Uncertainty Principle and minimum kinetic energy

AI Thread Summary
The discussion focuses on applying the Heisenberg uncertainty principle to estimate the minimum kinetic energy of an electron confined within an atom, initially analyzed as a one-dimensional region. The user successfully calculated the minimum momentum using the formula p = h/Δx and derived the kinetic energy from the momentum equation KE = p²/2m. A question arises regarding the transition from a one-dimensional to a three-dimensional analysis, prompting the need to express momentum in terms of its components px, py, and pz. The conversation emphasizes the importance of understanding the implications of dimensionality on kinetic energy calculations. This highlights the complexity of quantum mechanics when considering multi-dimensional systems.
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/\Deltax
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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