How Does the Uncertainty Principle Apply to a Particle in a Femtometer Sphere?

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SUMMARY

The discussion focuses on applying the Heisenberg Uncertainty Principle (HUP) to a particle confined within a spherical radius of one femtometer (10^-15 m). Participants clarify that the uncertainty in the x-coordinate is 2R, not R, which affects momentum calculations. The expected momentum values discussed include 20 keV/c, 200 keV/c, 200 MeV/c, and 2 GeV/c. The conclusion emphasizes that while precise answers are unattainable, selecting the nearest estimate is the best approach.

PREREQUISITES
  • Understanding of the Heisenberg Uncertainty Principle (HUP)
  • Familiarity with quantum mechanics and particle confinement
  • Knowledge of momentum calculations in quantum physics
  • Basic grasp of units such as keV/c and GeV/c
NEXT STEPS
  • Study the implications of the Heisenberg Uncertainty Principle in quantum mechanics
  • Explore momentum calculations for confined particles in quantum systems
  • Research the significance of volume in uncertainty calculations
  • Investigate the relationship between particle confinement and energy levels
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Students and professionals in physics, particularly those specializing in quantum mechanics, particle physics, and theoretical physics, will benefit from this discussion.

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A particle is confined within a spherical radius of one femtometer(10^-15 m)?

Its momentum can be expected to be about-
1. 20 keV/c
2. 200 keV/c
3. 200 MeV/c
4. 2 GeV/c

How should I go about using HUP on a problem like this one? I tried substituting x=10^-15 meters in px=h/4 pi but the answer is wrong. Apparently because the problem is about volume.
 
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We can only estimate the magnitude order of it; the answer is no way precise. Just pick the answer which is nearest to your answer.
By the way, the uncertainty in x-coordinate is 2R, not R.
 

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