Do Muons and Electrons with the Same Kinetic Energy Share Identical Wavelengths?

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Homework Help Overview

The discussion revolves around the relationship between the kinetic energy and wavelength of muons and electrons, specifically questioning whether muons with the same kinetic energy as electrons share identical wavelengths. The subject area includes concepts from quantum mechanics and particle physics, particularly the de Broglie wavelength and relativistic energy.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the implications of the equations relating energy and wavelength, questioning the validity of applying certain equations to massive particles like muons and electrons. There is a discussion about the differences in kinetic energy expressions and the relevance of relativistic effects.

Discussion Status

The discussion is ongoing, with participants raising questions about the assumptions made in the original statement. Some participants suggest that the equations used may not apply to the scenario described, particularly regarding the nature of the particles involved and their respective energies. There is no explicit consensus, but various interpretations are being explored.

Contextual Notes

Participants note that the problem statement does not explicitly mention the assumption of equal energy, which leads to confusion. There is also mention of the limitations of certain equations, particularly in relation to massless particles and the conditions under which they apply.

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Homework Statement



Consider the statement below made by a student: "Muons have a higher mass than electrons, but because the energy, E, is related to the wavelength by E=hc/[tex]\lambda[/tex], muons that have the same kinetic energy as electrons will also have the same wavelength."

Do you agree or disagree with this statement? Explain your reasoning.

Homework Equations



[tex]\lambda=h/p[/tex] (de Broglie wavelength)

The Attempt at a Solution



The statement seems wrong to me. If you substitute in for [tex]\lambda[/tex] in the first equation, you get cp, but kinetic energy is p^2/(2m) and those two can't be the same (solving for c gives c=v/2).

I'd never seen the first equation before, but looking in my textbook it looks like E is the change in energy of an atom when a photon is absorbed or emitted and I don't know how you could apply it to an electron/muon (can you?)
 
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[itex]\lambda[/itex] is different for different objects, so why should E be the same?

E is the total relativistic energy, not p^2/2m. Also, E = hf, where f is the frequency associated with the de Broglie wave.

Just do the simple math. Also, reading up on de Broglie wavelength would be a good idea.

EDIT:
-----

Are you talking about the muons and the electrons having the same energy, by any chance? This is not mentioned in the problem, so I assumed not.

Also, [itex]E=hc/\lambda[/itex] is valid only for massless particles which travel at speed c.
 
Last edited:
>[itex]\lambda[/itex] is different for different objects, so why should E be the same?
The question is assuming you have two particles with the same kinetic energy.

>For high speed particles, E is the total relativistic energy, not p^2/2m.
Ok, but I still doubt that cp=Ek for an electron. Is that wrong?

>Also, E = hf, where f is the frequency associated with the de Broglie wave.
And if f=v/[tex]\lambda[/tex], then E = vp. But v can't be c for an electron, so the equation can't work here (?)
 
Sorry, you posted while I was replying. Yes, that's the problem:
"muons that have the same kinetic energy as electrons..."

>Also, is valid only for massless particles which travel at speed c.

I'm guessing this is essentially the answer to the question
 

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