Although the Drude model was fairly successful in describing the electron motion within metals, it has some erroneous aspects: it predicts the Hall coefficient with the wrong sign compared to experimental measurements, the assumed additional electronic heat capacity to the lattice heat capacity, namely 3 2 k B per electron at elevated temperatures, is also inconsistent with experimental values, since measurements of metals show no deviation from the Dulong–Petit law. The observed electronic contribution of electrons to the heat capacity is usually less than one percent of 3 2 k B . This problem seemed insoluble prior to the development of quantum mechanics. This paradox was solved by Arnold Sommerfeld after the discovery of the Pauli exclusion principle, who recognised that the replacement of the Boltzmann distribution with the Fermi–Dirac distribution was required and incorporated it in the free electron model.