Chapter 43, Problem 28P

(a)

To determine

The quantity that fermi energy depends on according to free-electron theory of metals and the magnitude of dependency of the quantity.

(b)

To determine

To show that the equation of Fermi energy $E_F\left(0\text{K}\right)=\frac{h^2}{2m_e}{\left(\frac{3n_e}{8\pi }\right)}^{\frac{2}{3}}$ can be expressed as $E_F=\left(3.65\times {10}^{-19}\right)n_e^{\frac{2}{3}}$, where $E_F$ is in electron volts when $n_e$ is in electrons per cubic meter.

(c)

To determine

The factor by which free electron concentration in exceed than in potassium using Table 43.2.

(d)

To determine

Whether copper or potassium have larger Fermi energy.

(e)

To determine

The factor by which Fermi energy of Cu is larger than K.

(f)

To determine

Whether the behavior is consistent with that predicted by equation $E_F\left(0\text{K}\right)=\frac{h^2}{2m_e}{\left(\frac{3n_e}{8\pi }\right)}^{\frac{2}{3}}$.