CHAPTER 43 - 12 - (c)

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 O 8 18 (p, n) F 9 18 ( c ) From momentum conservation, the momenta of the  α  particle and the daughter will have equal  magnitudes: p Rn   =  p  = (2 m K ) 1/2   = [2(4 u)(1.66 × 10 –27  kg/u)(4.87 MeV)(1.6 × 10 –13  J/MeV)] 1/2  =       1.02 × 10 –19  kg     m/s . ( d ) The kinetic energy of the daughter is K Rn  =  p Rn 2 /2 m Rn   = (1.02 × 10 –19  kg     m/s) 2 /2(222 u)(1.66 × 10 –27  kg/u) = 1.4 × 10 –14  J =       0.088 MeV . Because this is less than 2% of the  Q -value, our approximation is valid. 63. Because the reaction   requires an input of energy, the  Q -value is negative: Q  = [ M ( 18 O) +  M ( 1 H) –  m (n) –  M ( 18 F)] c 2 ; – 2.453 MeV = [(17.999160 u) + (1.007825 u) – (1.008665 u) –  M ( 18 F)] c 2 (931.5 MeV/u c 2 ), which gives  M ( 18 F) =       18.000953 u .
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CHAPTER 43 - 12 - (c)

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