  In this work we calculate the correction to the ground state energy of the
hydrogen atom due to contributions arising from the presence of a minimal
length. The minimal length scenario is introduced by means of modifying the
Dirac equation through a deformed Heisenberg algebra (kempf algebra). With the
introduction of the Coulomb potential in the new Dirac energy operator, we
calculate the energy shift of the ground state of the hydrogen atom in first
order of the parameter related to the minimal length via perturbation theory.
