### Exercise 2: Temperature dependence of resistance in the Drude model
1. We first find the electron density using $n_e = \frac{ZnN_A}{W}$, where $Z=1$ is the number of free electrons per copper atom, *n* is the mass density of copper, $N_A$ is Avogadro's constant, and *W* is the atomic weight of copper. Then, we find the scattering time $\tau = 2.57 \cdot 10^{-14}$ s from the longitudinal Drude resistivity $\rho = \frac{m_e}{n_e e^2\tau}$.
2. $\lambda = \langle v \rangle\tau$ ($\lambda =3 nm $)
3.Scattering time $\tau \propto \frac{1}{\sqrt{T}}$; $\rho \propto \sqrt{T}$
4. In general, $\rho \propto T$ as the phonons in the system scales linearly with T (remember hightemperature limit of Bose-Einstein factor becomes $\frac{kT}{\hbar\omega}$ leading to $\rho \propto T$). Inability to explain this linear dependence is a failure of the Drude model.
2.Using $\lambda = \langle v \rangle\tau$, we get $\lambda =3$ nm
3.The scattering time $\tau \propto \frac{1}{\sqrt{T}}$, such that we find $\rho \propto \sqrt{T}$
4. In general, the measured resistivity scales as $\rho \propto T$. This can be understood by assuming that the scattering is caused by phonons, as their number scales linearly with T at high temperature (recall that the high-temperature limit of the Bose-Einstein distribution functions is $n_B = \frac{kT}{\hbar\omega}$ leading to $\rho \propto T$). The inability to explain this linear dependence is a failure of the Drude model.
### Exercise 3: The Hall conductivity matrix and the Hall coefficient
