Q. What is the density of energy states in metals? Obtain an expression for the density of states for free electron gas in metals.

Ans. Density of energy state is defined as the number of available energy states per unit energy range per unit volume.

To calculate density of energy state, let us introduce a 3 D space defined by. Each point in this space would represent an energy state and is associated with a volume element of one unity. Now if we draw a sphere of radius n in this space then each energy state defined by

The factor 1/8 accounts for the fact that only positive integers are allowable and thus only one octant of the sphere is available.