Need help on uncertainty principle

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SUMMARY

The discussion focuses on applying the uncertainty principle to calculate the kinetic energy of a neutron within a nucleus, specifically when its wavelength is smaller than 2 x 10-15 m. The relevant equation discussed is ΔE Δt > h/4π, which relates energy uncertainty to time uncertainty. A participant expresses confusion regarding the calculation of energy (E) and time (t), suggesting a need for clarity on the relationship between position and momentum as an alternative approach.

PREREQUISITES
  • Understanding of the uncertainty principle in quantum mechanics
  • Familiarity with the concepts of kinetic energy and rest mass energy
  • Basic knowledge of wave-particle duality
  • Experience with fundamental physics equations and constants, such as Planck's constant (h)
NEXT STEPS
  • Study the derivation and implications of the uncertainty principle in quantum mechanics
  • Learn how to calculate kinetic energy using the formula E = mc2 and its applications
  • Explore the relationship between position and momentum in quantum mechanics
  • Investigate the role of wave functions in determining particle behavior within a nucleus
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Students of physics, particularly those studying quantum mechanics, as well as educators and anyone seeking to deepen their understanding of the uncertainty principle and its applications in particle physics.

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Homework Statement


In order for a neutron can exist in a nucleus, its wavelength must be smaller than the size of the nucleus (say 2 x 10-15 m)
Use the uncertainty principle to calculate and show that a neutron would have a kinetic energy much smaller than its rest mass energy


Homework Equations



ΔE Δt > h/4π


The Attempt at a Solution



I had no clue in how to solve this problem. At first, I was thinking to solve for E, but figured that I don't know how to calculate for t.

Can anyone help me with this question?
 
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There's another version of the uncertainty principle, involving position and momentum. Try that.

p.s. welcome to PF.
 

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