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Simple positron diffraction problem

  1. Mar 3, 2014 #1
    1. The problem statement, all variables and given/known data

    A beam of positrons (positron ≡ antielectron) travels at 0.001% the speed of light and impinges on a slit that is 1 μm wide. Use modern units to find the angle θ between the center line and 3rd minimum of the resulting diffraction pattern. How far away (in cm) would you locate a detector so that the 3rd minimum is spaced 20 cm from the center line?

    2. Relevant equations
    wavelength = hc/pc where hc=1240nm*ev
    and i believe p=mv where mass is same as electron =9.1e-31 and so pc=mc2=0.511e6

    there is example in my notes where pc=mv*c=mc2(v/c) was used to find wavelength if v was given in % of c. but this is where I get confused because in the notes 0.1%*c becomes 0.001 somehow (10-2?)

    for minima: (n-0.5)*wavelength=d*sin(θ) where asked to find θ, d=1e-6m and n=3 for this problem.


    3. The attempt at a solution
    so.. after various incorrect attempts it give me what the answer should be but problem is I dont know how to get it :(

    θ = 46.7200 Degrees
    Tries 3/3
    L= 18.8339 cm
    Tries 3/3

    I think i should do something like find wavelength using 1240/(0.511e6*0.001) and if I do I get 2.43 nm. but i think im doing it wrong because I get wrong θ :(
     
    Last edited: Mar 3, 2014
  2. jcsd
  3. Mar 3, 2014 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Sure.
    100% = 1
    10% = .1
    1% = .01
    and so on.
     
  4. Oct 10, 2016 #3
    You used the wrong equation to find the angle. This is a question about diffraction, not interference. Your equation for the minima should be nλ=asinθ, where a is the slit width (in this case a=1e-6 m) and n=3.
    Your wavelength equation is correct. Wavelength should equal 242.7 nm.
    Use Y=Ltanθ to find L.
    20 cm is your vertical displacement from center line.
     
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