Solution to 1992 Problem 23

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.

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