In this work we investigate whether and how a molecule undergoing a nonadiabatic transition can show different energy mean values and distributions in the two electronic states that are populated. We analyze three models, of which models I and II mimick the limiting cases of almost adiabatic and almost diabatic regimes, respectively, and are solvable by first-order perturbation theory. Model III represents realistically the photodissociation of a diatomic molecule and is treated numerically. The three models provide a consistent picture of the energy selection effect. For a typical avoided crossing, the wavepacket component that undegoes the transition between the two adiabatic states has a larger mean value of energy than the other component, both for upward and for downward transitions. The analysis of model II shows that the Landau-Zener rule can be deduced in a fully quantum mechanical way. We believe that the energy selection effect can be observed experimentally in the photodissociation of diatomic molecules. The effect should be particularly relevant for wavepackets endowed with a broad energy spectrum, as the result of excitation with ultrashort light pulses.