9.4 Free Electron Model of Metals

What happens to the ground state energy of an electron if the dimensions of the solid increase?

If the electron number density (N/V) of a metal increases by a factor 8, what happens to the Fermi energy $\left(E_{\text{F}}\right) ?$

Why does the graph in the figure increase gradually from the origin?

What is the difference in energy between the $n_{x} = n_{y} = n_{z} = 4$ state and the state with the next higher energy? What is the percentage change in the energy between the $n_{x} = n_{y} = n_{z} = 4$ state and the state with the next higher energy? (b) Compare these with the difference in energy and the percentage change in the energy between the $n_{x} = n_{y} = n_{z} = 400$ state and the state with the next higher energy.

What value of energy corresponds to a density of states of $1.10 \times 10^{24} \text{eV}^{−1}$ ?

Consider a cube of copper with edges 1.50 mm long. Estimate the number of electron quantum states in this cube whose energies are in the range 3.75 to 3.77 eV.

Determine the Fermi energy and temperature for copper at $T = 0 \text{K}$.