The energies possessed by electrons in a metal is given by the energy distribution function.

Density of energy states D(E) d E=\frac{\pi}{4 h^3}(8 m)^{\frac{3}{2}} E^{\frac{1}{2}} d E

Energy Distribution graph

Fig (1)

• The energy distribution for the tungsten for T = 0° K  and T= 2500°K.
• The area of the curve gives the total number of particles per unit volume.
• Form the graph, it is clear that even for larger variation of temperature (2500°K) the distribution function changes very slightly.
• When temperature increases, only the electrons with near E_F are moved to the higher energy level and lower energy electrons are not disturbed.