Update 13_semiconductors.md - polish

src/13_semiconductors.md

@@ -223,8 +223,9 @@ $n_i$ is the **intrinsic carrier concentration**, and for a pristine semiconduct
 
 ## Exercises
 
-#### Exercise 1: Energy, mass, and momentum of electrons and holes
+#### Exercise 1: Energy, mass, velocity and cyclotron motion of electrons and holes
 
-  1. We consider the valence band of a semiconductor (see [above](#semiconductors-materials-with-two-bands)). Does an electron near the top of the valence band have a positive or a negative effective mass? Does the electron energy increase or decrease as $k$ increases from 0? Does the electron have a positive or negative group velocity for $k>0$?
-  2. Answer the same last 3 questions for a hole near the top of the valence band.
-  3. We consider an electron in a 2D semiconductor near the bottom of the conduction band, which is described by an energy dispersion $E=E_{G}+\frac{\hbar^2}{2m_{eff}}(k_x^2+k_y^2)$. Suppose we turn on a magnetic field $B$ in the $z$ direction. Write down the equation of motion for this electron (you may neglect collisions). What is the shape of the motion of the electron? What is the characteristic 'cyclotron' frequency of this motion? Suppose we now consider a hole instead of an electron. Is the chirality of the motion of the hole the same as that of the electron?
+  1. Consider the top of the valence band of a semiconductor (see [above](#semiconductors-materials-with-two-bands)). Does an electron near the top of the valence band have a positive or a negative effective mass? Does the electron's energy increase or decrease as $k$ increases from 0? Does the electron have a positive or negative group velocity for $k>0$?
+  2. Answer the same last 3 questions for a hole in the valence band.
+  3. We consider an electron in a 2D semiconductor near the bottom of the conduction band, which is described by an energy dispersion $E=E_{G}+\frac{\hbar^2}{2m_{eff}}(k_x^2+k_y^2)$. Suppose we turn on a magnetic field $B$ in the $z$-direction. Write down the equation of motion for this electron (you may neglect collisions). What is the shape of the motion of the electron? What is the characteristic 'cyclotron' frequency of this motion? What is the direction of the Lorentz force with respect to $\Nabla E$? 
+  4. Suppose we now consider a hole near the bottom of the conduction band and turn on a magnetic field $B$ in the $z$-direction. Is the chirality of the motion of the hole the same as that of the electron? Would the chirality change if we instead consider a hole (or electron) near the top of the valence band?