Minimum Kinetic Energy of a Proton Confined in a Uranium Nucleus

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SUMMARY

The discussion centers on calculating the minimum kinetic energy of a proton confined within a uranium nucleus, specifically with a radius of 8 x 10^-15 m. Participants clarify that the length (L) used in the uncertainty principle should be the diameter of the nucleus, not the radius. The confusion arises from the interpretation of delta-x, which is defined as L/2, leading to discrepancies in the kinetic energy equation. Ultimately, the correct interpretation of L is crucial for accurate calculations in quantum mechanics.

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  • Understanding of the Heisenberg Uncertainty Principle
  • Familiarity with quantum mechanics concepts
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  • Basic proficiency in mathematical manipulation of physical equations
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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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