3. Free electron model of sodium metal: a) Find the allowed values of wave vector for...

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3. Free electron model of sodium metal: a) Find the allowed values of wave vector for an electron in a cubic box of length L where we apply periodic boundary condition (as in the case of particle in a ring) to the free particle wavefunction such that (x + L) = (x), and similarly for the y and z directions. Find the allowed values of momentum and energy of such a particle. b) Consider sodium to have a body centered cubic crystal structure with the lattice constant of the conventional unit cell being 4.23 . Find the electron concentration in units of cm. 3. Free electron model of sodium metal: a) Find the allowed values of wave vector for an electron in a cubic box of length L where we apply periodic boundary condition (as in the case of particle in a ring) to the free particle wavefunction such that (x + L) = (x), and similarly for the y and z directions. Find the allowed values of momentum and energy of such a particle. b) Consider sodium to have a body centered cubic crystal structure with the lattice constant of the conventional unit cell being 4.23 . Find the electron concentration in units of cm.