Minimum Kinetic Energy of a Proton Confined in a Uranium Nucleus

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Homework Help Overview

The problem involves determining the minimum kinetic energy of a proton confined within a uranium nucleus, utilizing the uncertainty principle. The context is rooted in quantum mechanics, specifically relating to particle confinement in a potential well.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the definition of the length L in relation to the nucleus, questioning whether it should be the diameter or radius. There are also inquiries about the origin of the numerical values used in the equations, particularly the factor of 8.

Discussion Status

The discussion is ongoing, with participants providing clarifications and corrections regarding the interpretation of the problem. Some guidance has been offered regarding the definitions used, but no consensus has been reached on the correct approach to the calculations.

Contextual Notes

There appears to be confusion regarding the definitions of delta-x and L, as well as the implications of the uncertainty principle in this context. Participants are navigating through potential misinterpretations of the problem statement and the mathematical expressions involved.

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36. A proton is confined in a uranium nucleus of radius 8 x 10^-15 m. Determine the proton's minimum kinetic energy according to the uncertainty principle if the proton is confined to a one-dimensional box that has length equal to the nuclear diameter.

What's wrong with my equation and value I used for L^2?

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You defined L = 2\Delta x so that means L should be the diameter and not the radius of the nucleus.
 
nickjer said:
You defined L = 2\Delta x so that means L should be the diameter and not the radius of the nucleus.

Son of a... It does say diameter. :rolleyes: And so delta-x is the radius.

Where did the 8 come from?
 
Last edited:
I think the 8 came from if you pulled the 2 from 2*r out of the square it would be 4. And then you would have 2*4 = 8.
 
But the 1.6 x 10^-5 nm = 2r, so that term is already squared. She has 8*m*d^2, not 2*m*(2r)^2 which would be 8*m*r^2.

The definition of delta-x is arbitrary, right? But it has to make sense in the context of the wave function. It seems that delta-x = L/2 is a common definition.
 
Last edited:
I think your grader just corrected it twice. Not thinking that you would interpret at as a single correction.
 

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