CHAPTER 43 - 8

CHAPTER 43 - 8 - 39(a , Coulombbarrier. r =(1.2fm(12...

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39. ( a ) To initiate the reaction, the kinetic energy of the initial nuclei must be sufficient to overcome the  Coulomb barrier.  The radii of the two initial nuclei for the first reaction of the carbon cycle are r = (1.2 fm)(12) 1/3  = 2.75 fm; r p  = (1.2 fm)(1) 1/3  = 1.2 fm. We assume the total kinetic energy equals the Coulomb energy when the nuclei are in contact: K C-p  =  U C-p  =  Z C Z p e 2 /4p Å 0 ( r C  +  r p ). The radii of the two initial nuclei for the deuteron-tritium reaction are r = (1.2 fm)(2) 1/3  = 1.51 fm; r t  = (1.2 fm)(3) 1/3  = 1.73 fm. We assume the total kinetic energy equals the Coulomb energy when the nuclei are in contact: K d-t  =  U d-t  =  Z d Z t e 2 /4p Å 0 ( r d  +  r t ). Thus the ratio is K C-p / K d-t  =  Z C Z p ( r d  +  r t )/ Z d Z t ( r C  +  r p ) = (6)(1)(1.51 fm + 1.73 fm)/(1)(1)(2.75 fm + 1.2 fm) =     
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