Final answer:
The question requires calculating the density of states at different energy levels for an electron in a solid, using a provided equation. Specific values for the energy were not provided for calculating the DOS at the exact center of the band. The density of states is a key concept in solid-state physics for analyzing electronic properties in materials.
Step-by-step explanation:
The question involves calculating the density of states (DOS) at different energy levels using a given equation. The density of states g(E) in an energy band is given by the formula g(E) = 8π√2(me/h²)3/2 √E, where me is the mass of an electron, h is Planck's constant, and E is the energy. This equation provides a relationship between the energy E and the number of allowed quantum states per unit energy in a material. To compute the DOS at the center of the band, one must substitute the value of the energy at the band's center into the equation. However, the question does not provide a specific value for the center of the band. Typically, in a band with a width of approximately 10eV, the center would be around 5eV, but without additional context or clarification, we cannot proceed with the calculation. Remember, the DOS is an important concept in solid-state physics and plays a crucial role in understanding the electronic properties of materials.