De Broglie wavelength and diffraction

Therefore, in this case, diffraction will occur and it may affect the picture on the screen.In summary, to check if the calculations take relativity into account, check if the velocity is close to the speed of light. If so, the energy is not given by 1/2*mv^2. Additionally, if the neck of the tube is of a similar size to the wavelength, diffraction will occur and may affect the picture on the screen.
  • #1
josephcollins
59
0
Hi ppl I have a short question concerning the de Broglie hypothesis. I worked out the de Broglie wavelength of an electron in a TV picture tube accelerated by 20,000 V, using the fact that mv^2/2 = QV and then that lambda=h/mv. Now I need to answer whether this is relativistic or not, how do I do this? and then the neck of the tube is 5cm and I'm asked whether we have to worry about diffracttion blurring the picture on the screen. The wavelength is obviously much smaller than the neck of the tube, so diffraction will occur, will this then affect the picture? Thanks for any help, Joe
 
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  • #2
To check whether or not your calculations take relativity into account, first check to see if v is close to c. If it is then the energy is not given by 1/2*mv^2.

Secondly the neck of the tube has to be of the same order as the wavelength for diffraction to occur.
 

1. What is the De Broglie wavelength?

The De Broglie wavelength is a concept in quantum mechanics that describes the wavelength of a particle, such as an electron, based on its momentum. It is given by the formula λ = h/mv, where h is Planck's constant, m is the mass of the particle, and v is its velocity.

2. How does De Broglie wavelength relate to diffraction?

The De Broglie wavelength is related to diffraction because it determines the spacing between diffraction patterns. When a particle's wavelength is similar to the spacing between atoms in a crystal, it can diffract off of the crystal and produce a diffraction pattern.

3. Can all particles exhibit diffraction?

Yes, all particles, including macroscopic objects, can exhibit diffraction. However, the effect is most noticeable for particles with a small mass and high velocity, such as electrons.

4. How does the De Broglie wavelength change with increasing velocity?

As the velocity of a particle increases, its De Broglie wavelength decreases. This is because the momentum of the particle increases, and as a result, its wavelength becomes smaller according to the formula λ = h/mv.

5. What is the significance of De Broglie wavelength in quantum mechanics?

The De Broglie wavelength is significant in quantum mechanics because it helps explain the wave-like behavior of particles, which is a fundamental principle of quantum mechanics. It also allows for the prediction and understanding of phenomena such as diffraction and interference in the microscopic world.

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