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

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SUMMARY

The variation of mean momentum of a nucleon with the mass number A of a nucleus can be determined using the relationship R=R_0A^(1/3). The mean momentum must be zero to prevent nucleon escape, while the variance of motion and kinetic energy can be analyzed. The de Broglie relation indicates that momentum p is inversely proportional to the wavelength, which cannot exceed the nucleus size, leading to a conclusion that momentum varies as A^(-1/3). This analysis provides insights into the minimum momentum rather than the mean momentum.

PREREQUISITES
  • Understanding of nuclear physics concepts, specifically nucleon behavior.
  • Familiarity with the de Broglie relation and its implications on momentum.
  • Knowledge of variance and kinetic energy in confined systems.
  • Basic grasp of mathematical relationships involving mass number A and radius R.
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  • Explore the implications of the de Broglie wavelength on nucleon confinement in nuclei.
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Students and researchers in nuclear physics, particularly those studying nucleon dynamics and quantum mechanics related to atomic structure.

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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