Understanding Energy Differences in Free Electron Metals

In summary, the energy of electrons in a free electron metal cannot all be the same due to the presence of conduction and valence electrons with different energies. The Fermi-Dirac distribution, which explains this phenomenon, is a complex concept that involves the Pauli exclusion principle and applies to all fermions, not just electrons. Additionally, the specific heat of simple metals at room temperature is lower than that calculated for a classical gas of electrons due to the distribution of energy levels within the metal.
  • #1
blueyellow

Homework Statement



a) Explain why in a free electron metal it is not possible for all electrons to have the same energy.

b) Why is the specific heat of simple metals at room temperature much lower than that calculated for a classical gas of electrons?


The Attempt at a Solution



a) Because there are conduction and valence electrons which have different energies. Also draw some graph showing the range o energies electrons can have - but then, how would I explain the graph of g(E) vs E that is a curve?
 
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  • #2
Your g(E) vs. E is presumably the Fermi-Dirac distribution. Its provenance can't be explained in a short posting. It includes the Pauli exclusion principle and applies to all fermions, not just electrons.
 

1. What is a free electron metal?

A free electron metal is a type of material that has a high concentration of free electrons, which are not bound to any specific atom. This allows the electrons to move freely throughout the material, making it a good conductor of electricity.

2. How are free electron metals different from other types of metals?

Free electron metals are different from other types of metals because they have a higher number of free electrons. In most metals, the electrons are tightly bound to the atoms and are not able to move freely. However, in free electron metals, the electrons are able to move throughout the material, making them highly conductive.

3. What are some examples of free electron metals?

Some common examples of free electron metals include copper, silver, and gold. These metals have a high concentration of free electrons, which makes them good conductors of electricity.

4. How do free electron metals conduct electricity?

Free electron metals conduct electricity by allowing the free electrons to move freely throughout the material. When a voltage is applied, the free electrons flow in a specific direction, creating an electric current.

5. What are the properties of free electron metals?

Some properties of free electron metals include their high electrical and thermal conductivity, malleability, and ductility. They also tend to have a shiny appearance and are often used in electrical wiring, jewelry, and other applications that require good conductivity.

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