CHAPTER 43 - 3

# CHAPTER 43 - 3 - 14. Forthereaction 13 13 6 C(p , n )13N 7 1

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C 6 13 (p, n) N 7 13 R 1 d R 2 v 14. For the reaction  , we determine the  Q -value: Q   = [ M ( 13 C) +  M ( 1 H) –  m (n) –  M ( 13 N)] c 2   = [(13.003355 u) + (1.007825 u) – (1.008665 u) – (13.005739 u)] c 2 (931.5 MeV/u c 2 ) = – 3.003 MeV. The kinetic energy of the products is K n  +  K N  =  K p  +  Q . Because the kinetic energies «  mc 2 , we can use a non relativistic treatment:  K  =  mv 2 /2 =  p 2 /2 m .   The least kinetic energy is required when the product particles move together with the same speed.   With the target at rest, for momentum conservation we have p p  =  p n  +  p N  = ( m n  +  m N ) v ,   or    K p  =  p p 2 /2 m p  = [( m n  +  m N ) 2 /2 m p ] v 2  = [( m n  +  m N )/ m p ]( K n  +  K N ),  or   K n  +  K N  = [ m p /( m n  +  m N )] K p   . When we use this in the kinetic energy equation, we get

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## CHAPTER 43 - 3 - 14. Forthereaction 13 13 6 C(p , n )13N 7 1

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