expand the estimate of N_V (closes #10)

docs/lecture_7.md

@@ -147,9 +147,8 @@ $$N_V = 2\left(\frac{2\pi m_h kT}{h^2}\right)^{3/2}$$
 
 the number of holes with energy $E<T$ (compare with the rule above).
 
-**Question:** how large is $N_V$?
-
-**Answer:** If $kT \sim \textrm{eV}$, then $N_V \sim 1$. Therefore $N_V \sim (kT/\textrm{eV})^{3/2}\sim 1\%$.
+??? question "how large is $N_V$ at room temperature? (hard question)"
+    If $kT \sim 1\textrm{eV}$ (the typical energy size of a band), then electrons in the whole band may be excited and $N_V \sim 1$. On the other hand, $N_V \sim T^{3/2}$ Therefore $N_V \sim (kT/1 \textrm{eV})^{3/2}\sim 1\%$.
 
 Similarly for electrons: