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Lets try solving this

  1. Jun 25, 2005 #1
    hi,

    I have a problem and I am trying it out and would like to have suggestions as well. I would post the solution after I finish and will have opinions :smile: .Meanwhile I would like others to try this....I shall be obliged to get any ans... :smile:

    An unstable particle of rest energy 1000MeV decays into a meu-meson (Mo csqr=100MeV) and a neutrino with a mean life, when at rest, of 10^-8 sec.
    a) calculate the mean decay distance when the particle has a momentum of 1000MeV/c.
    b) What is the energy of the meu-meson if it is emitted at an angle 15 degrees.

    ps- i guess its the spelling of meu as i can't write the symbol,correct if it's wrong...
    and ^ stands for "raised to the power"
    Thanks
     
  2. jcsd
  3. Jun 25, 2005 #2

    OlderDan

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    I have an answer for a) as the product of the particle velocity times its time-dilated mean life. The velocity is found from the initial momentum and rest energy. Have you found this?

    I'm working on b)
     
  4. Jun 25, 2005 #3
    thanks...yes i have found a) in the same way...and have got the ans 3m...

    for 2nd one i am using four vectors......i always face difficulty in solving these problems using other methods...its almost solved but i hav not yet put the values to get the ans...
     
  5. Jun 26, 2005 #4
    four vectors----

    Px =( Px, jEx)

    P μ =(Pμ ,jEμ)

    P ν =( P ν , jE ν)

    [I tried to put arrow head but couldn't, its getting displaced]

    Now,

    P ν = Px - P μ

    Squaring we get

    P ν 2 = (Px - P μ) 2


    =>mx2 + mμ2 – 2Ex E μ + 2Px P μ cos θ = 0, θ = 15 degrees

    by putting values and neglecting mμ2 we get

    E μ =1115.36 MeV [here, E μ is equivalent to P μ ]

    :smile: is this correct?
     
    Last edited: Jun 26, 2005
  6. Jun 26, 2005 #5

    OlderDan

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    Deleted erroneous calculations and related comments
     
    Last edited: Jun 26, 2005
  7. Jun 26, 2005 #6
    thanks for the solution :smile: ...well i am not finding any sign error in my equation; its by solving 4 vectors... only i have multiplied the original eqn with -1 to write it in simplified way[i have not written all the steps here]....your equations are correct but i think we have a sign mismatch.. ...i generally avoid the term mμ sqr in such problems as in case of high energy muons, its negligible....
    please confirm if your eqns' signs are correct....

    thanks :smile:
     
    Last edited: Jun 26, 2005
  8. Jun 26, 2005 #7

    OlderDan

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    I did make an error, but it was worse than just a sign mistake. I now agree with your original equation, but my earlier result is way off. I have reproduced your result neglecting the rest mass of the muon. Without the approximation, it's a messy thing to be sure.
     
    Last edited: Jun 26, 2005
  9. Jun 26, 2005 #8
    thanks for your suggestions and cooperation..okay...so i can infer that my ans is correct :smile:


    thanks & regards
     
    Last edited: Jun 26, 2005
  10. Jun 26, 2005 #9

    OlderDan

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    Yep.. looks good to me now. I even managed to get through it without neglecting the muon rest mass. I thought it might be useful to have the general result in hand :smile: I got 1116.84Mev. Obviously not a big dfference for this problem.
     
  11. Jun 27, 2005 #10
    by NOT neglecting, i got somewhat similar results :smile: as yours...

    cheers
     
    Last edited: Jun 27, 2005
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