Abstract: This study regards the allowable momentum value of the free electronic gas in the metal (px,py,pz) as a three-dimensional random variable which obey the uniform distribution. Meanwhile, This study use probability knowledge to solve the problem of free electronic gas in the metal. It helps students to establish intuitive physical landscape and understand the relevant concepts of free electronic gas models in metal.

Key words: Freedom electronics gas, momentum space, chemical potential, Fermi energy level