# Problem set 6

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# Fission and Nuclear Reactors

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**1:**

The mass number of a given nucleus increases by one unit when a neutron is captured. Table 6.1 gives information about mass excess for three important isotope pairs. Calculate the difference in average binding energy between the pairs of nuclide and discuss why the ^{238}U/^{239}U pair differs so greatly from the other two pairs in regards to utilization of nuclear energy.

Nuclide 1 | Mass Excess (keV) |
Nuclide 2 |
Mass excess (keV) |

^{235}U |
40915 |
^{236}U |
42411 |

^{238}U |
47306 |
^{239}U |
50741 |

^{239}Pu |
48585 |
^{240}Pu |
50122 |

**2:**

Find the answers to the following questions:

- A specific thermal fission of
^{239}Pu gives^{99}Y + 2 neutrons + X. Which nuclei is X?

- Calculate the Q-value for the above fission from a mass table.

- Use a mass table to calculate the residual heat, that is the energy developed from disintegration after fission has taken place.

- A part of this energy is of no importance for the safety of the reactor, explain why.

**3:**

1.0 g ^{239}Pu is irradiated with a neutron flux of 1.0 10^{14} n cm^{-2} s^{-1}. Assume that all the fissions have the same Q-value as the one calculated under 2.b.

- Calculate the developed effect from fission in plutonium during the irradiation.
- How much
^{240}Pu is formed after 100 days of irradiation?

**4:** In a thorium breeder reactor, fissile ^{233}U is formed from fertile ^{232}Th.

- Write down the nuclear reaction and how the disintegration occurs.
- A specific thermal fission of
^{233}U gives^{99}Y + 2 neutrons + X. Which nuclei is X? - Assume one ton thorium is irradiated with a neutron flux of 1.0*10
^{14}n cm^{-2}s^{-1}. How long does it take to generate 100 grams of^{233}U? - What is the disintegration rate of this uranium?