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= Nuclear Reactions and Nuclear Reactors<br>  =
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=Fission and Nuclear Reactors =
  
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====== Return to [[Problem Solving Sets]] ======
  
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Return to [[Problem Solving Sets]]
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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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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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{| cellspacing="1" cellpadding="1" border="1" style="width: 452px; height: 135px;"
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|-
 
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| <sup>235</sup>U/<sup>236</sup>U<br>  
 
| <sup>235</sup>U/<sup>236</sup>U<br>  
| 6.55<br>  
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| align="right" | 6.58<br>  
| -0.004<br>
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| align="right" | -0.007<br>
 
|-
 
|-
 
| <sup>238</sup>U/<sup>239</sup>U<br>  
 
| <sup>238</sup>U/<sup>239</sup>U<br>  
| 4.81<br>  
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| align="right" | 4.64<br>  
| -0.012<br>
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| align="right" | -0.015<br>
 
|-
 
|-
 
| <sup>239</sup>Pu/<sup>240</sup>Pu<br>  
 
| <sup>239</sup>Pu/<sup>240</sup>Pu<br>  
| 6.53<br>  
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| align="right" | 6.53<br>  
| -0.003<br>
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| align="right" | -0.007<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>  
 
<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:&nbsp; <br> <br>  
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<br>2:&nbsp; <br>  
  
 
#<span class="texhtml"><sup>239</sup>Pu</span>+ n <math>\rightarrow</math> <span class="texhtml"><sup>99</sup>Y</span> + 2n + <span class="texhtml"><sup>139</sup>C</span>s<br>  
 
#<span class="texhtml"><sup>239</sup>Pu</span>+ n <math>\rightarrow</math> <span class="texhtml"><sup>99</sup>Y</span> + 2n + <span class="texhtml"><sup>139</sup>C</span>s<br>  
 
#Q-value: 191.42MeV  
 
#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;&nbsp;&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 &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <sup>139</sup>Cs: M(<sup>139</sup>Cs)-M(<sup>139</sup>La)=6.5MeV  
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#The energy which is released by disintegration after stability is<br> <sup>99</sup>Y: M(<sup>99</sup>Y)-M(<sup>99</sup>Ru)=17.4MeV<br><sup>139</sup>Cs: M(<sup>139</sup>Cs)-M(<sup>139</sup>La)=6.5MeV  
 
#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.<br>
 
#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.<br>
  
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<br> '''3:'''<br>
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#1.0 g <sup>239</sup>Pu = 2.5<math>\cdot</math>10<sup>21</sup> atoms. Number of fissions per seconds is σ<math>\cdot</math>ϕ<math>\cdot</math>N<sub>t</sub> = 1.89<math>\cdot</math>10<sup>14</sup>, which will give an effect of 3.6<math>\cdot</math>10<sup>16</sup>MeV (5811W)
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#The formation of <sup>240</sup>Pu: σ<math>\cdot</math>ϕ<math>\cdot</math>N<sub>t</sub>= 6.8<math>\cdot</math>10<sup>13</sup>s<sup>-1</sup>. After 100 days of irradiation 0.232 g Pu will be made.<br>
  
#1.0 g <sup>239</sup>Pu = 2.5<math>\cdot</math>10<sup>21</sup> atomer. Number of fissions per seconds is σ<math>\cdot</math>ϕ<math>\cdot</math>N<sub>t</sub> = 1.89<math>\cdot</math>10<sup>14</sup>, which will give an effect of 3.6<math>\cdot</math>10<sup>16</sup>MeV (5811W)
 
#The formation of <sup>240</sup>Pu: σ<math>\cdot</math>ϕ<math>\cdot</math>N<sub>t</sub>= 6.8<math>\cdot</math>10<sup>13</sup>s<sup>-1</sup>. After 100 days of irradiation 4<math>\cdot</math>10<sup>-6</sup> g Pu will be made.<br>
 
  
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#<span class="texhtml"><sup>232</sup>Th</span>+&nbsp;η <math>\rightarrow</math> <span class="texhtml"><sup>233</sup>T</span>h <math>\rightarrow</math> <sup>233</sup>Pa <math>\rightarrow</math> <sup>233</sup>U<br>  
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#<span class="texhtml"><sup>232</sup>Th</span>+&nbsp;n <math>\rightarrow</math> <span class="texhtml"><sup>233</sup>T</span>h <math>\rightarrow</math> <sup>233</sup>Pa <math>\rightarrow</math> <sup>233</sup>U<br>  
 
#<sup>133</sup>I.  
 
