teachers of undergraduate classical mechanics will appreciate these new insights on polar, parabolic, and elliptic–hyperbolic coordinate systems.
The Franck–Hertz experiment: Seeing cross sections by Luisa Lovisetti; Marco Giliberti; Kamil Fedus; Krzysztof Wejer; Grzegorz P. Karwasz. DOI: 10.1119/5.0309784
Editor's Note: The paper revisits the classical Franck–Hertz experiment with a fresh didactic lens, showing how a century-old setup can still illuminate modern quantum ideas. By comparing electron-scattering behavior in Ne and Hg, the authors reveal a richer landscape of phenomena than the familiar textbook I–V curve suggests. Their semiquantitative models make concepts like cross sections and inelastic collisions more accessible to students. It is a compelling reminder that classic experiments can still hold educational surprises.
Calorimetric experiments for teaching energy as a crosscutting quantitative concept by Avraham Merzel; Yaron Lehavi. DOI: 10.1119/5.0303048
Editor's Note: This paper shares calorimetry experiments that can be used individually or as a group to help students understand the concept of energy change. By adjusting experimental parameters, students will be able to determine how energy change depends on parameters such as mass, velocity, height, and time. Supplementary material provides sample data and useful tips for implementing the experiments. These experiments could be useful at a range of instructional levels from pre-college through university, as well as for teacher preparation.
INSTRUCTIONAL LABORATORIES AND DEMONSTRATIONS
INSTRUCTIONAL LABORATORIES AND DEMONSTRATIONS
Journey from the center of the Poincaré sphere by Yael Gutiérrez; José M. Saiz. DOI: 10.1119/5.0331548
Editor's Note: In this paper, the authors revisit an experiment proposed by Arago in which light is polarized using a stack of dielectric plates arranged at Brewster's angle. Using Stokes formalism and the Poincaré sphere, the manner in which the degree of polarization increases as the number of plates increases is derived theoretically. This prediction is then accurately verified experimentally with a simple laboratory setup. This polarization-related project will allow instructional laboratory instructors to expose their students to Stokes formalism and the Poincaré sphere representation.
Computer-controlled sinusoidal drive mechanism by Eric Ayars; Nicholas Nelson. DOI: 10.1119/5.0307519
Editor's Note: This paper presents the design for a relatively simple and very affordable sinusoidal driver controlled by a microcontroller. Given the importance of driven oscillations and resonance throughout physics, the device is useful for classroom demonstrations and instructional laboratories in introductory as well as upper-level courses. The limitations of commercial drivers is explained, while a mathematical derivation presents how this device overcomes those limitations. Details of the construction of the device are available on GitHub.
NOTES AND DISCUSSIONS
ChatGPT as a tutor?—between supporting students and giving away all the answers by Eva Glomski; Cem Yilmaz; Holger Dau; Marcus Kubsch. DOI: 10.1119/5.0311016
Editor's Note: The authors share their experience in creating a customized LLM-based chatbot that provided a sufficient level of assistance that students were willing to use it when solving homework problems. They found that students wanted more direct assistance than they received from the initial Socratic-style chatbot and would instead choose to get the full answer directly from an LLM. However, when they adjusted the prompt so that the LLM told the students how to get started without fully solving the problem, they found higher levels of student buy-in.
ADVANCED TOPICS
The cosmological constant problem: An accessible introduction by Ali Kaya; Adam Lahey. DOI: 10.1119/5.0319051
Editor's Note: Here is an opportunity to bring to the attention of advanced undergraduate physics students the unresolved problem involving the predicted quantum origin of an impossibly massive cosmological constant that would govern the evolution of the universe. All that is required is a beginning instruction in quantum field theory and general relativity. This could perhaps attract participation in attempts to engage in an eventual resolution of the quantum gravity conundrum!
Extending the Schrödinger quantum field to parametrized quantum field theory: A variational approach using the Pavšič–Barut action by John R. Fanchi. DOI: 10.1119/5.0264852
Editor's Note: This partially historical introduction to a lesser-known approach to quantum particle theory could offer valuable insights into ongoing debates on quantum field theory. Many instructors may not be aware of the number of respected theorists who have engaged over several decades in this dispute, and they may wish to bring it to the attention of students.
Teaching decoherence by simulating quantum channels on quantum computers by Berkley Delmonico; Lucas Nelson; James K. Freericks. DOI: 10.1119/5.0328433
Editor's Note: This paper describes an instructional sequence that uses the IBM Quantum Platform to teach about decoherence. It could be used in a course that explores quantum information.
Additional Resources
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