Three-Dimensional Models for Visualizing the Quantum States of the Hydrogen Atom: An Instructional Approach to Teaching Modern Physics

Resumo

The teaching of Modern and Contemporary Physics at the secondary school level presents significant challenges, particularly because many of its concepts involve a high degree of abstraction and are commonly represented through mathematical formulations, symbolic representations, and two-dimensional illustrations. In this context, this study presents the development of three-dimensional instructional models designed to represent the quantum states of the hydrogen atom and to support the teaching and learning of Modern Physics. The models were developed by selecting quantum-mechanical concepts amenable to three-dimensional representation, followed by digital modeling using three-dimensional design software and fabrication through 3D printing with polylactic acid (PLA) filament at an internal infill density of 20%. The resulting physical models represent different quantum states of the hydrogen atom and provide a tangible representation of spatial probability distributions associated with the electron. The models can be manipulated and examined from different perspectives, establishing a direct connection between mathematical and theoretical descriptions and their corresponding spatial representations. The proposed instructional resource is intended to support teachers in addressing abstract concepts related to atomic structure, quantum states, and quantum numbers. By enabling students to observe and manipulate three-dimensional representations of the hydrogen atom, the models may facilitate spatial visualization, strengthen conceptual understanding, and promote more meaningful learning experiences. The proposed approach therefore offers a potentially useful and accessible resource for incorporating Modern and Contemporary Physics into secondary education.