In simple metals the phonon contribution to the electrical resistivity at temperature T is

Solution (By Examveda Team)

In simple metals, the phonon contribution to the electrical resistivity at temperature T follows specific trends based on the Debye temperature:

Option A: This option is correct. Above the Debye temperature, the phonon contribution to the electrical resistivity is directly proportional to T. Below the Debye temperature, it is proportional to T³. This behavior is in accordance with the Debye theory of solids, which predicts these dependencies.

Option B: This option is incorrect. The phonon contribution to electrical resistivity is not inversely proportional to T for all temperatures in simple metals.

Option C: This option is incorrect. The phonon contribution to electrical resistivity is not independent of temperature for all temperatures in simple metals.

Option D: This option is incorrect. While it states a direct proportionality above the Debye temperature, it incorrectly suggests a proportionality to T⁵ below the Debye temperature. The correct dependency below the Debye temperature is T³, not T⁵. Therefore, this option is not accurate.