Which solid configuration has the highest density of states for electrons?

In summary, the conversation discusses the number of states available to electrons in different types of solids, such as polycrystalline iron, quartz, and semiconductors. It is mentioned that the former discrete nature of allowed energies for an electron is turned into thick energy bands when it is part of a solid. This leads to a large number of states being available to the electrons. However, the question of which solid has the most states available is considered ill-posed, as the number of available states can vary depending on factors such as crystal structure. The concept of density of states is also mentioned, which would require specifying relevant bands and energy/momentum range.
  • #1
cube137
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With regards to the number of states available to the electrons in these solids.

1. a mass of polycrystalline iron (plenty of free electrons)
2. quartz (has practically no free electrons).
3. semiconductors

Which of them has the most number of states available to the electrons?
Which has the most ease of getting them to change states considered against the ease with which they change states by themselves?
 
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  • #2
To rephrase it. An electron in isolation has discrete value. When it is part of solid, The formerly discrete nature of allowed energies for an electron is turned into thick energy bands, within which electrons can occupy any energy they desire (well, almost). In this sense, you have many states available to the electrons.

Which of these... iron, quartz or semiconductors have most states available to the electrons?

What other solid configuration has the most states available to the electrons?
 
  • #3
This is an ill-posed question. If you look at hydrogen atoms, the allowed bound states have energies equal to ## E_n = \frac {Ry} {n^2} ## and n is the main quantum number ranging from 1 to ... infinity. In other words, there is an infinite number of available electronic states in a single hydrogen atom. It is true for any atom as well. Now, when atoms form a solid, each of these atomic state is split into a band and within each band, there are as many allowed states as there are atoms in the entire solid (ok, strictly speaking, each band has as many states as there are primitive unit cells within the entire solid but number of bands gets multiplied by number of atoms within a primitive unit cell).
So, you have an infinite number of states multiplied by a very large number of atoms in a piece of solid.
Which infinity is greater?
 
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  • #4
cube137 said:
To rephrase it. An electron in isolation has discrete value.

This is false. If you mean an electron "in isolation" as in free electron (i.e. not encumbered by any external potential), then it does not have "discrete values" in terms of the allowed energies and momentum. Try it. Solve the Schrodinger equation for a free electron.

When it is part of solid, The formerly discrete nature of allowed energies for an electron is turned into thick energy bands, within which electrons can occupy any energy they desire (well, almost). In this sense, you have many states available to the electrons.

See your mistaken idea above.

Which of these... iron, quartz or semiconductors have most states available to the electrons?

What other solid configuration has the most states available to the electrons?

As has been stated, this is an ill-posed question. If you are talking about the density of states, then that's a different issues, because you will have to indicate the relevant bands and relevant energy and momentum range. Asking for a total number of states does not make sense.

And not only that, even for a particular solid, such as iron, changing its crystal structure can change its density of states. So just specifying an element alone, or a semiconductor alone, isn't sufficient.

Zz.
 
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FAQ: Which solid configuration has the highest density of states for electrons?

1. What are electron bands in solids?

Electron bands in solids refer to the energy levels that electrons can occupy within a solid material. These energy levels are created by the interactions between the electrons and the atoms in the solid, and they determine the electrical and optical properties of the material.

2. How are electron bands formed in solids?

Electron bands are formed through the process of electron wave interference. When electrons are confined to a small space, such as within a solid material, their wave-like properties cause them to interfere with each other, resulting in the formation of energy bands.

3. What is the significance of electron bands in solids?

Electron bands play a crucial role in determining the electrical conductivity, thermal conductivity, and optical properties of a solid material. They also affect the material's mechanical and magnetic properties. Understanding electron bands is essential for designing and developing new materials for various applications.

4. What factors affect the formation of electron bands in solids?

The formation of electron bands is influenced by the crystal structure of the solid, the number of electrons in the material, and the strength of the interactions between the electrons and the atoms. External factors such as temperature and pressure can also affect the formation of electron bands.

5. Can electron bands be manipulated?

Yes, electron bands can be manipulated through various methods such as doping, applying an external electric or magnetic field, or changing the temperature and pressure of the material. These manipulations can alter the material's properties, making it suitable for different applications.

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