Relativistic Calculations for De-Broglie Wavelength

AI Thread Summary
The discussion focuses on determining the energy at which the non-relativistic calculation of the De Broglie wavelength for an electron and a proton becomes inaccurate by 5%. Two approaches to the problem yield different results, leading to confusion about the correct method. The second approach correctly emphasizes that the De Broglie wavelength depends on momentum rather than solely on kinetic energy. It is noted that using kinetic energy in non-relativistic mechanics does not yield accurate results at relativistic speeds. The conversation highlights the importance of understanding the relationship between momentum and energy in relativistic contexts.
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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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