LEO SZILARD National Physics Competition

FINAL, 1998
 

1. Heavy nuclei, such as , can easily split, upon the impact of neutrons, into medium heavy nuclei. The fission fragments are radioactive and release b - and g rays.

a) Why does not occur a - and b +-decay among the fission fragments?

b) Why do not develop free protons upon splitting the uranium nuclei?

(6 scores)

 
  1. Heavy water is required for the operation of certain reactor types. One way of producing heavy water is electrolysis: during the electrolysis of ground waters the lighter hydrogen segregates in higher amount in gas form than the heavier and sluggish deuterium. This means that the deuterium can be enriched in the residual water by electrolysis. What is the most suitable water for production of heavy water by electrolysis: snow-water, rainwater, Danube water, waters of ocean, perhaps the water of Dead Sea?

(4 scores)

     

    3. The binding energy of 3H nucleus is 1.334 pJ, but the binding energy of 3He nucleus is 1.2143 pJ only. In spite of this fact the following disintegration occurs:

    ,

    where the energy of the produced b particle may reach 2.88 J. How is it possible without breaching the energy conservation law?

    (5 scores)

    Information available: the mass of the neutron: 1.67482 kg. The mass of the proton is 1.67252 kg.

     

    Task:
  1. Gold can be produced from mercury by nuclear reaction (the dream of the alchemists of the Middle Ages can be fulfilled) as follows: radioactive isotope is generated by irradiation of isotopes with neutron (neutron activation).

nucleus comes into being during the positive b decay of their radioactive isotope. In order to produce gold, 1 gram mercury was irradiated for 100 seconds in a nuclear reactor. The activity of the specimen removed from the reactor was 1620 Bq.

a) How many radioactive nuclei were produced?

b) What is the mass of gold that can be produced from the sample?

c) How long irradiation period would be required to extract the maximum amount of gold from mercury? (Assume that the neutron activation rate is kept constant.)

d) Explain why the condition in question c) can not be fulfilled and whether or not such gold production is economically efficient.

(15 scores)

Information available: The ratio of isotope in the natural mercury is 0.15 %. The half life of the radioactive isotope is 2.7 days.

5. The fuel assemblies used in Paks Nuclear Power Plant consist of fuel pellets containing 4 grams uranium-dioxid.

a) Please estimate the activity and the radiation power of the fresh pellets (not yet loaded into reactor). (Assume that there are only a -decaying uranium isotopes in the pellet.)

b) What is the thermal power of one pellet originating from atomic fission, if the pellet is loaded into reactor and the reactor is operating under normal conditions? Please compare the thermal power to the radiation power.

c) Assume that an initially fresh fuel pellet had stayed for a period of 1 hour in the core of the reactor operating in normal conditions and then it was decayed for a 30 days period. What will be the total activity of the uranium fuel pellet this time?

(15 scores)

The 235U isotope enrichment of the fuel pellet is 3 %, while the 238U content is 97%. The half time of the isotopes is 710 million years and 4.5 billion years, respectively. The energy of the released a particles is 0.67 pJ. The weight of the fuel load for one reactor is 42 tons, while its thermal power in normal operation is 1375 MW. The energy released during the fission of one uranium nucleus is cca. 30 pJ. The total activity of the various fission products generated during the fission of the uranium nuclei can be approached with the use of the following empirical formula:

,

with the activity for one fission event on the left side ( is the number of fissions), and t time elapsed from the occurrence of the fission, in days, on the right side.
  1. A dotlike g radiation source with 107 Bq activity and 53.4 days half live is placed into a 2 cm diameter cave at the centre of a lead ball with an outside diameter of 10 cm. 7 days later someone approaches the specimen to a distance of 3 meters and stays there for 1 hour to perform an experiment.

a) Estimate the number of g photons received by him/her during the stay.

b) What is the yearly whole-body radiation dose that this person can receive while, as part of his/her work, repeating this experiment at intervals of one week? What is the ratio of the received dose to the yearly population dose of 3 mSv/person?

(15 scores)

The thickness of the lead shell, halving the g radiation, is 2.5 cm (each 2.5 cm of the lead shell halves the radiation rate). The cross sectional area of the man perpendicular to g radiation is cca. 0.5 square meter. The quality factor for the radiation is 1. The energy of g photon is 0.07 pJ. The radiation absorption of the air can be neglected.

