Difference between revisions of "Solutions 6"
From mn/safe/nukwik
(Created page with "= Nuclear reactions and nuclear reactors<br> = <br> <br> 1: It is noteworthy to notice the Q-value for the neutron capture and the change in binding energy per nucleon for eac...") |
|||
Line 1: | Line 1: | ||
− | = Nuclear reactions and nuclear reactors<br> = | + | = Nuclear reactions and nuclear reactors<br> = |
− | <br> | + | <br> |
− | <br> | + | <br> |
− | 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> | + | 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 | + | |+ Table 6.2: Calculated Q-values and change in binding energy per nukleon |
|- | |- | ||
− | | Pair of nuclide<br> | + | | Pair of nuclide<br> |
− | | Q-value for neutron capture (MeV)<br> | + | | 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> | + | | <sup>235</sup>U/<sup>236</sup>U<br> |
− | | 6.55<br> | + | | 6.55<br> |
| -0.004<br> | | -0.004<br> | ||
|- | |- | ||
− | | <sup>238</sup>U/<sup>239</sup>U<br> | + | | <sup>238</sup>U/<sup>239</sup>U<br> |
− | | 4.81<br> | + | | 4.81<br> |
| -0.012<br> | | -0.012<br> | ||
|- | |- | ||
− | | <sup>239</sup>Pu/<sup>240</sup>Pu<br> | + | | <sup>239</sup>Pu/<sup>240</sup>Pu<br> |
− | | 6.53<br> | + | | 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> | + | <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> | + | <br>2: <br> |
− | #<sup></sup><math> | + | #<sup></sup><span class="texhtml"><math>^{239}Pu + \eta \> ^{99}Y + 2\eta + ^(139)Cs</span> |
− | #Q-value: 191.42MeV | + | #Q-value: 191.42MeV |
− | #The energy which is released by disintegration after stability is reached: | + | #The energy which is released by disintegration after stability is reached: <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. | + | #<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 < | + | #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'' (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> | + | <br> 3: <br> |
− | #<sup> | + | #<sup></sup><math>^{232}Th+\eta\>^{233Th\>^{233}Pa\>^{233}U</math> |
− | #<sup>133</sup>I | + | #<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> It will take 37hours of irradiation to form enough | + | #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> 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> | ||
<br> | <br> |
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.
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:
- 133I
- 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.
- 100g 233U: D=λN = 3.56*1010Bq(35.6Gbq)