Lecture16NuclearReactions_002

Lecture16NuclearReactions_002 - Lecture 16 Nuclear...

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Lecture 16 Nuclear Reactions II D. Decay During Bombardment 1. Production of radioactive products that decay during bombardment is an important consideration in isotope preparation (secular equilibrium). dN dt = R N Production Decay Rate Rate 2. Solution to Differential Equation N = R (1 e  T ) , where T = bombardment time ( a s s u m e R f (time) ; i.e., constant) 3. Saturation Factor: 1 e  t e . g . T = t 1/2 , N = (R/ )(1-1/2) = (R/ )(1/2) T = 2 t 1/2 , N = (R/ )(1-1/4) = (R/ )(3/4) ; 50% more T = 3 t 1/2 , N = (R/ )(1-1/8) = (R/ )(7/8) ; 25% more That is, after one half-life bombardment time, reach a point of diminishing returns; cost of accelerator operation is constant. 4. Rearranging Above Result N = R (1 e  T ) = A c 5. Chronology Accelerator ON Accelerator OFF Measure Sample 14 C production in atmosphere also time 0 T t A + B C C D C D N c (T) = (R/ )(1 e  T ) = N c (t-T) = N c (T) e  (t-T) ) =
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E. Neutron-Induced Reactions No Coulomb barrier (Z p = 0) Only Q influences energetics and Q is always positive ; E th =0 0 1 Z A Z A+1 n + X X + Q [ NOTE: in reverse reaction Q = B n 1. Neutron Beams: n Same expression as for charged particles R = I x 2. Nuclear Reactors: Common Situation GEOMETRY: Neutron gas that permeates volume of solid, liquid or gas (1) All target nuclei are accessible to neutrons: N T (2) Neutrons fill volume of sample (neutron gas) n n (neutrons/cm 3 ) velocity (cm/s) = , NEUTRON FLUX = n n v i.e., higher the the neutron density and velocity, more likely to react. Rate = R =  N T N = R(1 e  T )
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3. N a.
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Lecture16NuclearReactions_002 - Lecture 16 Nuclear...

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