Enabling Covariational Reasoning in Einstein’s Formula for Photoelectric Effect

Abstract

Research has identified several students’ misinterpretations of the scientific underpinnings of the photoelectric effect. Studies pointed out that the graphical representation of kinetic energy of the ejected electrons versus frequency of incident photons is unclear when a blend of mathematical and scientific reasoning is applied. Students cannot find a scientific sense of the formula using the graph despite the fundamental linear dependence inherited in it. While research suggests various ways to help improve the understanding, little attention is given to the algebraic structure of the equation KMax = hf − Wo and its corresponding graphical representation. Detailed scrutiny revealed that some phases of the photoelectric effect’s algebraic expression do not support its visual representation. This paper suggests a more consistent alignment of the rules of mathematics with the photoelectric effect process to allow coherence. This suggestion emerged as an alternative algebraic representation of the law of conservation of energy in the form of a piecewise linear function. It is hypothesized that such covariational relation between photons’ frequency and the ejected electrons’ kinetic energy is more consistent with observable phenomena behaviour and students’ math knowledge. Mathematical modelling of the photoelectric effect that concluded with a linear piecewise function was supported by a physics simulation The Photoelectric Effect (http://phet.colorado.edu) and delivered to a group of twenty (N = 20) high school physics students. A didactical outline of the instructional unit and a general evaluation of the student’s responses are included. This study in its ealier version was published in Physics Education Journal (Sokolowski 2021).