# Difference between revisions of "Solutions 6"

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## Latest revision as of 10:02, 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.

Pair of nuclide |
Q-value for neutron capture (MeV) |
Change in E_{B}/A (MeV) |

^{235}U/^{236}U |
6.58 |
-0.007 |

^{238}U/^{239}U |
4.64 |
-0.015 |

^{239}Pu/^{240}Pu |
6.53 |
-0.007 |

The nuclide pair ^{238}U/^{239}U have a significantly lower Q-value and a significantly bigger fall in E_{B}/A than the other pairs. This can be explained by the pair-pair configuration in the ^{238}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_{f}).

2:

^{239}Pu+ n^{99}Y + 2n +^{139}Cs

- Q-value: 191.42MeV
- The energy which is released by disintegration after stability is

^{99}Y: M(^{99}Y)-M(^{99}Ru)=17.4MeV^{139}Cs: M(^{139}Cs)-M(^{139}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.

**3:**

- 1.0 g
^{239}Pu = 2.5 10^{21}atoms. Number of fissions per seconds is σ ϕ N_{t}= 1.89 10^{14}, which will give an effect of 3.6 10^{16}MeV (5811W) - The formation of
^{240}Pu: σ ϕ N_{t}= 6.8 10^{13}s^{-1}. After 100 days of irradiation 0.232 g Pu will be made.

**4:**

^{232}Th+ n^{233}Th^{233}Pa^{233}U

^{133}I.- One ton
^{232}Th equals to 2.6 10^{27}atoms. The rate of formation for neutron capture (^{233}Th): σ ϕ N_{t}= 7.37 10^{24}cm^{2}10^{14}n cm^{-2}s^{-1}2.6 10^{27}atomer= 1.91 10^{18}atoms s^{-1} - It will take 37hours of irradiation to form enough
^{233}Th to give 100 g^{233}U, but disintegration of^{233}Pa to^{233}U must be waited. - 100 g
^{233}U: D=λN = 3.56 10^{10}Bq(35.6Gbq)