What is the Difference Between Free Electron Model and Nearly Free Electron Model?
🆚 Go to Comparative Table 🆚The main difference between the free electron model and the nearly free electron model lies in the way they account for the interaction between electrons and the periodic potential of a crystalline solid. Here are the key differences:
- Free Electron Model:
- This model treats electrons as non-interacting free particles, completely neglecting the potential of ion cores.
- It is a quantum mechanical model that describes the behavior of electrons in a solid, assuming that the electrons move freely without any obstacles.
- Developed by Arnold Sommerfeld in 1927, it combines the classical Drude model with quantum mechanical Fermi-Dirac statistics.
- Nearly Free Electron Model:
- This model is a modification of the free electron model, which includes a weak periodic perturbation to account for the interaction between conduction electrons and the ions in a crystalline solid.
- It does not take into account electron-electron interactions, and the independent electron approximation is still in effect.
- The nearly free electron model enables the understanding and calculation of electronic band structures, especially of metals, and is an improvement over the free electron model, which neglected the ions.
In summary, the free electron model assumes that electrons move freely without any interaction with the periodic potential of a crystalline solid, while the nearly free electron model accounts for the weak interaction between electrons and the periodic potential.
Comparative Table: Free Electron Model vs Nearly Free Electron Model
The Free Electron Model and the Nearly Free Electron Model are both quantum mechanical models that describe the behavior of electrons in solids. Here is a table summarizing the differences between the two models:
| Free Electron Model | Nearly Free Electron Model |
|---|---|
| Developed by Arnold Sommerfeld in 1927 | Developed as an extension of the Free Electron Model |
| Treats electrons as non-interacting free particles | Takes into account the potential of ion cores |
| Assumes electrons are completely free and not bound to any specific atom or nucleus | Considers electrons as plane waves that are weakly interacting with the lattice potential |
| Useful for understanding the behavior of electrons in simple metals | Provides a more accurate description of electron behavior in solids, including band structures and energy levels |
The key difference between the two models is that the Free Electron Model treats electrons as completely free and non-interacting, while the Nearly Free Electron Model takes into account the potential of ion cores and considers electrons as weakly interacting with the lattice potential. The Nearly Free Electron Model provides a more accurate description of electron behavior in solids, including band structures and energy levels.
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