Variation of mean momentum of a nucleon with the mass number....

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Homework Help Overview

The discussion revolves around determining the variation of mean momentum of a nucleon with the mass number A of a nucleus. The context includes concepts from nuclear physics and quantum mechanics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between mean momentum and mass number, questioning the assumptions regarding the de Broglie wavelength and its relation to the size of the nucleus. There are discussions about the implications of momentum being zero and considerations of variance in motion and kinetic energy.

Discussion Status

The discussion is active, with participants raising various points about the assumptions made regarding the de Broglie relation and the size of the nucleus. Some participants suggest that the minimum momentum can be derived, while others inquire about the distribution of allowed momenta and the validity of the assumptions being made.

Contextual Notes

There is an emphasis on the limitations of the assumptions regarding the size of the nucleus and the de Broglie wavelength, as well as the implications of these assumptions on the calculated momentum.

nunuhoyv
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Homework Statement


How to determine variation of mean momentum of a nucleon with the mass number A of nucleus?

Homework Equations


R=R_0A^(1/3)

The Attempt at a Solution


Can't find a solution with elementary approach.
 
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The mean momentum has to be zero, otherwise the nucleon escapes. But you can find the mean variance of motion, variance of the kinetic energy or similar things.

What do you know about the energy of things confined to a space of limited size?
 
deBroglie relation gives momentum p = h/lambda, and lambda can't be greater than size of nucleus~R-0*A*(1/3). So momentum varies as A*(-1/3). This gives the minimum momentum, not the mean, doesn't it? Also how good is the assumption about lambda and size of nucleus?
 
nunuhoyv said:
Also how good is the assumption about lambda and size of nucleus?
That is good.
nunuhoyv said:
This gives the minimum momentum, not the mean, doesn't it?
Right. What is the distribution for other allowed momenta? Focusing on one dimension is fine for now.
 

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