Difference between revisions of "Solutions 6"
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#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> | ||
− | <br> | + | <br> '''3:'''<br> |
− | '''3:'''<br> | ||
#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) | #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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#<span class="texhtml"><sup>232</sup>Th</span>+ 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> | #<span class="texhtml"><sup>232</sup>Th</span>+ 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<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> | + | #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> | + | #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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Revision as of 16:10, 25 June 2012
Nuclear Reactions 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.
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:
- 239Pu+ n 99Y + 2n + 139Cs
- Q-value: 191.42MeV
- The energy which is released by disintegration after stability is
99Y: M(99Y)-M(99Ru)=17.4MeV
139Cs: M(139Cs)-M(139La)=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.
3:
- 1.0 g 239Pu = 2.5 1021 atoms. Number of fissions per seconds is σ ϕ Nt = 1.89 1014, which will give an effect of 3.6 1016MeV (5811W)
- The formation of 240Pu: σ
4:
- 232Th+ n 233Th 233Pa 233U
- 133I.
- One ton 232Th equals to 2.6n cm-2s-1 2.6 1027atomer= 1.91 1018atoms s-1 1027 atoms. The rate of formation for neutron capture (233Th): σ ϕ Nt = 7.37 1024cm2 1014
- It will take 37hours of irradiation to form enough 233Th to give 100 g 233U, but disintegration of 233Pa to 233U must be waited.
- 100 g 233U: D=λN = 3.56