When is Indistinguishability Neglected in Atom Sample Calculations?

In summary, the conversation discusses the concept of indistinguishability and how it relates to the de Broglie wavelength and average distance between atoms. The speaker has found that a single order of magnitude difference between the two is generally considered a reasonable cut-off, but suggests reporting the significance and allowing the person who assigned the task to make their own judgment. The question of how much is considered 'a lot less' remains subjective.
  • #1
benedwards2020
41
0
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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  • #2
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.
 

FAQ: When is Indistinguishability Neglected in Atom Sample Calculations?

What is "ignoring indistinguishability" in science?

Ignoring indistinguishability is a concept in science where we treat identical particles or objects as completely interchangeable and indistinguishable from one another. This means that it is impossible to tell the difference between these particles or objects based on their physical properties.

Why is ignoring indistinguishability important in scientific research?

Ignoring indistinguishability is important in scientific research because it allows us to simplify complex systems and focus on the overall behavior of a group of particles or objects rather than individual characteristics. This can help us make accurate predictions and understand fundamental principles in physics, chemistry, and other fields.

What are some examples of systems where indistinguishability is important?

Indistinguishability is important in many systems, including gases, liquids, and solids. For example, in a gas, individual particles are constantly colliding and exchanging energy, but we can still describe the overall behavior of the gas using macroscopic variables like temperature and pressure, without considering the individual properties of each particle.

How do scientists account for indistinguishability in their research?

Scientists use mathematical models and statistical methods to account for indistinguishability in their research. These models take into account the probability of finding a particle in a certain state and the interactions between particles, rather than treating each particle as a unique entity.

Are there any situations where ignoring indistinguishability is not applicable?

Ignoring indistinguishability is not applicable in situations where individual properties of particles or objects are important, such as in quantum mechanics or in the study of biological systems. In these cases, scientists must consider the unique characteristics of each particle or object to fully understand the system's behavior.

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