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Homework Help: HELP - electron diffraction/relativity problem

  1. Jan 30, 2008 #1
    1. The problem statement, all variables and given/known data
    A beam of electrons is accelerated from rest through a potential difference of 0.100 kV and then passes through a thin slit. The diffracted beam shows its first diffraction minima at [tex]\pm[/tex]11.5 degrees from the original direction of the beam when viewed far from the slit. a) Do we need relativity formulas? How do you know? b) How wide is the slit?

    2. Relevant equations
    1) M = [tex]\gamma[/tex]m (possibly needed)
    2) [tex]\lambda[/tex] = [tex]\frac{h}{\sqrt{2meV_{accelerating}}}[/tex]
    3) [tex]\theta[/tex] = [tex]\frac{\lambda}{w_{slit}}[/tex]

    3. The attempt at a solution

    I can solve b) by just plugging in my numbers. The problem is a). If the electron is accelerated through 0.1 kV, it will have energy 0.1 keV, which puts its speed at a decent fraction of the speed of light. Classically, we would need Einstein's special relativity equations. However, electron diffraction is a quantum phenomenon - does this make the electron's mass immune to the effects of relativity or do I have to calculate its speed, find the new mass, and use that instead of the rest mass?
    Last edited: Jan 30, 2008
  2. jcsd
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