KE of Electrons to give same theta as light in double slit diffraction

In summary, the conversation discussed the use of coherent light passing through two narrow slits to produce an interference pattern, with the second-order bright fringe located at an angle of theta. The question was posed about using electrons instead of light and determining the necessary kinetic energy for them to also produce a second-order maximum at theta. The conversation then explored the equations h=p lambda and E=hf, and how momentum and kinetic energy relate. Ultimately, the solution was found using the equation Ek = p^2/(2m) and n lambda = d sin theta.
  • #1
Silly Sausage
4
0

Homework Statement



Coherent light is passed through two narrow slits whose separation is d. The second-order bright fringe in the interference pattern is located at an angle of theta.

If electrons are used instead of light, what must the kinetic energy of the electrons be if they are to produce an interference pattern for which the second-order maximum is also at theta?

Homework Equations



No relevant equations givven

The Attempt at a Solution



Well, I started by saying that the wavelength of the electrons will be the same as the wavelength of light, and thought of using h=p lambda and then E=hf.

However I then confused myself because for h=p lamba I need the momentum and for that I need the speed. E=hf will give me kinetic energy wouldn't it? Can I please have some hints and pointers as to what direction I should be thinking in?
 
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  • #2
Silly Sausage said:
Well, I started by saying that the wavelength of the electrons will be the same as the wavelength of light, and thought of using h=p lambda
Good. Use that to find the momentum of the electrons.
and then E=hf.
That would apply for photons, not electrons.

How does momentum relate to kinetic energy?
 
  • #3
OK. I used Ek = p^2/(2m) and h=p lambda

to give Ek= h^2/(lambda^2*2m)

now do I use n lmbda = dsin theta?
 
  • #4
done it! thanks guys!
 
  • #5
Sounds good to me.
 

1. What is the relationship between the kinetic energy of electrons and the angle of diffraction in a double slit experiment?

The kinetic energy of electrons and the angle of diffraction in a double slit experiment are directly proportional. This means that as the kinetic energy of electrons increases, the angle of diffraction also increases. This relationship is described by the equation KE = hλ/2d sin(θ), where KE is the kinetic energy, h is Planck's constant, λ is the wavelength of the electrons, d is the distance between the slits, and θ is the angle of diffraction.

2. How does the kinetic energy of electrons compare to the energy of light in a double slit experiment?

The kinetic energy of electrons is much smaller than the energy of light in a double slit experiment. This is because electrons have a much smaller mass compared to photons (particles of light). Even at high speeds, the kinetic energy of electrons is still significantly lower than the energy of light, which is why electrons are used in diffraction experiments instead of light.

3. Can the kinetic energy of electrons be adjusted to give the same angle of diffraction as light in a double slit experiment?

Yes, the kinetic energy of electrons can be adjusted to give the same angle of diffraction as light in a double slit experiment. This is achieved by changing the energy of the electrons using an electron gun or by adjusting the voltage of the electron beam. By varying the kinetic energy, the wavelength of the electrons can also be changed, resulting in the same angle of diffraction as light.

4. Why is it important for the kinetic energy of electrons to match the energy of light in a double slit experiment?

It is important for the kinetic energy of electrons to match the energy of light in a double slit experiment because it allows for a direct comparison between the two. By matching the kinetic energy, the wavelength of the electrons can also be adjusted to match the wavelength of the light, resulting in similar interference patterns. This allows for a better understanding of the wave-particle duality of matter.

5. What other factors can affect the kinetic energy of electrons in a double slit experiment?

Other factors that can affect the kinetic energy of electrons in a double slit experiment include the potential difference applied to the electron beam, the distance between the electron gun and the slits, and any external magnetic or electric fields present. These factors can alter the speed and direction of the electrons, ultimately affecting their kinetic energy and resulting in changes to the diffraction pattern.

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