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

AI Thread Summary
The discussion centers on determining the variation of mean momentum of a nucleon with the mass number A of a nucleus. It highlights that the mean momentum must be zero to prevent nucleon escape, while exploring the variance of motion and kinetic energy. The deBroglie relation is referenced, indicating that momentum p is inversely related to the size of the nucleus, suggesting a variation of momentum as A^(-1/3). The conversation also questions the validity of assumptions regarding the wavelength and nuclear size. Ultimately, the focus remains on understanding the distribution of allowed momenta in a confined space.
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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