Enabling covariational reasoning in Einstein’s formula for photoelectric effect

Abstract

Research has identified several students’ misinterpretations of the principles of the photoelectric effect (PE). Students cannot interpret the formula using the graph’s context despite the linear dependence inherited in it. Many 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. While research suggests various ways to help improve the understanding, little attention is given to the algebraic structure of the equation K Max = h f − W o and its corresponding graphical representation. Detailed scrutiny revealed that some phases of the PE’s algebraic expression do not support its visual representation. This paper suggests a more consistent alignment of the rules of mathematics with the PE process. 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’ mathematics knowledge. While formulating the law of conservation of energy, a physics simulation, The Photoelectric Effect (http://phet.colorado.edu), was used. The process of mathematical modelling of the PE that concluded with a covariational relation of the kinetic energy of ejected electrons was delivered to a group of 20 (N = 20) high school physics students. A didactical outline of the instructional unit is included.