DeBroglie matter waves and double-slit

In summary, using the equations provided, we can determine the angular position of the electrons in the fifth order when they strike an array of atoms with a kinetic energy of 1.00 MeV and a distance of 0.25 nm between the atoms. However, special relativity may need to be taken into consideration when finding the momentum and wavelength of the electrons.
  • #1
Darrinr769
1
0

Homework Statement


A beam of electrons with a kinetic energy 1.00 MeV strikes normally at an array of atoms separated by 0.25 nm. in what direction can we expect the electrons in the fifth order?


Homework Equations


Ek= hf - W
p=h/λ
dsinθ=nλ

The Attempt at a Solution


i tried my hardest, but i didnt know where to start
 
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  • #2
Your last equation is for working out the angular position, θ, of the interference maxima when you have waves that are normally incident on a diffraction grating. I think the idea here is that the spaces between the atoms work like gaps in a diffraction grating so it's not quite a double slit set up like you described in the title - but no matter, just use that last equation to find the angle when n = 5.

Your problem is that you don't know the wavelength of the electrons. I suspect that things get a bit more complicated because at 1 MeV the electrons are going to be moving fast enough that you're going to have to take special relativity into consideration when finding the momentum. You need the momentum to get the wavelength with your second equation. I'm not sure what to do with your first equation - it looks like the the equation that describes the photoelectric effect and I'm not sure that it fits in anywhere.

Anyway, do you have any special relativity type equations are to do with the energy of a particle?

PS

When I work though this I get a really neat answer - I think you just have to work through some large and messy numbers to get there!
 
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Related to DeBroglie matter waves and double-slit

1. What are DeBroglie matter waves?

DeBroglie matter waves, also known as matter waves or de Broglie waves, are a concept in quantum mechanics that describes the wave-like behavior of particles, such as electrons, at the atomic and subatomic level. These waves are associated with the motion of particles and can exhibit interference patterns similar to those seen in light waves.

2. How are DeBroglie matter waves related to the double-slit experiment?

The double-slit experiment is a classic experiment that demonstrates the wave-like behavior of particles. In this experiment, particles, such as electrons, are fired at a barrier with two parallel slits. The resulting pattern on the other side shows interference fringes, which can only be explained by the presence of matter waves that interfere with each other as they pass through the slits.

3. What is the significance of DeBroglie matter waves?

The concept of matter waves has significant implications in the field of quantum mechanics. It helped to bridge the gap between the wave-like and particle-like behavior of particles, and it also provided a new way of understanding the behavior and properties of particles at the atomic and subatomic level.

4. How are the properties of DeBroglie matter waves determined?

The de Broglie wavelength, which describes the wavelength of a matter wave, is determined by the momentum of the particle. The more momentum a particle has, the shorter its de Broglie wavelength will be. This means that particles with higher energies will have shorter de Broglie wavelengths and exhibit more wave-like behavior.

5. Can DeBroglie matter waves be observed in everyday life?

DeBroglie matter waves are typically only observed at the atomic and subatomic level. However, some experiments have shown that larger molecules, such as buckyballs, can also exhibit wave-like behavior. In everyday life, the effects of matter waves are not noticeable, as they are too small to be seen without specialized equipment.

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