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

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SUMMARY

The discussion centers on a calculation error related to Fermi energy in a physics problem. The correct calculation of 6.4/1.381 yields 4.634, while the book incorrectly states 5.624, which corresponds to an incorrect energy value of 0.485 eV. The error may stem from a misrepresentation of the Boltzmann constant, suggesting a possible digit swap. This highlights the importance of verifying constants in scientific calculations.

PREREQUISITES
  • Understanding of Fermi energy and its significance in physics
  • Familiarity with the Boltzmann constant (1.381 x 10^-23 J/K)
  • Basic knowledge of energy conversion between eV and Joules
  • Proficiency in algebraic calculations and error analysis
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  • Research the implications of Fermi energy in solid-state physics
  • Learn about the significance of the Boltzmann constant in thermodynamics
  • Explore common errors in scientific calculations and how to avoid them
  • Study energy conversion techniques between electronvolts and Joules
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Physics students, educators, and researchers interested in thermodynamics and solid-state physics will benefit from this discussion.

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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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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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here is the problem:

electron_zpspzmpaowo.jpg
 
6.4 1020 is the 0.4 eV expressed in Joules.
 
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.
 

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