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Quantum Phenomena question

  1. Mar 11, 2010 #1
    1. The problem statement, all variables and given/known data
    Hi, I'm fairly new to these forums and I'm stuck on a problem. Just wondered if anyone could give me any hints or tips on how to get started on the following question:
    An unstable particle produced in a high-energy collision has a mass of m and an uncertainty in mass that is p of the particle's mass. Estimate the liftime of the particle.


    2. Relevant equations

    I am assuming this question has something to do with Heisenbergs Uncertainty Principle. i.e
    [tex] \Delta x*\Delta p >= \hbar [/tex] where p is momentum and x is some distance
    From the information given I assume I have to use the above formula to get:
    [tex] \Delta x*(p/m)*v >= \hbar [/tex] ....? where p/m is the uncertainty in the mass described in the question

    3. The attempt at a solution
    As I said at the begining I don't really know how to get started on this question, and thus the derived relationship above is all I have managed to come up with thus far. I am begining to think that this question requires me to calculate the energy of the particle by calculating the minimum uncertainty on the momentum (i.e (p/m)*V). If the equation that I have formulated so far is correct, what am I supposed to use for delta x? From the information given I cannot see any way to deduce this. Any indication on whether im on the right lines here or any other help would be very much appreciated. Thanks in advance, Kam.
     
    Last edited: Mar 11, 2010
  2. jcsd
  3. Mar 12, 2010 #2
    Can anyone please give me an idea whether I am heading in the right direction here, or indicate to me that I need to show more working before anyone will assist me further? Thanks.
     
  4. Mar 12, 2010 #3

    collinsmark

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    Okay, I'll bite. You are correct that this is related to Heisenberg's Uncertainty Principle.

    You are also correct that position and momentum are canonical conjugates under the uncertainty principle. But I don't think that position and momentum are related to this problem.

    Time and Energy are also canonical conjugates under the uncertainty principle. Also, from special relativity, an uncertainty in mass is the same thing as uncertainty in energy. :wink:

    I don't think "p" here (originally from the problem statement, "...uncertainty in mass that is p of the particle's mass...") refers to momentum. Rather I suspect that it refers to a probability related fraction. For example, if due to uncertainty, the particle's mass can vary by 25%, interpret the problem statement as saying "...uncertainty in mass that is 0.25 of the particle's mass..."

    From that, you should have the information necessary to estimate the lifetime of the particle.

    [Edit: and I suspect that you are supposed to express your answer in terms of 'p' and 'm']
     
    Last edited: Mar 12, 2010
  5. Mar 12, 2010 #4
    Ok I will take on board what you have said and I will try and solve this problem. I did not know that the uncertainty principal could be related to time and energy. Thank you for your help :)
     
  6. Mar 13, 2010 #5
    Ok so I now have the equation [tex] \Delta t \Delta E = \hbar [/tex]
    I have used the equation E = mc^2 and substituted the values into the Heisenberg equation to get:
    [tex] \Delta t = hm/(2 \pi c^2 p) [/tex]
    However mastering physics is saying that this answer is incorrect :(
     
  7. Mar 13, 2010 #6

    ehild

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    Check your formula. Is m at the proper place?


    ehild
     
  8. Mar 13, 2010 #7
    Hi, I used the value p/m for the mass as I assumed this would represent the ratio of the uncertainty of the mass to the actual mass of particle. When I divide through by (p/m)c^2 (In the Heisenberg equation) doesn't the m go to the top? Or have I got my relationship between p and m wrong, should the uncertainty in the mass be p*m not p/m? Thanks.

    [EDIT Problem solved, thanks!]
     
    Last edited: Mar 13, 2010
  9. Mar 13, 2010 #8

    Redbelly98

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    Glad you have solved it. Here is a tip for the future:

    Units are your friend! :smile: p/m does not have units of mass; p*m does have units of mass. (As long as you realize that p is unitless.)
     
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