The dispersion relation of electrons in three dimensions is ε(k) = ℏvFk, where vF is the Fermi velocity. If at low temperatures (T << TF) the Fermi energy ε_F depends on the number density n as εF(n) ∝ nα, the value of α is

Among the various materials related to electronics, the energy band gap is maximum in ________.

A cubic sample of edge length L is maintained at a temperature of 4 K. The speed of sound in the material of the sample is 5 × 103 m/s. The minimum value of L required to excite the lowest frequency phonon mode is closest to: