The Solid State

Answer: The forbidden energy gap (band gap) for a germanium (Ge) crystal at absolute zero temperature (0 K) is approximately 0.71 eV. Therefore, the correct option is (D) 0.71 eV.

Explanation:

The forbidden energy gap, also known as the band gap, is the energy difference between the valence band and the conduction band in a semiconductor. At absolute zero (0 K), the electrons are in the lowest energy state, and for germanium (Ge), this gap is approximately 0.71 eV. This is a key characteristic of the material that determines its electrical properties.

Therefore, the correct answer is: 0.71 eV (option D).

The resistivity of a semiconductor material at room temperature typically falls within a specific range. Semiconductors, like silicon (Si) and germanium (Ge), exhibit electrical conductivity between that of a conductor (like copper) and an insulator (like glass). This intermediate conductivity is what makes them useful in electronic devices.

The resistivity range for semiconductors at room temperature (approximately 20-25°C or 293-298 K) is approximately:

10^-3 to 10⁸ Ω⋅m

Therefore, semiconductors have resistivity values spanning several orders of magnitude, influenced by factors such as the type of semiconductor, doping concentration, and temperature.