LEO SZILARD National Physics Competition |
| FINAL 2000 |
Paks, April 27 1. How would the world look like if the mass of the neutron were less by one thousandth (0.999) of the current mass? Data: The mass of neutron is 1.6749543× 10-27 kg. The mass of the proton is 1.6726486× 10-27 kg and the mass of the electron is 0.9109534× 10-30 kg. (Problem of the National Szilárd Competition, Final, 2000.) 2. In chemical factory Tokai-Mura in Japan chemical purification of uranium dioxide is carried out in order to manufacture fuel for nuclear reactors. The chemically purified uranium dioxide is educed and it settles down on the bottom of the vessel in form of precipitate. In order to transfer the heat generated during the chemical reaction water surrounds the vessel. The cooling water flows through the water shell entering it in cold condition through a pipe and then the heated cooling water is released through another pipe. In the fall of 1999 instead of the usual uranium dioxide with 3 % enrichment another type of uranium dioxide with 18% enrichment (for high temperature reactors) was being processed, but violating the rules the work was carried out with the same quantity of material. This way the settled uranium dioxide reached the critical mass and a fission chain reaction started. The spontaneous reactor controlled itself and was in operation continuously for 17 hours. Since the chain reaction was not expected in the chemical factory radiation monitors, controls or other intervening automatic devices were not installed in the room. Due to the unexpectedly appeared high neutron field it was not possible to enter the room. After 17 hours the chain reaction could be stopped by external interference. a.) What kind of processes could play roles in the self-regulation of
the fission chain reaction?
(5 scores)
3. In the Sun the 1H3 ® 4He nuclear fusion (in several steps) produces the energy that provides the sunlight. a.) What would have happened to the Sun if the 2He isotope existed in stable form? b.) What would have happened to the Sun if the 2H isotope did not exist? (5 scores) 4. Compare the coal, gas and nuclear power plants (working at the same power level) from the point of view of environmental protection and cleanliness of the environment. (5 scores) 5. After the Chernobyl accident the 134Cs/137Cs ratio was measured in Poland (The two isotopes release g radiation of different energy level and that makes distinguishing possible). Based on the measuring results it could be established that the fuel elements had been in the reactor for a long time. a.) Why could it serve as a basis for a conclusion that the reactor had not been used for producing material for nuclear weapons? b.) Soon after this the 134Cs/137Cs ratio was measured in Northern Italy in one type of mushrooms. It was concluded that the mushroom contained almost exclusively only 137Cs. Does it mean that mushrooms are able to distinguish different isotopes of a certain element? (5 scores) Data: The half-life time of 134Cs is 2 years, the half-life time of 137Cs is 30 years.
6. In red giant stars the elements with higher atomic number are built up from 4He by fusion. This chain of the fusion process has a difficult start, because the final product of the nuclear reaction 4He+4He3 ® 8Be is unstable and decays almost immediately. Fred Hoyle assumed that in case of high enough density it can happen that the 8Be during its very short life time meets another 4He and in this case in the process 8Be+4He3 ® 12C a 12C atom can be produced. Since this requires the contact of three a -particles during a very short period of time, this process is called the 3a process. However, according to Hoyle’s calculations this can be significant only if the nucleus 12C has such an excited level, which can easily be formed from three a particles, and which can then decay to the ground state by releasing g -photon. Soon afterwards following Hoyle’s prediction Fowler, at the California Institute of Technology experimentally discovered this excited level of the 12C. What is the excitation energy of this level? (5 scores) Data: The mass of the 4He atom is 6.64296669× 10-27 kg, and the mass of the 12C is 19.91593977× 10-27 kg. Let us assume that the a particles have to approach each other to the distance 4 m in order to ensure the fusion.
7. Prove that in a plasma operating by fusion 2H+2H3 ® 3He+n on permanent temperature the power density is proportional to the square of the plasma density. (5 scores) 8. In plutonium storage metallic plutonium spheres of uniform size are stored in a way that they are placed on safe distance from each other. There are spheres made of pure 239Pu and others of pure 240Pu. Unfortunately the identification labels are not readable. Please provide simple methods how to distinguish them. (5 scores) Data: The half-life time of 239Pu is 24100 years and the half-life time of the 240Pu is 6560 years.
9. Imagine that you work in the Patent Office. A patent application has been received, which proposes that in the uranium enrichment process instead of uranium-hexafluoride gas (UF6) used up to now uranium-hexachloride (UCl6) should be implemented. It provides the followings justification: this compound is less toxic and corrosive than the UF6, therefore the enrichment equipment could be built up from cheaper materials. How do you assess this proposal? (5 scores)
10. How would have developed the world’s destiny if the half-life time of the 235U were 2.25 billion years? (5 scores) |
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