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E1 = E2 = ÅÅÅÅ Etotal = ÅÅÅÅ K + m c2 º 1.011 MeV
2
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(b) (c) Ø Here is what you should already know:
p1,y =  p2,y
(1)
p1,x = p2,x
(2)
So you only need to solve for the momentum of one of the g rays.
It's a good idea to start with conservation of momentum.
p1,x + p2,x = pfinal = pe
(3)
Combining (2) and (3) gives
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p1,x = ÅÅÅÅ pe
(4)
2
We can find pe from K using
"################ #########
2 ########
E He L = Hm c2 L + H pe cL2 = K + m c2
which yields
!!!!!!!!!!!!
1 è !!!!!!!!!!!!!!!!
pe = ÅÅÅÅ K 2 + 2 K m c2
c
which means that we have p1,x !
!!!!!!!!!!!!
1 è!!!!!!!!!!!!!!!!
MeV
p1,x = ÅÅÅÅÅcÅÅ K 2 + 2 K m c2 º 0.711 ÅÅÅÅÅÅÅÅÅÅÅÅ
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c
How do we find p1,y then? We can use the energy E1 to find the magnitude p1 ,
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p1 = E1 ê c = ÅÅcÅÅ H ÅÅÅÅ K + m c2 L
2
2 + p 2 = p2 and solve for p
and then use p 1 1,x 2, x final e Combining (2) and (3) gives
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p1,x = ÅÅÅÅ pe
(4)
2
We can
quiz2solns.nb find pe from K using
"############...
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This document was uploaded on 02/26/2014 for the course PHYS 2D at UCSD.
 Fall '08
 Hirsch
 Physics

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