DeBroglie wavelength considering relativistic effects

They ask for assistance in finding the mistake. In summary, the conversation discusses the acceleration of electrons in an electron microscope and the calculation of their de Broglie wavelength, taking into account relativistic effects.
  • #1
*Alice*
26
0
"Electrons are accelerated by a potential of 350kV in an electron microscope. Calculate the de Broglie wavelength of those electrons taling relativistic effects into account"


I attempted the following:

W = W(kin) = 350keV

now

[tex]W(kin)= (1-gamma)mc^2 [/tex]

so, now one could solve for gamma and find the velocity of the particle.


afterwards [tex] p=m*v=h/lambda [/tex]

HOWEVER: I get a negative result in a root when I try to solve for v. Therefore I think that my energy formula must be wrong (I already excluded calculation errors). Can anyone see it?
 
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  • #2
*Alice* said:
"Electrons are accelerated by a potential of 350kV in an electron microscope. Calculate the de Broglie wavelength of those electrons taling relativistic effects into account"


I attempted the following:

W = W(kin) = 350keV

now

[tex]W(kin)= (1-gamma)mc^2 [/tex]

It's [itex] (\gamma -1) m c^2 [/itex] (the gamma factor is always larger or equal to 1)


Patrick
 

What is the DeBroglie wavelength?

The DeBroglie wavelength is a concept in quantum mechanics that describes the wave-like behavior of matter particles, such as electrons. It is defined as the wavelength associated with a particle's momentum and is given by the equation λ = h/mv, where h is Planck's constant, m is the mass of the particle, and v is its velocity.

How does this wavelength change with relativistic effects?

As particles approach the speed of light, their mass increases and their momentum changes. This leads to a change in their DeBroglie wavelength. The equation for the DeBroglie wavelength in the presence of relativistic effects is given by λ = h/mv(1-v^2/c^2)^1/2, where c is the speed of light.

Can the DeBroglie wavelength be observed in experiments?

Yes, the DeBroglie wavelength has been observed in several experiments, such as the double-slit experiment, where electrons were found to exhibit wave-like behavior. The wavelength can also be calculated and observed in particle accelerators.

What is the significance of the DeBroglie wavelength?

The DeBroglie wavelength is significant because it helped to establish the wave-particle duality of matter, which is a fundamental principle of quantum mechanics. It also allows us to understand and predict the behavior of particles on a microscopic level.

How does the DeBroglie wavelength relate to the uncertainty principle?

The DeBroglie wavelength is related to the uncertainty principle, which states that it is impossible to know both the position and momentum of a particle with absolute certainty. The smaller the DeBroglie wavelength, the more uncertain the particle's momentum becomes, and vice versa.

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