Relativistic Calculations for De-Broglie Wavelength

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Homework Help Overview

The discussion revolves around determining the energy at which a non-relativistic calculation of the De Broglie wavelength for an electron and a proton becomes inaccurate by 5%. Participants are exploring the implications of relativistic effects on the calculations.

Discussion Character

  • Conceptual clarification, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants present differing approaches to the problem, with some asserting that the De Broglie wavelength is dependent on momentum, while others question the validity of substituting momentum with kinetic energy in the context of relativistic speeds.

Discussion Status

The discussion is ongoing, with participants examining the correctness of their approaches and questioning assumptions regarding the relationship between momentum and energy in relativistic scenarios. There is no explicit consensus yet, but some guidance has been offered regarding the limitations of non-relativistic calculations.

Contextual Notes

Participants are navigating the complexities of relativistic versus non-relativistic mechanics, particularly in relation to the De Broglie wavelength, and are addressing potential errors in their calculations.

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Homework Statement


At what energy will a non-relativistic calculation of the De Broglie wavelength of an electron be in error by 5%? What is this energy for a proton? Comment on your results.

Homework Equations


I have two (seemed to be) logical answers for this question, but with different values

how to resolve this, there must be at least one wrong answer

i need a resolution [/B]

The Attempt at a Solution


Solution 1
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Solution 2
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The second approach has the right relativistic de-Broglie wavelength. It depends on the momentum, not on "the energy above the rest energy plugged into the nonrelativistic expression".
 
As far as i understand, there is nothing in the first approach states that the De-Broglie wavelength depend in anything but the momentum
in the first approach i replaced the momentum by the kinetic energy, and this is a valid replacement

please explain your point
 
You replaced momentum by the kinetic energy in nonrelativistic mechanics. It won't give the right result for relativistic speeds.
 
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