(a) (i) What are the main assumptions of the free electron model?
(ii) Give an example where the free electron model is in good agreement with experiment.
(iii) Give an example where the free electron model fails.
(b) (i) How does the nearly free electron model improve on the free electron model?
(ii) Describe one of the successes of the nearly free electron model over the free electron model.
Free electron theory explains many of the properties of metals, like their heat capacity, thermal and electrical properties, why a metallic lattice is transparent free electrons etc. The given solution describes, the basic assumptions used in the formulation of free electron theory or the concept of free electron fermi gas. Heat capacity and mean free path of electrons are explained. A comparison of free electron theory with that of nearly free electron model and failure of free electron theory are well explained.