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Pion decaying into 2 photons

  • #1

Homework Statement


The neutral pion is an unstable particle that decays very quickly after its creation into two photons (“particles” of light: v = c, mo = 0). The pion has a rest-mass energy of 135 MeV. Consider a pion that has a kinetic energy of 90 MeV
1) Determine the v of this pion
2) Determine the momentum of the pion
3) Determine the sum of the energies of the photons


Homework Equations


1) moc2[tex]\gamma[/tex] = KE + Rest E
2) mov[tex]\gamma[/tex] = p
3) Ephotons= pc


The Attempt at a Solution


I'm pretty sure I got 1 and 2. For 1 I added the KE + RE, converted to proper units, and finally got v = .80c
For 2 I got p = 9.6 x 10-20 kg m/s
Now I'm not so sure about #3. I think Ephotons = pc because momentum is conserved, and all of the pion's momentum gets turned into the photons' momentum. However, what about adding up the original rest mass energy + KE of the pion? If I do that I get a bigger energy then if I do pc. Thanks for all the help!
 

Answers and Replies

  • #2
Nabeshin
Science Advisor
2,205
16

Homework Statement


The neutral pion is an unstable particle that decays very quickly after its creation into two photons (“particles” of light: v = c, mo = 0). The pion has a rest-mass energy of 135 MeV. Consider a pion that has a kinetic energy of 90 MeV
1) Determine the v of this pion
2) Determine the momentum of the pion
3) Determine the sum of the energies of the photons


Homework Equations


1) moc2[tex]\gamma[/tex] = KE + Rest E
2) mov[tex]\gamma[/tex] = p
3) Ephotons= pc


The Attempt at a Solution


I'm pretty sure I got 1 and 2. For 1 I added the KE + RE, converted to proper units, and finally got v = .80c
For 2 I got p = 9.6 x 10-20 kg m/s
Now I'm not so sure about #3. I think Ephotons = pc because momentum is conserved, and all of the pion's momentum gets turned into the photons' momentum. However, what about adding up the original rest mass energy + KE of the pion? If I do that I get a bigger energy then if I do pc. Thanks for all the help!
Just using pure energy conservation, how much energy is there before and after the decay?
 
  • #3
Just using pure energy conservation, how much energy is there before and after the decay?
According to my calculations, E before = (90 + 135) MeV = 225 MeV
After E = pc = 181.25 MeV
 
  • #4
I calculated p a different way this time, p = sqrt(2mKE) where m is the relativistic mass. When I do this then multiply p by c to get E, I get E = 201 MeV. Oh boy...

edit: actually I'm not sure if that equation works for speeds close to c...
 
Last edited:
  • #5
Nabeshin
Science Advisor
2,205
16
According to my calculations, E before = (90 + 135) MeV = 225 MeV
After E = pc = 181.25 MeV
Hrm, you're letting the calculations get bogged down too much. The change in energy is zero, right? You know initial energy, so final energy must be.. the same.
 
  • #6
I get what you're saying, but I don't understand why the equations don't work here. It seems to me that momentum isn't conserved.
 
Last edited:
  • #7
and there is one more part to this problem which I thought I could get myself, but I can't. Here is a pic of the question/diagram

http://i44.tinypic.com/k12kja.gif
 

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