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Homework Help: Calculating quantum wavelengths

  1. Oct 23, 2007 #1
    1. The problem statement, all variables and given/known data
    Ok,as part of my dissertation I'm trying to explain about how quarks have a bigger quantum wavelength than protons so when you localise a quark inside a proton, the uncertainty in energy of the system becomes really big so there's a load of creation/anhilitation of other particles going on inside the proton.
    This is how my supervisor explained it but I'm not sure I get it...



    3. The attempt at a solution
    This is what my supervisor said;
    (I'm using D as 'uncertainty in', and h means h bar)

    to work out quantum wavelength of a proton;
    Start with Heisenberg

    1)DpDx>h (for a start I think this should be h/2)

    2)then use E=pc ------I don't understand why you can use this- it's not a realtivistic case. My supervisor said it works if you say that the proton is gaining energy by being hit with photons... but then

    3) sub equation (2) into(1)

    DE>hc/Dx

    but the momentum in 1) is the momentum of the proton and in 2) its the momentum of the photon so how does that work?

    4) then you sub in E=mc^2 to get; Dx>hc/mc^2

    and the quantum wavelength is h/mc

    I don't think this is right does anyone have a better argument?
     
    Last edited: Oct 23, 2007
  2. jcsd
  3. Oct 23, 2007 #2

    Gokul43201

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    That's a poor argument, though the end result is correct (to within some factors of pi and 2). The correct argument involves the limitation that dE be less than mc^2, in order that you do not create two particles out of one.
     
  4. Oct 23, 2007 #3
    I still don't quite understand- do you still start from heisenberg?

    Ok is it something like;

    DpDx>h/2

    then I'm thinking maybe use kinetic energy/ momentum relation to get to energy?
    (p=(2mE)^-1/2)

    and when you say dE<mc^2 is that the mass of the proton? cause surely it should be the mass of any other possible particle...?
     
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