In the nearly-free-electron model, energy gaps occur at values of wavevector corre- sponding to bragg reflection. (i) using this model, calculate the directions in a simple cubic structure in which the first, second and third energy gaps occur (ii) calculate the electron energies at which these gaps occur for a lattice constant a 4x 10-10 m. (b) the energy e of an electron in the conduction band of a metal is related to the wavevector k by e 2x 10-10 m. given the fermi wavevector is 2.618 x 109 m-1 and the fermi a sin2 ka. here, a is a constant and a is the lattice spacing - energy is 1 ev, determine the effective mass of the conduction electrons measured in a transport experiment that probes the electrons at the fermi level