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How long does a moun live during a measurement

  1. Sep 5, 2012 #1
    1. The problem statement, all variables and given/known data
    A muon with a kinetic energy of 200 ± 0.05 MeV
    is produced in a linear accelerator. The rest
    mass of the muon is 106 MeV/c2.
    (a) Calculate the speed of the muon (in units of c),
    (b) Calculate the linear momentum (in units of eV/c),
    (c) How long does it live during the measurement?
    (d) Find the lifetime of the muon.
    (e) What is the distance traveled by muon in laboratory
    before it disappears (use c = 3 x 108 m/s)? Could
    this distance be measured?
    (f) For identifying a muon what method do you think
    that is better: (1) based on measurements of energy
    or (2) based on measurements of distance? Why?

    I am having trouble with part c


    2. Relevant equations
    (1 stands for naught)
    E = E1 + K
    deltaE dot deltaT = h (I dont understand this equation)
    deltaT = h/deltaE


    3. The attempt at a solution
    I found this and the solution online I understand part a and b then answers are respectivley v=.938c and p=287MeV/c. It is part c that im struggling with this is what my instructor does he says deltaE dot deltaT = h which isnt on my equation sheet so im not sure about this. Then he states E = K + E1 remains constant, then sets deltaE=deltaK = .1MeV I think I understand where he got the equality part and I think I get how he got .1 I assume he did this .05-(-.05) = .1 = deltaK = deltaE. But I am not sure as to why he did this. Then deltaT = h/deltaE = (6.58e-16 eV.s)/(1e5 eV) = 6.58e-21s. How the heck did he obtain 6.58e-16 I am confused?
     
  2. jcsd
  3. Sep 6, 2012 #2
    Ouch! no replies yet very weird I guess maybe I was confusing or something.
     
  4. Sep 6, 2012 #3
    The equation you don't understand seems to be the uncertainty principle for energy and time.
     
  5. Sep 6, 2012 #4
    lol after looking up the uncertainty principle I agree thats what it is but I really need to know where the .1 and 6.58e-16 came from?
     
  6. Sep 7, 2012 #5
    .1 comes from the uncertainty of energy. 6.58e-16 is Planck's constant in eV.s.
     
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