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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)


    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


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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;


    then I'm thinking maybe use kinetic energy/ momentum relation to get to energy?

    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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