What is the cause of the mistake in calculating Fermi energy?

In summary, Fermi energy simplification is a mathematical approximation used in solid state physics to simplify the calculations of electron energy levels in materials. It is based on the assumption of even energy distribution and is used to predict the behavior and properties of materials. However, it has limitations and is only applicable at low temperatures and in thermal equilibrium. The Fermi energy is related to the Fermi level, which is often used to describe the energy of the highest occupied electron state. Some applications of Fermi energy simplification include materials science, solid state electronics, and condensed matter physics.
  • #1
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Here is a simplification of a problem given in my book. I don't get the simplification part.

Could you please help at this ? It seems book has done the calculation wrongly.

simplification_zpsu8kjnvmu.jpg
 
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  • #2
6.4/1.381 = 4.634. There is no obvious typo that would lead to 5.624 and the Boltzmann constant is correct. I don't understand the calculation done in the book.
 
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  • #3
here is the problem:

electron_zpspzmpaowo.jpg
 
  • #4
6.4 1020 is the 0.4 eV expressed in Joules.
 
  • #5
The 5.624 would correspond to 0.485 eV, 7.77E-20 J, or a wrong Boltzmann constant of 1.138 instead of 1.381.

Maybe the last one is the cause of the mistake, it can be explained by swapping the digits.
 

Related to What is the cause of the mistake in calculating Fermi energy?

1. What is Fermi energy simplification?

Fermi energy simplification is a mathematical approximation used to simplify the calculations of the energy levels of electrons in a solid material. It is based on the assumption that the energy levels are evenly distributed, which makes the calculations easier to perform.

2. How is Fermi energy simplification used in solid state physics?

Fermi energy simplification is used to understand the behavior of electrons in solid state materials, such as metals, semiconductors, and insulators. It helps to predict the electrical and thermal properties of these materials and is an important tool in the study of condensed matter physics.

3. What are the limitations of Fermi energy simplification?

Fermi energy simplification is only applicable to materials at low temperatures, typically below the melting point of the material. It also assumes that the material is in thermal equilibrium, which may not always be the case.

4. How does Fermi energy relate to the Fermi level?

The Fermi energy is the energy level at which the probability of finding an electron is equal to 1/2 at absolute zero temperature. The Fermi level, on the other hand, is the energy level at which the probability of finding an electron is equal to 1/2 at any temperature. The Fermi level is often used to describe the energy of the highest occupied electron state in a material.

5. What are some applications of Fermi energy simplification?

Fermi energy simplification is used in various fields such as materials science, solid state electronics, and condensed matter physics. It is particularly useful in the design and development of electronic devices, such as transistors and diodes, as well as in the study of electrical and thermal conductivity of materials.

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