False. At higher energy levels in the valence band, the number of free electrons does not increase. In fact, the valence band is already fully occupied by electrons in their lowest energy states. The valence band represents the highest energy level that electrons can occupy while still being bound to the atoms in a solid material.
When sufficient energy is supplied to an electron in the valence band, it can be excited to a higher energy level in the conduction band, where it becomes a free electron. The conduction band is the energy band above the valence band, and it contains vacant energy states that electrons can move into and become free to move throughout the material.
Therefore, it is the excitation of electrons from the valence band to the conduction band, rather than an increase in the number of free electrons within the valence band itself, that leads to the presence of more free electrons in a material.