List of top Physics Questions on Position of Fermi Energy Level

Consider one mole of a monovalent metal at absolute zero temperature, obeying the free electron model. Its Fermi energy is \( E_F \). The energy corresponding to the filling of \( \frac{N_A}{2} \) electrons, where \( N_A \) is the Avogadro number, is \( 2^n E_F \). The value of \( n \) is:
At some temperature \( T \), two metals A and B, have Fermi energies \( \epsilon_A \) and \( \epsilon_B \), respectively. The free electron density of A is 64 times that of B. The ratio \( \frac{\epsilon_A}{\epsilon_B} \) is ............ (Round off to two decimal places).