Question

Compute the fermi energy and the corresponding fermi temperature of aluminium (trivalent metal) using the following data: Mal=0.2698kg and ro=2670kgm-3

Answer 1

Answer on Question 39913, Physics, Solid State Physics

The Fermi energy is given by $E_{F} = \frac{\hbar^{2}}{2m} (3\pi^{2}n)^{2 / 3}$ . Concentration of electrons is $n = \frac{N}{\nu} = \frac{\rho}{M_{at}}$ . Since the density is given in $\frac{kg}{m^3}$ , one must convert mass of aluminum given in atomic mass units to kg units using $1u = 1.67 \cdot 10^{-27}kg$ .

Thus, $E_{F} = \frac{\left(1.054\cdot 10^{-34}J\cdot s\right)^{2}}{\left(2\cdot9.11\cdot 10^{-31}kg\right)}\cdot \left(\frac{3\cdot3.14^{2}\cdot 2670\frac{kg}{m^{3}}}{0.2698\cdot 1.67\cdot 10^{-27}kg}\right) = 1.91\cdot 10^{-17}J.$