Help with Exams This Week? Ask Bobster!

[Bobster]

Exams This Week...need Help Please !

hi guys ! good 2c every1 again..been a while..ive got my 3rd year uni exams..and it aint lookin good...can ne1 help me with this one ?

Homework Statement

An inertial observer sees a particle moving at a speed 3c/5..Its then seen to decay into 2 photons..draw an accurate diagram to illustrate the situation before and after the decay takes place.

What energies,expressed in terms of the rest mass energies of the initial particle would the observer measure for the 2 photons ?

Homework Equations

Using theory of conservation of 4 momentum/energy..maybe use of invariance of scalar product in any intertial frame..

The Attempt at a Solution

im ok with the diagram...its a line of form y [ct] = 5/3 x + C..right ? and then it splits into two 45 degree lines that correspond to worldlines for photons but in opposite directions at some time t...

now the 2nd bit...gamma is g =5/4 and v =3/5 c

i did P initial = P particle = (g 5/4 mc,g mv,0,0)=(g 5/4 mc,3/4 mc,0,0)

so taking dot product with itself i get -17/8 m^2 c^2

now i take a new frame..centre of momentum frame where its at rest the decays to two photons in opp directions...
here P final =(E tot/c,0,0,0) where e tot is total energy in this frame

so takin dot product wit itself and equating to above i get

0.5 root(17/8) E = E (tot) where E was rest mass energy of particle initially = m c^2 and E(tot)/2 gives energy of each photon in rest frame of initial particle...


can any1 help me ? is this right ?

cheers for any help

bobster

 

[Bobster]

any ideas folks ?

 

[mjsd]

don't have comment on the first bit (i guess you can cross check that easily once you have got 2nd bit correct)
you method for the 2nd bit seems fine to me, but the dot product was evaluated incorrectly (or my calc was wrong instead) either way, u should double check. remember the metric for the dot product is either -+++ or +---.