When is Indistinguishability Neglected in Atom Sample Calculations?

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SUMMARY

The discussion centers on the conditions under which indistinguishability can be neglected in atom sample calculations, specifically referencing the de Broglie wavelength in relation to atomic separation. The criterion established is that the de Broglie wavelength must be significantly smaller than the average distance between atoms, quantified as de Broglie wavelength << average distance. The contributor notes that a de Broglie wavelength one order of magnitude less than atomic separation is generally acceptable for neglecting indistinguishability, suggesting that this threshold is a reasonable cutoff. The contributor also emphasizes the subjective nature of determining significance in this context.

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benedwards2020
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I have been asked to find whether or not indistinguishability may or may not be ignored from a given sample of atoms at a given temperature.

The calculation I have done fine, but my question is given that the criterion for neglecting indistinguishability has to satisfy

de broglie wavelength << average distance between atoms

How much is considered 'a lot less'?

In my answer I have found the de Broglie wavelength to be a single order of magnitude less than the separation. Is this considered a lot less??
 
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In my experience, one order of magnitude is generally a reasonable cut-off for the vague >> and << notions.

Perhaps it would be better to report how significant it is, and let the person who gave you this task to judge for themselves, since "may or may not be ignored" is completely subjective.
 

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