Finding wavelength of an electron

You'll need to use the relativistic expression for the de Broglie wavelength, which is \lambda=h/(mc)(1+(K/E0,e)2)1/2.In summary, the conversation was about finding the wavelength of an electron with a given kinetic energy. The original equation used was incorrect for relativistic energies, and the correct equation to use is the relativistic expression for the de Broglie wavelength.
  • #1
kraigandrews
108
0

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


[itex]\lambda[/itex]=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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  • #2
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:
  • #3
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.
 

FAQ: Finding wavelength of an electron

What is the wavelength of an electron?

The wavelength of an electron is a physical quantity that represents the distance between two consecutive peaks or troughs of its wave-like behavior. It is commonly denoted by the Greek letter lambda (λ) and is measured in units of meters (m).

How is the wavelength of an electron calculated?

The wavelength of an electron can be calculated using the de Broglie equation, which states that the wavelength (λ) is equal to Planck's constant (h) divided by the momentum (p) of the electron. This can also be expressed as λ = h/p.

Why is it important to find the wavelength of an electron?

Finding the wavelength of an electron is important in understanding the wave-particle duality of matter, which is a fundamental concept in quantum mechanics. It also has practical applications in electron microscopy and other fields of research.

What factors can affect the wavelength of an electron?

The wavelength of an electron can be affected by its energy, velocity, and the potential difference it is passing through. It can also be influenced by external factors such as electric and magnetic fields.

Can the wavelength of an electron be measured experimentally?

Yes, the wavelength of an electron can be measured experimentally using diffraction or interference techniques. These methods involve passing electrons through a barrier or a series of slits and measuring the resulting diffraction or interference patterns to determine the wavelength.

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