# In-class exercises

These exercises are presented to the class about half way through a lecture. They take 5 to 10 minutes to complete. Students work in pairs using either a white board or chalk board.

Day | Exercise |
---|---|

1 | Estimate free carrier density in Al. |

Estimate the Fermi wavelength in Al | |

2 | Sketch Re{Ψ(x)} for an electron in the n=1, k=π/4a state of a 1d chain of H atoms |

4 | Estimate v_F in Al (application of semiclassical dynamics |

5 | Estimate the energy of highest energy phonon in a typical crystal (starting point: Typical cohesive energy is 1 eV per atom) |

6 | 1d subbands: Draw 3d k-space and mark the allowed states when the confinement potential is long and skinny |

8 | Show that conservation of canonical momentum gives same result as Lorentz force when a charged particle moves through a magnetic field |

9 | Find the phonon scattering length given a plot weak localization data |

10 | Use the Thomas-Fermi screening constant to find the carrier density such that K_s is equal to the effective Bohr radius for dopant atoms in semiconductor |

11 | Estimate the typical wavelength of an electron in the conduction band of a lightly n-doped semiconductor at room temparture |

12 | Draw I_tunnel(V_bias) for an STM experiment based on a specific D_tip(E) and D_sample(E) |

13 | Given T_c = 7.2 K in lead, estimate the superconducting condensation energy per unit volume at T = 0 using the BCS result Δ(T = 0) = 1.7 kT |

14 | Estimate B_crit for lead, using info from previous excerise. |

### Other ideas

- Graphene is to be used as a transparent top contact of an LED. Choose a typical sheet density of charge and calculate lateral resistance for a square of graphene assuming mobility of 10,000. (It needs to be < 10 Ohm for breakthrough applications).