 

7. The isotope is an a radiant. The kinetic energy of the a particles is 0.76 pJ.

a) Check whether the disintegration can be reversed. (i.e. is it possible that the a particle produced during the disintegration penetrates into another radon nucleus and a radium nucleus comes into being again?)

b) Please determine whether or not Rutherford were able to use radioactive radium to initiate the first artificial nucleus transformation.

The empirical formula for the radius of the atomic nuclei is: , where R0=1.4m. The equation of the first nuclear reaction is:

 

 

1. Heavy nuclei, such as , can easily split, upon the impact of neutrons, into medium heavy nuclei. The fission fragments are radioactive and release b - and g rays.

a) Why there is no - a - and b + - radiant among the fission fragments?

b) Why do not develop free protons upon splitting the uranium nucleus?

(6 scores)
  1. In the nature, Hydrogen has three isotopes, stable hydrogen, deuterium and tritium decaying with 12 years halving time. Heavy water is required for the operation of certain reactor types (one or two atoms of it is deuterium and very rarely tritium). One way of producing heavy water is electrolysis: during the electrolysis of ground waters the lighter hydrogen segregates in higher amount in gas form than the heavier and sluggish deuterium, thus the deuterium can be enriched in the residual water by electrolysis.

What is the most suitable water for the preparation of heavy water by electrolysis: snow-water, rainwater, Danube water, waters of ocean, perhaps the water of Dead Sea?

(4 scores)

3. A wine shop keeper offers a cobwebby bottle of allegedly 300 years old wine originating from the Rákóczis’ cellar in Tokaj, for huge price to a rich foreigner. The gentleman who is interested in buying this bottle of wine takes the wine to a nuclear laboratory where the intent of the shopkeeper to defraud turned out soon. (Not by testing the flavour of the wine.)

Explain what kind of nuclear test can be performed to find out that the wine certainly can not be 300 years old but much younger than this age.

(5 scores)

Tasks:

4. The fuel assemblies used in Paks Nuclear Power Plant consist of pellets containing 4 grams uranium-dioxid.

a) What is the thermal power of the fuel pellet in the core of the reactor operating in normal conditions?

b) What capacity electric bulb could be continuously operated by the electric power gained from the fuel pellet and what would be the cost for one year continuous operation if the price of 1 kWh was 15 Forints?
    1. Please estimate the volume of natural gas the combustion of which could supply the energy released from the fuel pellet during a day?

(15 scores)

Information available: The weight of the fuel load for one reactor is 42 tons, while its thermal power in normal operation is 1375 MW. The electrical power is 460 MW. The caloric power of the natural gas is .

5. Assume that the waste heat of the 4 units of Paks Nuclear Power Plant is used for melting ice.

a) Estimate how long time would be required for melting the 10 cm thick ice cover of the lake Balaton? (Please determine the area of the lake Balaton by estimation.)
    1. How large area should be covered by solar cells for the construction of a solar power plant the peak power of which would be the same as for the constant electrical power of Paks Nuclear Power Plant.

(15 scores)

Information available: the density of the ice is 920 kg/m3, while the melting heat is 5 kJ/kg. The power of the sunshine to the Earth surface is 600W/m2 (in clear weather and with perpendicular incidence). The efficiency of the transformation of solar energy to electric power is 15%.

6. The yearly dose equivalent of the Hungarian population on average is 3 mSv per person. Please estimate how many liters of water of 0° C temperature could be warmed up to 100° C with the energy of the absorbed radiation collected by the entire population of Hungary during a period of one year.

(15 scores)

The specific heat of the water is 4.2 kJ/kg° C. Its density is 1000 kg/m3. (The number of the Hungarian population is 10 millions. The average weight of the persons can be taken as 50 kg.) A large portion of the radiation dose originates from b and g radiation. Their quality factor is 1. Caesium shows b and g decay, and its decay half time is 30 years. (Accordingly, 733 nuclei of 1 thousand million caesium nuclei decay in a second.) The energy is 0.081 pJ for the produced electrons, and 0.1 pJ for the gamma photons.

7. The isotope is an alpha radiant. The kinetic energy of the a particles is 0.76 pJ.
    1. Please make upper limit estimation for the radius R of the nuclei of the radon daughters with the use of the energy of the a particles.
    2. Determine the radius of the nucleus from the relation , given by the scattering experiments, where R0 = 1.4 m.
    3. Compare the radiuses determined by the two ways. How could you explain the result?

(15 scores)
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