Finding wavelength of an electron

AI Thread Summary
To find the wavelength of an electron with a kinetic energy of 2.00 MeV and 2.08 GeV, the de Broglie wavelength equation must be adjusted for relativistic conditions since these energies exceed the electron's rest energy of 511.0 keV. The original equation used is not suitable for relativistic electrons, leading to unrealistic results. It is essential to ensure all units are consistent when performing calculations. The correct approach involves using relativistic equations to accurately determine the wavelength. Accurate calculations will yield realistic wavelengths for high-energy electrons.
kraigandrews
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Homework Statement


What is the wavelength of an electron with a kinetic energy of 2.00 MeV?

What is the wavelength of an electron with a kinetic energy of 2.08 GeV?

(Possibly useful constants: hc = 1239.8 eVnm, rest energy of the electron: E0,e = 511.0 keV.)


Homework Equations


\lambda=hc/(2(mc2)K)1/2



The Attempt at a Solution


Should be pretty straightforward, I keep getting the wrong answer though, should just be plug and chug, i would think.
 
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Are you sure that's a correct equation for the de Broglie wavelength? I've never seen it written that way, though I guess the units do check out...Making sure to put everything in the same units?

I did a rough calculation and you're right, the answers don't seem realistic.
 
Last edited:
Your equation for the wavelength is for a non-relativistic electron. Those kinetic energies, however, are greater than the rest energy of the electron, so you're in the relativistic regime.
 

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