QB_PH_SEC7_025: Band Theory of Solids & Semiconductors

A metal has a Fermi energy of $E_F = 5.0\text{ eV}$. What is the Fermi temperature $T_F$ (in $10^4\text{ K}$)? Take the Boltzmann constant $k_B = 8.617 \times 10^{-5}\text{ eV/K}$. (Round off your answer to one decimal place)

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Fermi Temperature Definition**: $E_F = k_B T_F \implies T_F = \frac{E_F}{k_B}$ 2. **Parameter Substitution**: - $E_F = 5.0\text{ eV}$ - $k_B = 8.61733 \times 10^{-5}\text{ eV/K}$ 3. **Evaluation**: $T_F = \frac{5.0\text{ eV}}{8.61733 \times 10^{-5}\text{ eV/K}} = 58022.6\text{ K} = 5.802 \times 10^4\text{ K}$ 4. **Official Value**: 5.8 (in units of $10^4\text{ K}$).