#<sup>133</sup>I.  
#One ton <sup>232</sup>Th equals to 2.6<math>\cdot</math>10<sup>27</sup> atoms. The rate of formation for neutron capture (<sup>233</sup>Th): σ<math>\cdot</math>ϕ<math>\cdot</math>N<sub>t</sub> = 7.37<math>\cdot</math>10<sup>24</sup>cm<sup>2</sup><math>\cdot</math>10<sup>14</sup><span class="texhtml"><span style="font-family: sans-serif;">n</span></span> cm<sup>-2</sup>s-1<math>\cdot</math>2.6<math>\cdot</math>10<sup>27</sup>atomer= 1.91<math>\cdot</math>10<sup>18</sup>atoms s<sup>-1</sup>  
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#One ton <sup>232</sup>Th equals to 2.6<math>\cdot</math>10<sup>27</sup> atoms. The rate of formation for neutron capture (<sup>233</sup>Th): σ<math>\cdot</math>ϕ<math>\cdot</math>N<sub>t</sub> = 7.37 <math>\cdot</math>10<sup>24</sup>cm<sup>2</sup><math>\cdot</math>10<sup>14</sup><span class="texhtml"><span style="font-family: sans-serif;">n</span></span> cm<sup>-2</sup>s<sup>-1</sup><math>\cdot</math>2.6 <math>\cdot</math>10<sup>27</sup>atomer= 1.91 <math>\cdot</math>10<sup>18</sup>atoms s<sup>-1</sup>  
 
#It will take 37hours of irradiation to form enough <sup>233</sup>Th to give 100 g <sup>233</sup>U, but disintegration of <sup>233</sup>Pa to <sup>233</sup>U must be waited.  
 
#It will take 37hours of irradiation to form enough <sup>233</sup>Th to give 100 g <sup>233</sup>U, but disintegration of <sup>233</sup>Pa to <sup>233</sup>U must be waited.  
#100 g <sup>233</sup>U: D=λN = 3.56<math>\cdot</math>10<sup>10</sup>Bq(35.6Gbq)<br>
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#100 g <sup>233</sup>U: D=λN = 3.56 <math>\cdot</math>10<sup>10</sup>Bq(35.6Gbq)<br>
  
 
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[[Category:Solved Problem]] [[Category:Bachelor]]

Latest revision as of 09:02, 9 July 2012

Fission and Nuclear Reactors

Return to Problem Solving Sets


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
6.58
-0.007
238U/239U
4.64
-0.015
239Pu/240Pu
6.53
-0.007


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. 239Pu+ n [math]\rightarrow[/math] 99Y + 2n + 139Cs
  2. Q-value: 191.42MeV
  3. The energy which is released by disintegration after stability is
    99Y: M(99Y)-M(99Ru)=17.4MeV
    139Cs: M(139Cs)-M(139La)=6.5MeV
  4. 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.


3:

  1. 1.0 g 239Pu = 2.5[math]\cdot[/math]1021 atoms. Number of fissions per seconds is σ[math]\cdot[/math]ϕ[math]\cdot[/math]Nt = 1.89[math]\cdot[/math]1014, which will give an effect of 3.6[math]\cdot[/math]1016MeV (5811W)
  2. The formation of 240Pu: σ[math]\cdot[/math]ϕ[math]\cdot[/math]Nt= 6.8[math]\cdot[/math]1013s-1. After 100 days of irradiation 0.232 g Pu will be made.


4:

  1. 232Th+ n [math]\rightarrow[/math] 233Th [math]\rightarrow[/math] 233Pa [math]\rightarrow[/math] 233U
  2. 133I.
  3. One ton 232Th equals to 2.6[math]\cdot[/math]1027 atoms. The rate of formation for neutron capture (233Th): σ[math]\cdot[/math]ϕ[math]\cdot[/math]Nt = 7.37 [math]\cdot[/math]1024cm2[math]\cdot[/math]1014n cm-2s-1[math]\cdot[/math]2.6 [math]\cdot[/math]1027atomer= 1.91 [math]\cdot[/math]1018atoms s-1
  4. It will take 37hours of irradiation to form enough 233Th to give 100 g 233U, but disintegration of 233Pa to 233U must be waited.
  5. 100 g 233U: D=λN = 3.56 [math]\cdot[/math]1010Bq(35.6Gbq)