Update 13_semiconductors_solutions.md - typo

src/13_semiconductors_solutions.md

@@ -134,7 +134,7 @@ $$
 \begin{align}
 n_e &= \int_{E_G}^{\infty} f(E)g_c(E)dE\\
 &\approx \int_{E_G}^{\infty} e^{-\beta (E-\mu) g_c(E)} dE\\
-&=\frac{\sqrt{\pi}k_B T e^{\beta (\mu - E_G)}}{a \sqrt{t_{cb}}}.
+&=\frac{\sqrt{\pi k_B T} e^{\beta (\mu - E_G)}}{a \sqrt{t_{cb}}}.
 \end{align}
 $$
 
@@ -142,7 +142,7 @@ Analoguous, we find for the hole density
 $$
 \begin{align}
 n_h &= \int_{0}^{\infty} f(E_h) g_h(E_h) dE_h\\
-&\approx \frac{\sqrt{\pi}k_B T e^{-\beta \mu}}{a \sqrt{t_{vb}}}. 
+&\approx \frac{\sqrt{\pi k_B T} e^{-\beta \mu}}{a \sqrt{t_{vb}}}. 
 \end{align}
 $$