In solids, what defines the spread of energies of large numbers of electrons in matter over two bands?

The spread of energies of large numbers of electrons in solids is best defined by energy bands. In solid-state physics, energy bands arise from the interactions between a large number of atoms in a crystal lattice. When atoms come together, their individual energy levels combine and spread out into bands due to the overlapping of atomic orbitals. This leads to the formation of a range of allowed energy levels (the energy band) and forbidden energy gaps between them.

In a solid, electrons can occupy these energy bands, which allows them to move and conduct electricity under the right conditions. The concept of energy bands is crucial for understanding the electrical properties of materials, as it helps to explain why some materials are conductors, some are insulators, and others are semiconductors.

Energy levels refer to the quantized states of electrons in a single atom, energy spectrum generally refers to the distribution of energies of particles in a system, and energy states can refer to specific energy levels in a broader context. However, when specifically discussing the collective behavior of electrons in solids and their distribution across multiple bands, the term energy bands is the most accurate and relevant choice.