Consider a 3-D gas of N electrons at absolute zero. Since the model consists of free electrons, the internal energy is equal to total kinetic energy of the system. At 0 K the system is in its ground state and the energy is given by : ?k? 2m 1. Find the number of quantum states N(). 2. Find the density of state g() (Hint : use g() = dN/d) 3. Proof that the density of state can be written as: 3N g() 2