diff --git a/src/4_sommerfeld_model.md b/src/4_sommerfeld_model.md index 0b297fce27bd6d5409b8be230c2ce80cadedf74c..7231ec26d9924834004b7116cac1cb1651ac9d04 100644 --- a/src/4_sommerfeld_model.md +++ b/src/4_sommerfeld_model.md @@ -466,7 +466,7 @@ Using the answer for 1, find $g(k)$ for 1D, 2D and 3D. 7. Work out these integrals for $T = 0$. ### Exercise 3: a hypothetical material -A hypothetical metal has a Fermi energy $\varepsilon_F = 5.2 \, \mathrm{eV}$ and a density of states per unit volume $g(\varepsilon) = 2 \times 10^{10} \, \mathrm{eV}^{-\frac{3}{2}} \sqrt{\varepsilon}$. +A hypothetical metal has a Fermi energy $\varepsilon_F = 5.2 \, \mathrm{eV}$ and a density of states $g(\varepsilon) = 2 \times 10^{10} \, \mathrm{eV}^{-\frac{3}{2}} \sqrt{\varepsilon}$. 1. Give an integral expression for the total energy of the electrons in this hypothetical material in terms of the density of states $g(\varepsilon)$, the temperature $T$ and the chemical potential $\mu = \varepsilon_F$. 2. Find the ground state energy at $T = 0$.