The standard model classifies particles into elementary leptons and hadrons composed of quarks. In this article the existence of an alternate ordering principle will be demonstrated giving particle energies to be quantized as a function of the fine-structure constant, α. The quantization can be derived using an appropriate wave function that acts as a probability amplitude on the electric field. The value of α can be approximated numerically by the gamma functions of the integrals for calculating particle energy. The series expansion of the energy equation provides quantitative terms for Coulomb, strong and gravitational interaction. The relationship of the model with gravitational effects is corroborated by the possibility to derive the basic equations directly from the Einstein field equations. The only parameters of the model are the values of the speed of light and the elementary charge.