When a free electron moves near or through a periodic structure, it can emit radiation known as Smith-Purcell radiation, a phenomenon well recognized in physics. The conventional formula for predicting the frequency of photons emitted through Smith-Purcell radiation in a dielectric material is based on Minkowski’s theory. According to Minkowski’s theory, the momentum of a photon in a medium is assumed to be \({\text{p}}_{{\text{M}}} = n\hbar {\upomega }/{\text{c}}\) . However, there is an opposing theory, known as Abraham’s theory, which assumes the momentum of a photon in a medium to be \({\text{p}}_{{\text{A}}} = \hbar {\upomega }/\left( {n{\text{c}}} \right)\) . As of now, there is insufficient evidence to definitively establish the correctness of either theory. In this study, we have devised a new formula for predicting the photon frequency of Smith-Purcell radiation by integrating the energy-momentum conservation law with Abraham’s theory. Our findings indicate significant deviations between the photon frequencies calculated using our formula and those obtained via the conventional formula. Specifically, in our formula, the central frequency increases with rising electron kinetic energy and reaches a saturation point at 1.5 meV, whereas the conventional formula shows a saturation point at 1.0 meV. Moreover, at this saturation point, the central frequency in our formula is \(5.8 \times 10^{15}\)  Hz, compared to \(3.6 \times 10^{15}\)  Hz in the conventional formula. These substantial disparities present opportunities for experimental validation of both Minkowski’s theory and Abraham’s theory in the context of Smith-Purcell radiation. Our findings offer a pathway for accurately determining the photon frequency of Smith-Purcell radiation.