 Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2018/s3/1/c/solution

λ ≃ d

with the convention of part b. Then

T_{e} ≃ \frac{h ^{2}}{m _{e} k _{B} d ^{2}} ≃ 3.9 \times 1 0^{5} K .

Thus ordinary solid-state temperatures are far below this rough overlap scale. The electrons need quantum statistics and quantum states throughout that regime. The number is an order-of-magnitude wavelength criterion, not an exact Fermi temperature: electron density, electronic band structure, effective mass and the numerical convention all matter.

 New to topics? Read the docs here!