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Lifetime of J/ψ meson - easy

  1. Apr 24, 2005 #1
    I'm just being introduced to particle physics and wondering if I'm going about this correct..can someone help me? thanks

    The measured width of the J/ψ meson is 88 keV. Estimate its lifetime.

    Lifetime (s) of J/ψ meson is 8E-21 s
    Using uncertainty principle: ΔE = h/2πΔt isolate for delta t?
    8E-21s – 5E-22s
    = 7.5E-21 s ?
     
    Last edited: Apr 24, 2005
  2. jcsd
  3. Apr 24, 2005 #2

    dextercioby

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    Yes,u have to use the uncertainty time-energy...It should be ~[itex] 7\cdot 10^{-21}s [/itex]

    Daniel.
     
  4. Apr 24, 2005 #3

    thanks Daniel,

    sorry to bother you again but do you think you can detail that out for me a little more..I think I'm having a little trouble following the steps of proportion to get [itex] 7\cdot 10^{-21}s [/itex]

    thanks
     
  5. Apr 24, 2005 #4

    dextercioby

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    Okay.Assume the general uncertainty relation being satisfied in the equality limit also for time & energy (nice discussion on this relation,chapter 2 of [1]).

    [tex] \Delta E\Delta t=\frac{\hbar}{2} [/tex]

    Therefore

    [tex] \Delta t=\frac{\hbar}{2\Delta E}\simeq\frac{6.626\cdot 10^{-34}\mbox{Js}}{4\pi\cdot 88\cdot 10^{3}\cdot 1.6\cdot 10^{-19}\mbox{J}}\simeq 3.74\cdot 10^{-21} \mbox{s} [/tex]

    The difference from the prior result (post #2) comes from using [itex] =\frac{\hbar}{2} [/itex] instead of [itex]\approx\hbar [/itex] which is cusomery as well.


    Daniel.


    ------------------------------------------------------
    [1] J.J.Sakurai,"Modern Quantum Mechanics",any of the 2 editions.
     
    Last edited: Apr 24, 2005
  6. Apr 24, 2005 #5

    dextercioby

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    Hmmmm,something weird here. :grumpy: The above message appears as unposted. :confused: Can anyone see it...?

    Daniel.
     
  7. Apr 24, 2005 #6
    thankyou Daniel,

    I see now. But why did you use 4pi instead of 2pi?

    thanks,
    Jason
     
  8. Apr 24, 2005 #7

    dextercioby

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    It comes from
    [tex] \frac{\hbar}{2}=\frac{h}{4\pi} [/tex].​


    Daniel.
     
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