**September 2024 Issue**

**Volume 92, No. 9**

Bringing graphene into the undergraduate classroom

We present an undergraduate instructional laboratory experiment that introduces students to the most well-known van der Waals material, graphene. Like all van der Waals materials, graphene is a crystal that can be peeled into layers, in some cases, down to atomic thicknesses. In this experiment, students first fabricate a sample consisting of few-layer graphene flakes atop of a silicon wafer substrate using the mechanical exfoliation method. The students then use a microscope setup to acquire images of the sample under white-light and LED illumination. These images are analyzed to produce optical contrast values (a measure of the reflectance of the graphene flakes) as a function of illumination wavelength. A theoretical model for optical contrast is developed based on thin-film interference and the resulting theory and experiment are compared, yielding a value for the graphene flake's thickness. This experiment is designed for advanced instructional laboratory and upper level optics courses. It may also be simplified into a qualitative introductory physics laboratory, demonstration, or outreach workshop activity.

#### EDITORIAL

In this issue: September 2024 by Mario Belloni; John Essick; Beth Parks; B. Cameron Reed; Todd Springer; Keith Zengel. DOI: 10.1119/5.0230218

#### LETTERS TO THE EDITOR

Entropy production diagrams by Ramandeep S. Johal. DOI: 10.1119/5.0226811

It is time to honor Emmy Noether with a momentum unit by Geoff Nunes, Jr. DOI: 10.1119/5.0229624

#### RESOURCE LETTERS

Resource Letter ALC-1: Advanced Laboratory Courses Editor’s Pick by Walter F. Smith. DOI: 10.1119/5.0209841

Editor's Note: For many undergraduate students, the advanced laboratory course is instrumental in their development into experimental physicists. Over the past two decades, the advanced laboratory course has seen a renaissance with over 250 articles written describing experiments that can be adapted and adopted for these courses. This Resource Letter provides a detailed list of resources spanning books and articles to organizations and vendors that support advanced laboratory courses.

#### PAPERS

Data science education in undergraduate physics: Lessons learned from a community of practice by Karan Shah; Julie Butler; Alexis V. Knaub; Anıl Zenginoğlu; William Ratcliff; Mohammad Soltanieh-ha. DOI: 10.1119/5.0203846

Editor's Note: Are you interested in adding data science concepts to your physics curriculum, but unsure where to start? If so, you may be interested in the new Data Science Education Community of Practice that offers guidance, inspiration, and resources for physics teachers like you, along with the results of faculty and industry surveys highlighting the skills that will be most useful to your students.

Application of the heat equation to the study of underground temperature by Mathis Caprais; Oriane Shviro; Ugo Pensec; Hermann Zeyen. DOI: 10.1119/5.0196139

Editor's Note: Frequently, modeling the three-dimensional world is too challenging for a class exercise, and we instead teach students using unrealistic one-dimensional problems. So it is wonderful when a one-dimensional model turns out not only to be fairly accurate, but also to have real world implications. That is the case with heat flow through the soil, which can be treated with a one-dimensional model, and which is important to energy-efficient solutions such as underground housing and ground-source heat pumps. This paper finds the underground temperature as a function of depth through measurements, analytical solutions, and computational solutions. These solutions can form the basis for a very interesting class assignment. In addition to considering heat transport through conduction, the model also includes heat transport through the flow of rain water.

A linear-algebraic derivation of the Lorentz transformation by Phil Schwartau. DOI: 10.1119/5.0216153

Editor's Note: Physics instructors know there are many ways to derive the Lorentz equations, and we all have our favorites. But take a look at this one, and you may find a new favorite. Appropriate for special relativity courses, as long as the students have some familiarity with linear algebra.

Photon under repeated transverse Lorentz boosts: An apparent paradox by Tugdual LeBohec. DOI: 10.1119/5.0193902

Editor's Note: Could two observers see the same photon traveling in opposite directions? It doesn't seem possible without introducing faster-than-light travel or causality issues, yet all you need is a few successive perpendicular Lorentz boosts to arrive at a frame of reference where the photon momentum direction is reversed. The author introduces this new special relativity paradox and its resolution, offering new ways to think about the symmetries of the Lorentz transformation and pedagogical motivations for the Wigner rotation.

