Range of speeds of particle confined in box

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SUMMARY

The discussion focuses on estimating the speed range of a proton confined within an atomic nucleus of diameter 3.80 femtometers (fm). Utilizing the uncertainty principle, participants derive the speed using the equation 3.80 fm * mv = h/2, leading to a calculated speed of approximately 5.22 x 107 m/s. The final speed range is confirmed as 0 ≤ v ≤ 2.6 x 107 m/s. Clarifications regarding the use of Planck's constant (h) versus reduced Planck's constant (h-bar) are also discussed, emphasizing the importance of the correct constant in calculations.

PREREQUISITES
  • Understanding of the Uncertainty Principle in quantum mechanics
  • Familiarity with the concept of confinement in quantum systems
  • Basic knowledge of particle physics, specifically protons and their properties
  • Proficiency in algebraic manipulation of physical equations
NEXT STEPS
  • Study the implications of the Uncertainty Principle in quantum mechanics
  • Explore the differences between Planck's constant (h) and reduced Planck's constant (h-bar)
  • Research the behavior of particles in confined spaces, such as quantum wells
  • Learn about the application of quantum mechanics in nuclear physics
USEFUL FOR

Physicists, students studying quantum mechanics, and anyone interested in the behavior of particles at the atomic level will benefit from this discussion.

Linus Pauling
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1. A proton is confined within an atomic nucleus of diameter 3.80 fm. Estimate the smallest range of speeds you might find for a proton in the nucleus.



2. Uncertainty Principle



3. 3.80fm * mv = h/2

Soliving for h, using mass of proton = 1.67*10-27kg, I obtain v = 5.22*107. Then, dividing by two I obtain a final answer:

0 less than/equal to v less than/equal to 2.6*107

Is this correct?
 
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That is how I would set it up. I got a different answer though. You are using h-bar not h right?
 
Why h-bar? The uncertainty principle is delta(x)delta(p) greater than/equal to h/2
 
any luck with this question? I have the same question with different values am not sure how to approach it
 
dc5itr888 said:
any luck with this question? I have the same question with different values am not sure how to approach it

Op set it up right he just used h instead of h-bar.
 

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