LEO SZILARD National Physics Competition |
| FINAL 1999 |
1. Tritium is being used for a medical test. An injection of 104 Bq radioactivity has been given to the patient. How long does it take till the additional tritium radioactivity in the body drops to the level of 5 Bq. The physical half-life of the tritium is 12.3 years and the biological half-life is 10 days. (Biological half-life: half of the hydrogen atoms of the organism is being replaced in 10 days by metabolism.) 2. The average radioactivity of low level radioactive waste (originated from outside the reactor) from the Paks Nuclear Power Plant is 108Bq/kg. The radioactivity is due to the isotopes 90Sr and 137Cs with half-life of 30 years, which are dangerous for the living organisms. The regulatory committee requires 600 years long safe underground storage.
3. What material and wall thickness would you use as a protective barrier as a protection against a , b , g and neutron radiation? All the types of radiation should be considered pure and separated. 4. The natural Uranium consists 0,7 % of 235U, which splits by thermal neutrons. The 238U absorbs the neutrons. That is why using natural water as a moderator the chain reaction can be started only in uranium enriched at least up to 2%. The Frenchmen discovered in Middle Africa that the uranium found there consists less than 0.7% of 235U. They made the conclusion the in the past geological terms a natural nuclear reactor operated there. How could it happen and when? 5. The radon radioactivity in the air of a room is 100 Bq/m3. A man in this room takes a breath every five seconds and every times approximately 3 litres of air enter his lungs. How many radon nuclide will decay in his lungs during one hour? 6. Compare the reactors at Paks and Chernobyl from the point of view of their stability (protection against “runaway “ of reactor power). 7. A neutron star has approximately the same mass as the Sun (2·1030 kg), and the same density as the atomic nucleus.
8. Leo Szilárd and Walter Zinn determined that in average 2,5 neutrons are emitted by fission. Let us consider 100 decays in an imaginary reactor. From the neutrons emitted during this time 10 neutrons will leave the reactor, 8 will be absorbed in the cooling water, 40 will be absorbed by the 238U, some of them will be absorbed in the control rods and the rest are going to cause further fission. What percentage of the neutrons has to be absorbed by the control rods to ensure conditions in which the number of neutrons does not change in time? 9. During nuclear fusion one of the reactions is the fusion of two deuterium nuclei to helium. During fusion (in case of high enough temperature and pressure) the reaction a 2 H + 2H ® 3He+n will take place. The reaction 2H + 2H ® 4He will not take place at all and the reaction 2H + 2H ® 4He + g will take place with a very low probability.
10. A piece of a mummy has been incinerated in thoroughly controlled conditions and the obtained carbon-dioxide gas has been captured. The captured gas with mass of 220 mg has been introduced into a gas-filled counter, which detect the decay of radiocarbon. It was measured in advance that the counter provided 1600 “background counts” during 20 hours. After filling the carbon-dioxide the counter provided 2500 counts during 20 hours.
The 235U has a half-life period of 0.7 billion years, the 238U 4.5 billion years, and the 222Rn 3.8 days. The 14C/12C balance in the air is 210-12. The half-life of the 14C is 5568 years. The mass of a proton is 1.672·10-27 kg, the mass of a neutron is 1.674·10-27 kg, the mass of 2H is 3.34·10-27 kg, the mass of 4He is 6.645·10-27 kg, the mass of 3He is 5.0066·10-27 kg. |
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