Remarks on the yield of fission bombs by J. M. Pearson; B. Cameron Reed. DOI: 10.1119/5.0166291

Editor's Note: Both awe-inspiring and terrifying, a nuclear explosion is a spectacular display of microscopic physics profoundly affecting the human scale. This paper explores the physics of nuclear explosions and addresses the counter-intuitive fact that the total energy released by a fission bomb is independent of the energy released in a single fission. While this was known to the scientists who developed the atomic bomb, much of their work is classified and their knowledge remains inaccessible to the general public. With only a few historical documents to go on, the authors of this article attempt to recreate a calculation by Manhattan Project scientists and clearly show why the total energy yield is independent of the energy released by each fissioning nucleus. This article will be of interest to readers interested in nuclear physics or in the history of the Manhattan Project.

Understanding exotic black hole orbits using effective potentials by Steven Pakiela; Brett Bolen; Benjamin P. Holder; Monica Rizzo; Shane L. Larson. DOI: 10.1119/5.0149655

Editor's Note: Newtonian orbital mechanics is clean and orderly, with bound orbits being closed ellipses. Relativistic effects spoil this simplicity; in a weak gravitational field (e.g., the solar system), general relativity famously predicts orbital precession. In the strong gravitational field near a black hole, orbits can become tumultuous, appearing chaotic and unpredictable. “Zoom-whirl orbits” are extreme examples of this behavior, where the orbiting object plunges close to the black hole, whirls around it many times, and then heads back out to a larger radius. The authors of this article demonstrate how these complex orbits (which are of interest in gravitational wave astronomy) can be understood using the undergraduate physics of effective potentials. Computational tools are also developed and are freely provided to anyone interested in studying gravitational wave signatures from such orbits. Readers interested in black holes and relativity (and who have been intimidated by advanced mathematical treatments elsewhere in the literature) will find this article fascinating and instructive.

#### INSTRUCTIONAL LABORATORIES AND DEMONSTRATIONS

Probing coherent phonons in the advanced undergraduate laboratory by Nicholas J. Brennan; Joseph Peidle; Anna Wang-Holtzen; Jieping Fang; Kathryn Ledbetter; Matteo Mitrano. DOI: 10.1119/5.0190019

Editor's Note: This paper provides an introduction to modern time-domain spectroscopy using ultrafast lasers, an experimental technique used to observe fundamentally important phenomena in condensed matter physics as well as in other fields. As a specific example, the authors demonstrate the generation and detection of coherent phonons in three solids. The paper provides an undergraduate-accessible discussion of the theory of coherent phonon spectroscopy in terms of classical harmonic oscillator physics. Then, a relatively low-cost ultrafast pump-probe spectroscopy system and the experimental procedures that the authors use in their experiment are described. Finally, typical experimental data and analysis methods are presented. This laboratory experiment is a welcome addition to the undergraduate physics curriculum, introducing a system that is suitable for examining a variety of ultrafast and nonequilibrium phenomena in an advanced instructional laboratory.

Bringing graphene into the undergraduate classroom by Andrew Seredinski; Tedi Qafko; Nathanael Hillyer; Alexander Norman. DOI: /10.1119/5.0164700

Editor's Note: An experiment that introduces students to ultrathin graphene is presented. In this experiment, students fabricate a sample consisting of few-layer graphene flakes atop of a silicon wafer substrate using the mechanical exfoliation method and then use a microscope to acquire images of the sample under white-light and LED illumination. The images are analyzed to produce optical contrast values (a measure of the reflectance of the graphene flakes) as a function of illumination wavelength and these experimental values are compared to a theoretical model for optical contrast based on thin-film interference, yielding a value for the graphene flake's layer thickness. This experiment is designed for advanced instructional laboratory and upper level optics courses. It may also be simplified into a qualitative introductory physics laboratory, demonstration, or outreach workshop activity.

#### NOTES AND DISCUSSIONS

Bose and the angular momentum of the photon by Kirk T. McDonald. DOI: 10.1119/5.0229168

Comment on “Which is greater: or πe? An unorthodox physical solution to a classic puzzle” [Am. J. Phys. 92(5), 397–398 (2024)] by Roderick M. Macrae. DOI: 10.1119/5.0221403

Editor's Note: In a recent paper [Am. J. Phys. 92(5) 397–398 (2024)], Vallejo and Bove used the second law of thermodynamics to show that eπ > πe by imagining a finite body of initial temperature π placed in contact with a reservoir at temperature e. This comment on that work explores the situation more generally, showing that the result depends upon neither the value of π or the second law. Rather, Vallejo and Bove's result is a limited proof of the second law in the case of their particular example. Appropriate for thermodynamics students at all levels.

#### BOOK REVIEWS

Beautiful experiments: An illustrated history of experimental science by Rena J. Zieve. DOI: 10.1119/5.0231571

#### BOOKS RECEIVED

Am. J. Phys. 92, 720 (2024) https://doi.org/10.1119/5.0231574