Uncertainty Principle and minimum kinetic energy

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SUMMARY

The discussion focuses on applying the Heisenberg uncertainty principle to estimate the minimum kinetic energy of an electron confined within an atom, specifically a region of approximately 1.7 x 10-10 m. The user successfully calculated the minimum momentum using the formula p = h/Δx and derived the kinetic energy using KE = p2/2m. The conversation then shifts to the implications of extending this analysis from a one-dimensional to a three-dimensional region, prompting the need to express momentum in terms of its components px, py, and pz.

PREREQUISITES
  • Understanding of the Heisenberg uncertainty principle
  • Basic knowledge of quantum mechanics
  • Familiarity with kinetic energy equations
  • Concept of momentum in three dimensions
NEXT STEPS
  • Research the implications of the Heisenberg uncertainty principle in three-dimensional systems
  • Learn how to express momentum in three dimensions using px, py, and pz
  • Explore quantum mechanics concepts related to electron confinement in atoms
  • Study the relationship between kinetic energy and momentum in quantum systems
USEFUL FOR

Students and professionals in physics, particularly those studying quantum mechanics, as well as educators looking for practical applications of the Heisenberg uncertainty principle in atomic physics.

cwatki14
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An atom represents a region about 1.7 10-10 m wide in which an electron is confined. Use the Heisenberg uncertainty principle to estimate the minimum kinetic energy of the electron, expressing your result in electron-volts (eV).

So I got the problem right when I analyzed the atom as a 1 d region. How will this change if it is a 3d region? I found minimum momentum=h/[tex]\Delta[/tex]x
and then used the equations KE=p^2/2m...
 
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Can you write p2 in terms of px, py, and pz?
 

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