The Fermi temperature $T_F$ is defined as the Fermi energy $E_F$ divided by the Boltzmann constant $k_B$ . The average speed of a conduction electron corresponds to a kinetic energy equal to the Fermi energy. That is
$\begin{align*}T_F k_B = \frac{1}{2} m_e v^2\end{align*}$
We solve this for $v$ to obtain
$\begin{align*}v = \sqrt{\frac{2 T_F k_B}{ m_e}} = \sqrt{\frac{2 \cdot 80000 \mbox{ K} \cdot 1.38 \cdot 10^{-23} \mbox{ J/K}}{...$
Therefore, answer (E) is correct.

Solution to 1992 Problem 23