Final answer:
To determine the thermal velocity of holes in silicon at 92°C, one must use the formula v = sqrt(3kT/m). However, without the exact value of the effective mass of the hole, we cannot compute the thermal velocity.
Step-by-step explanation:
The thermal velocity of holes in silicon at 92°C can be estimated using the thermal energy given to carriers in a semiconductor. The average thermal energy (E) at a temperature T is given by the equation E = (3/2)kT, where k is the Boltzmann constant. To find the velocity, we use the formula for kinetic energy: (1/2)mv² = (3/2)kT, where m is the effective mass of the hole in silicon, and v is the velocity. By rearranging and solving for v, we find v = sqrt(3kT/m). However, the effective mass of the hole (m) is not provided in the question, and it is necessary to know the value to calculate the velocity. Typically, for silicon, the effective mass of holes is around 0.49 times the mass of a free electron, m0 = 9.11 × 10⁻³± kg, but without the exact value, we can't calculate the exact thermal velocity.