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= Nuclear reactions and nuclear reactors<br> =
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= Nuclear reactions and nuclear reactors<br> =
  
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1: It is noteworthy to notice the Q-value for the neutron capture and the change in binding energy per nucleon for each of the isotope pairs, see table 6.2.<br><br>
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1: It is noteworthy to notice the Q-value for the neutron capture and the change in binding energy per nucleon for each of the isotope pairs, see table 6.2.<br><br>  
  
 
{| cellspacing="1" cellpadding="1" border="1" style="width: 452px; height: 135px;"
 
{| cellspacing="1" cellpadding="1" border="1" style="width: 452px; height: 135px;"
|+ Table 6.2: Calculated Q-values and change in binding energy per nukleon
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|+ Table 6.2: Calculated Q-values and change in binding energy per nukleon  
 
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|-
| Pair of nuclide<br>
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| Pair of nuclide<br>  
| Q-value for neutron capture (MeV)<br>
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| Q-value for neutron capture (MeV)<br>  
 
| Change in E<sub>B</sub>/A (MeV)<br>
 
| Change in E<sub>B</sub>/A (MeV)<br>
 
|-
 
|-
| <sup>235</sup>U/<sup>236</sup>U<br>
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| <sup>235</sup>U/<sup>236</sup>U<br>  
| 6.55<br>
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| 6.55<br>  
 
| -0.004<br>
 
| -0.004<br>
 
|-
 
|-
| <sup>238</sup>U/<sup>239</sup>U<br>
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| <sup>238</sup>U/<sup>239</sup>U<br>  
| 4.81<br>
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| 4.81<br>  
 
| -0.012<br>
 
| -0.012<br>
 
|-
 
|-
| <sup>239</sup>Pu/<sup>240</sup>Pu<br>
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| <sup>239</sup>Pu/<sup>240</sup>Pu<br>  
| 6.53<br>
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| 6.53<br>  
 
| -0.003<br>
 
| -0.003<br>
 
|}
 
|}
  
<br>The nuclide pair <sup>238</sup>U/<sup>239</sup>U have a significantly lower Q-value and a significantly bigger fall in E<sub>B</sub>/A than the other pairs. This can be explained by the pair-pair configuration in the <sup>238</sup>U nucleus, which makes it less favorable to bind another neutron. On the other hand, for pair-odd nuclides it is much more favorable to bind another neutron to achieve a pair-pair configuration. This is shown from the cross sections for interaction with thermal neutrons (σ and σ<sub>f</sub>).<br>
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<br>The nuclide pair <sup>238</sup>U/<sup>239</sup>U have a significantly lower Q-value and a significantly bigger fall in E<sub>B</sub>/A than the other pairs. This can be explained by the pair-pair configuration in the <sup>238</sup>U nucleus, which makes it less favorable to bind another neutron. On the other hand, for pair-odd nuclides it is much more favorable to bind another neutron to achieve a pair-pair configuration. This is shown from the cross sections for interaction with thermal neutrons (σ and σ<sub>f</sub>).<br>  
  
<br>2: <br>
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#<sup></sup><math>239Pu+n/>99Y+2n+139Cs</math>
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#<sup></sup><span class="texhtml"><math>^{239}Pu + \eta \> ^{99}Y + 2\eta + ^(139)Cs</span>  
#Q-value: 191.42MeV
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#Q-value: 191.42MeV  
#The energy which is released by disintegration after stability is reached: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 99Y: M(99Y)-M(99Ru)=17.4MeV<br>139Cs: M(139Cs)-M(139La)=6.5MeV<br><br>
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#The energy which is released by disintegration after stability is reached: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; <sup>99</sup>Y: M(<sup>99</sup>Y)-M(<sup>99</sup>Ru)=17.4MeV<br><sup>139</sup>Cs: M(<sup>1</sup><sup>39</sup>Cs)-M(<sup>139</sup>La)=6.5MeV<br><br>  
#<sup></sup>2/3 of this energy will disappear with neutrinos. Some of the disintegrations have too long half-lives to have an effect on the reactor safety.
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#<sup></sup>2/3 of this energy will disappear with neutrinos. Some of the disintegrations have too long half-lives to have an effect on the reactor safety.  
#1.0g <sup>239</sup>Pu = 2.5 *10<sup>21</sup> atomer. Number of fissions per seconds is σ*ϕ*Nt = 1.89*10<sup>14</sup>, which will give an effect of <math>3.6*1016MeV/>5811W</math>
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#1.0g <sup>239</sup>Pu = 2.5 *10<sup>21</sup> atomer. Number of fissions per seconds is σ*ϕ*Nt = 1.89*10<sup>14</sup>, which will give an effect of <span class="texhtml">3.6 * 10<sup>16</sup>''M''''e''''V''&nbsp; (5811''W)''</span>  
 
#The formation of <sup>240</sup>Pu: σ*ϕ*Nt= 6.8*10<sup>13</sup>s<sup>-1</sup>. After 100 days of irradiation 4*10<sup>-6</sup> g <sup>240</sup>Pu will be made.
 
#The formation of <sup>240</sup>Pu: σ*ϕ*Nt= 6.8*10<sup>13</sup>s<sup>-1</sup>. After 100 days of irradiation 4*10<sup>-6</sup> g <sup>240</sup>Pu will be made.
  
