How to change density of states to eV

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Discussion Overview

The discussion revolves around the conversion of density of states to electron volts (eV), specifically addressing the dimensional analysis and unit conversion involved in this process.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that multiplying by e^(3/2) can facilitate the conversion to eV, but seeks clarification on the reasoning behind this.
  • Another participant points out that converting units with dimensions of [J^-3] to [eV] is not possible, questioning if the intent is to convert to [eV^-3] instead.
  • A subsequent response confirms the intention to convert to [eV^-3].
  • Further, a participant introduces a comparison involving the conversion of units from cubic miles to cubic meters, drawing a parallel to converting from cubic joules to cubic electron volts.
  • Lastly, a participant expresses gratitude for the assistance provided in the discussion.

Areas of Agreement / Disagreement

The discussion contains multiple viewpoints regarding the conversion process and the appropriate units, indicating that there is no consensus on the method to achieve the desired conversion.

Contextual Notes

Participants have not fully resolved the assumptions regarding the conversion factors and the dimensionality of the units involved, leaving some steps in the conversion process unclear.

lioric
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I know that if I multiply e^3/2 (e= 1.602x10^-19) to the unit below I can change it to eV
image.jpg

Can somebody help me I don't know why
 
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1J = 6.242e+18eV
You cannot convert units with dimensions [J^-3] into units with dimensions [eV]
Do you want to convert to units of [eV^-3]?
 
Simon Bridge said:
1J = 6.242e+18eV
You cannot convert units with dimensions [J^-3] into units with dimensions [eV]
Do you want to convert to units of [eV^-3]?
Ya
 
let X = 6.242e+18 to save typing. Then there are X eV/J

If you have 1 Y per cubic mile and you want to know how many Y per cubic meter that is, given that 1mile = 1760 m, what do you do?
If you have 1 Y per cubic joule and you want to know how many Y per cubic electron volt you have...

Put another way: you have $$\frac{1\text{kg}^{3/2}}{1\text{J}^3 \times 1\text{s}} = \cdots$$ ... so what is 1J equal to?
 
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Thank you very much
 

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