Position Of Fermi Energy Level

Step 1: Relate the Fermi energy to electron density.
The Fermi energy is related to the electron density by the following equation for a free electron gas: Since the free electron density of metal A is 64 times that of metal B, we have Step 2: Express the ratio of Fermi energies.
Substituting the relation for the electron density in terms of Fermi energy, we get Taking the cube root of both sides, Step 3: Final Answer.
Thus, the ratio .