## Exercise 1: Energy, mass, velocity and cyclotron motion of electrons and holes

### Subquestion 1

Electrons near the top of the valence band have a negative effective mass, their energy decreases as $k$ increases from 0, and they have a positive group velocity for $k>0$.

### Subquestion 2

Holes near the top of the valence band have a positive effective mass, their energy increases as $k$ increases from 0, and they have a positive group velocity for $k>0$.

### Subquestion 3

The equation of motion for an electron near the bottom of the conduction band is: