Wave properties of matter

JaWiB

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

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

3. 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?)

Shooting Star

[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:
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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.

JaWiB

>[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 (?)

JaWiB

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