Consider the free electron gas. 4. the number of electron states g(e)de for the free electrons in metal is the exact same form with the number of standing waves g(j)dj= 2-(1/8) (4,7jd derived from the condition of standing wave existence in the cube cavity for the blackbody radiation. explain why you can use the exact same form? 2 show that for a free electron gas, one may write g(e)=c3y2 where d is the dimensionality of the gas (i. e. 1,2, or 3). and calculate c, for each case. for each dimension, express the fermi energy in terms of (n/v), where n is the number of free electrons. for each dimension, express the average energy of total electrons in terms of the fermi energy at t-0. for example, the average energy in 3-d is 0.6s