<br> 3: <br>
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<br> 3: <br>  
  
#<sup>232</sup>Th+n-&gt;<sup>233</sup>Th-&gt;<sup>233</sup>Pa-&gt;<sup>233</sup>U
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#<sup></sup><math>^{232}Th+\eta\>^{233Th\>^{233}Pa\>^{233}U</math>  
#<sup>133</sup>I
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#<sup>133</sup>I  
#One ton <sup>232</sup>Th equals to 2.6*10<sup>27</sup> atoms. The rate of formation for neutron capture (<sup>233</sup>Th): σ*ϕ*Nt = 7.37*10^-24cm^2*10^14n cm-2s-1*2.6*10^27atomer= 1.91*10<sup>18</sup>atomer s<sup>-1</sup>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; It will take 37hours of irradiation to form enough 233Th to give 100g 233U, but disintegration of <sup>233</sup>Pa to <sup>233</sup>U must be waited.
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#One ton <sup>232</sup>Th equals to 2.6*10<sup>27</sup> atoms. The rate of formation for neutron capture (<sup>233</sup>Th): σ*ϕ*Nt = 7.37*10^-24cm^2*10^14n cm-2s-1*2.6*10^27atomer= 1.91*10<sup>18</sup>atomer s<sup>-1</sup>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; It will take 37hours of irradiation to form enough <sup>233</sup>Th to give 100g <sup>233</sup>U, but disintegration of <sup>233</sup>Pa to <sup>233</sup>U must be waited.  
 
#100g <sup>233</sup>U: D=λN = 3.56*10<sup>10</sup>Bq(35.6Gbq) <br><br>
 
#100g <sup>233</sup>U: D=λN = 3.56*10<sup>10</sup>Bq(35.6Gbq) <br><br>
  
 
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Revision as of 14:08, 18 June 2012

Nuclear reactions and nuclear reactors



1: It is noteworthy to notice the Q-value for the neutron capture and the change in binding energy per nucleon for each of the isotope pairs, see table 6.2.

Table 6.2: Calculated Q-values and change in binding energy per nukleon
Pair of nuclide
Q-value for neutron capture (MeV)
Change in EB/A (MeV)
235U/236U
6.55
-0.004
238U/239U
4.81
-0.012
239Pu/240Pu
6.53
-0.003


The nuclide pair 238U/239U have a significantly lower Q-value and a significantly bigger fall in EB/A than the other pairs. This can be explained by the pair-pair configuration in the 238U nucleus, which makes it less favorable to bind another neutron. On the other hand, for pair-odd nuclides it is much more favorable to bind another neutron to achieve a pair-pair configuration. This is shown from the cross sections for interaction with thermal neutrons (σ and σf).


2:

  1. [math]^{239}Pu + \eta \; ^{99}Y + 2\eta + ^(139)Cs\lt /span\gt #Q-value: 191.42MeV #The energy which is released by disintegration after stability is reached:                      \lt sup\gt 99\lt /sup\gt Y: M(\lt sup\gt 99\lt /sup\gt Y)-M(\lt sup\gt 99\lt /sup\gt Ru)=17.4MeV\lt br\gt \lt sup\gt 139\lt /sup\gt Cs: M(\lt sup\gt 1\lt /sup\gt \lt sup\gt 39\lt /sup\gt Cs)-M(\lt sup\gt 139\lt /sup\gt La)=6.5MeV\lt br\gt \lt br\gt #\lt sup\gt \lt /sup\gt 2/3 of this energy will disappear with neutrinos. Some of the disintegrations have too long half-lives to have an effect on the reactor safety. #1.0g \lt sup\gt 239\lt /sup\gt Pu = 2.5 *10\lt sup\gt 21\lt /sup\gt atomer. Number of fissions per seconds is σ*ϕ*Nt = 1.89*10\lt sup\gt 14\lt /sup\gt , which will give an effect of \lt span class="texhtml"\gt 3.6 * 10\lt sup\gt 16\lt /sup\gt ''M''''e''''V''  (5811''W)''\lt /span\gt #The formation of \lt sup\gt 240\lt /sup\gt Pu: σ*ϕ*Nt= 6.8*10\lt sup\gt 13\lt /sup\gt s\lt sup\gt -1\lt /sup\gt . After 100 days of irradiation 4*10\lt sup\gt -6\lt /sup\gt g \lt sup\gt 240\lt /sup\gt Pu will be made. \lt br\gt 3: \lt br\gt #\lt sup\gt \lt /sup\gt \lt math\gt ^{232}Th+\eta\;^{233Th\;^{233}Pa\;^{233}U[/math]
  2. 133I
  3. One ton 232Th equals to 2.6*1027 atoms. The rate of formation for neutron capture (233Th): σ*ϕ*Nt = 7.37*10^-24cm^2*10^14n cm-2s-1*2.6*10^27atomer= 1.91*1018atomer s-1           It will take 37hours of irradiation to form enough 233Th to give 100g 233U, but disintegration of 233Pa to 233U must be waited.
  4. 100g 233U: D=λN = 3.56*1010Bq(35.6Gbq)