Calculating Proton's Min KE Confined in Uranium Nucleus

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In summary, the conversation is discussing the determination of the minimum kinetic energy of a proton confined in a uranium nucleus using the uncertainty principle. The attempt at a solution involves finding the minimum change in momentum and attempting to relate it to the minimum kinetic energy using the equation change in KE= change in p*c. However, this is incorrect as it only applies to massless particles.
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PhyzicsOfHockey
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Homework Statement



A proton is confined in a uranium nucleus of radius 7.41 fm. Determine the proton's minimum kinetic energy K less than or equal to delta K according to the uncertainty principle if the proton is well approximated by a Gaussian wave packet confined by the nuclear diameter.


Homework Equations



change in momentum * change in x is greater than or equal to h(bar)/2
I don't know



The Attempt at a Solution



I found the minimum change in momentum but can't seem to relate that to the minimum KE. I tried change KE= change in p*c but that was wrong.
since it is confined by the diameter do I times the radius by 2? Thats how I did it.

dx=14.82E-15 m
h(bar)/2=1.0546E-34/2=5.273E-35
5.273E-35/14.82E-15= 3.54E-21
3.54E-21*3E8= 1.0674E-12 J

But this is wrong and I don't have a clue as to why. Can someone help me out please?
 
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  • #2
First of all, try to put units on ALL of your quantities, ok? Otherwise, people can only guess what '3.54E-21' might be supposed to stand for. Having said that, it looks like you got delta(p) ok. But I am completely unable to guess what the '3E8' in the last line might be. How do you go from momentum to energy?
 
  • #3
Oh, I get it. You really are using p*c=E! That only holds for massless particles. The proton is hardly massless.
 

1. How is the minimum kinetic energy of a proton confined in a uranium nucleus calculated?

The minimum kinetic energy of a proton confined in a uranium nucleus is calculated using the formula KE = (1/2)mv^2, where m is the mass of the proton and v is the velocity. This formula is based on the principle of conservation of energy, where the potential energy of the proton inside the nucleus is equal to its kinetic energy.

2. What is the significance of calculating the minimum kinetic energy of a proton in a uranium nucleus?

Calculating the minimum kinetic energy of a proton in a uranium nucleus is important in understanding the stability of the nucleus. It helps in determining the minimum amount of energy required to overcome the strong nuclear force, which holds the nucleus together. This information is crucial in studying nuclear reactions and in the development of nuclear energy.

3. How is the mass of the proton and the velocity of the proton determined in this calculation?

The mass of the proton can be determined experimentally using various methods, such as mass spectrometry. The velocity of the proton can be calculated using the principles of quantum mechanics, taking into account the confinement of the proton in the nucleus and the uncertainty principle.

4. Are there any other factors that affect the minimum kinetic energy of a proton in a uranium nucleus?

Yes, there are other factors that can affect the minimum kinetic energy of a proton in a uranium nucleus. These include the size and shape of the nucleus, the number of neutrons in the nucleus, and the distribution of charge within the nucleus. These factors can slightly alter the calculated minimum kinetic energy.

5. How does the minimum kinetic energy of a proton in a uranium nucleus compare to other particles in the nucleus?

The minimum kinetic energy of a proton in a uranium nucleus is typically lower than that of other particles, such as neutrons. This is because protons are positively charged and are confined to a small space within the nucleus, making it harder for them to escape. On the other hand, neutrons are electrically neutral and can move more freely within the nucleus, resulting in a higher minimum kinetic energy.

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