Consider a 3-D gas of N electrons at absolute zero. Since the model consists of free...

 

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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 : ħ?k? 2m 1. Find the number of quantum states N(ɛ). 2. Find the density of state g(ɛ) (Hint : use g(ɛ) = dN/dɛ) 3. Proof that the density of state can be written as: 3N g(ɛ) 2ɛ 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 : ħ?k? 2m 1. Find the number of quantum states N(ɛ). 2. Find the density of state g(ɛ) (Hint : use g(ɛ) = dN/dɛ) 3. Proof that the density of state can be written as: 3N g(ɛ) 2ɛ