**Physics-432**

**Homework Set (5)**

This homework set is due on Tuesday (26^{th} of Muharram) at 10.00
p.m.

If you need help, please e-mail me or visit me in my office.

Please solve fully and clearly, state assumptions, circle final answers, and comment wisely (when applicable).

__Do not discuss this homework with your colleagues
in any way, shape or form!__

**Question #1:**

A free electron system consists of (N) atoms, having electrons of mass
(m), in a 3-D lattice of dimensions (L^{3}).

- Find the average electronic energy in terms of N, m and L at absolute zero temperature.
- Comment on the average electronic energy at room temperature.

**Question #2:**

The pressure (P) exerted by the electron gas is:

P = _{}

where E is the system's ground state energy, N is the number of electrons in the gas system.

The bulk modulus (B) and compressibility (K) are derived through the relation:

B = 1/K = _{}

Show that this gives approximately 9 GPa for sodium and 3 GPa for potassium.

How does this compare with experimental results?

**Question
#3:**

- Derive the Wiedemann-Franz law, and evaluate the Lorenz number.
- Derive equation 6-56, and argue that, in metals, electrons normally carry more heat current than phonons.

**Question #4:**

e-mail me (zhyamani@kfupm.edu.sa) two web-site URLs that describe the free electron model and the expected behavior of metals regarding heat and electricity.