Physics-432
Homework Set (5)
This homework set is due on Tuesday (26th 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 (L3).
- 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.