LEO SZILARD National Physics Competition

FINAL, 1998

 

Selecting competition

1400 - 1700 on 17 March, 1998

“Set worth-while aims for yourself but do not ask whether they are achievable;

Look upon them as a model and example but not a work to be done to a deadline.“

( 4 August 1939, from the Testimony of Szilárd Leo)

Questions

1. Which of the below listed energy sources, used by humans, have a relationship with nuclear processes? (Please underline your ‘yes’ or ‘no’ selection and describe the potential nuclear process.)

(Make a copy of this table to your Result Sheet.)

Energy Sources

Relationship with nuclear processes

Description of the nuclear process
Mineral coal

yes – no

 
Mineral oil

yes – no

 		 
Solar energy

yes – no

 		 
Nuclear energy (in power plants)

yes – no

 		 
Geothermal energy

yes – no

 		 
Hydropower

yes – no

 		 
Wind power

yes – no

 		 

(5 scores)

2. The formation and decay of the radioactive radon gas can be studied in the following decay chain.

a) Please indicate on the dotted line above the arrows what kind of radioactivity is associated with each atomic transformation.

b) What kind of radioactivity can be detected, with the use of suitable detectors, in houses exposed to high radon gas concentration? Please confirm, whether a or b radioactive isotopes have larger activity concentration () in the dust free airspace of the room? Why?

c) When is the risk of health damage is higher to people living in a room with high radon gas concentration: if the air of the room is dusty or dust free? Why?

(Please keep in mind that radon is noble gas which is reluctant to adhere to other materials. However, its daughters are metals ready to stick to other materials, such as dust particles in the air or wall of the room.)

(8 scores)

3. The activity, half time, and energy of particles of two radioactive materials ‘A’ and ‘B’ are identical. Material ‘A’ shows a -decay, while Material shows ‘B’ b -decay.

a) Which of ‘A’ and ‘B’ materials, located at the same distance from the human body, is more dangerous and why?

b) If any of ‘A’ and ‘B’ radioactive materials enters and remains in the human organism, which of them may cause a higher health damage and why?

(6 scores)

4. Leo Szilárd, having been informed in 1939-ben of the discovery of the atomic fission by German scientists, believed that the nuclear chain reaction was feasible.

a) Why did Leo Szilárd think that nuclear chain reaction could be produced by nuclear fission?

b) In general, what features shall the fissile nuclei have to enable the chain reaction to develop?

c) When and where was the first chain reaction initiated? Who of the scientists of Hungarian birth took part in this event?

(10 scores)

5. No spontaneous nuclear chain reaction could develop today on Earth in natural manner. However, traces of an ‘ancient reactor’, from the ages before 2 billion years, were discovered by researchers in the neighbourhood of rich uranium sites in South Africa (in Oklo, Gabon Republic).
    1. What could be the traces from which the prehistoric existence of an ancient controlled chain reaction could be concluded?
    2. What conditions existed 2 billion years ago that could lead to the development of spontaneous controlled chain reaction? How could this nuclear chain reaction evolve?

(8 scores)

6. Two stable isotopes of the helium available on Earth are and the more frequent isotopes. The concentration of is significantly higher in air than in natural gas. How was it possible that such a high difference developed? (Keep in mind that the natural gas originates from inside of Earth, where the radioactivity is high.)

(8 scores)

7. In order to learn the internal structure of the atom, in early this century Rutherford and his colleagues exposed thin gold foils to a -rays perpendicularly. The measurements performed during the experiment showed that a large portion of the a particles passed through the gold foils with an insignificant diffraction, but rarely, some a particles ‘bounced back’ perpendicularly from the plate (i.e. they had a diffraction of nearly 180° ).

a.) It was demonstrated by the measurements that an average of 4 of 100 thousands of a particles were reflected from the plate. Considering that the plate consists of some 10 thousands atomic layers, please estimate what is the ratio of the diameter of the gold nuclei, causing the reflection of the a particles, to the diameter of the atoms.

b) Please calculate the density of the atomic nucleus from the estimated ratio of diameters, considering that the density of the gold is 19300 kg/m3.

c) How would the reflection ratio of the a particles change if a gold plate thicker by a factor of 1000 were used in the experiments? How could this change be explained? Please confirm whether larger or smaller estimated nucleus size values could be concluded from the test results, in comparison to the original thin plate.

(15 scores)
  1. Four reactors operate in Paks Nuclear Power Plant. The thermal power of each reactor is 1375 MW, while the electrical power is 460 MW.
    1. Consider the fuel load of one reactor keeping in mind that the fissile 235U isotope content of the fuel is cca. 3% and the isotope concentration (for the entire load) reduces by an average of 1.14% per year. Assume, that the released energy originates, for the most part, from fission of 235U nuclei, where an amount of 32 pJ energy releases for each fission. (The reactors are operating for a 330 days period a year.)
    2. Estimate the temperature rise of the water used for cooling the power plant if the water discharge of the canal is 100 m3/sec.
    3. What would be the yearly fuel supply demand of a thermal power plant, with the same thermal power as for the Paks Nuclear Power Plant, if its fuel was coal with 24.5 MJ/kg caloric power?
    4. Estimate the yearly volume of the

      5. gas discharged by a coal-fired power plant in normal operational conditions. How thick would be this carbon dioxide gas layer over the area of Hungary, which is 100 000 km2?

(15 scores)

9. 8 gram of isotope is used for thyroid examinations, 50% of which infiltrates and remains in the thyroid gland. The balance of the sample evacuates during a period of 24 hours. The half time of this isotope is 8 days, (which means that an average of 1 atomic nucleus of 1 million disintegrates in a second).

    a) What is the initial activity of the sample?

    b) What will be the activity of the iodine in the thyroid gland after 4 days?

    c) In how long time will the activity in the thyroid gland be surely lower than 1% of the initial activity of the iodine accumulated in the thyroid gland?

    d) Estimate the whole-body radiation exposure (dose equivalent) in mSv that can be received by a person, with 60 kgs weight, from the radiation of the iodine built-up in the thyroid gland, if the g radiation of is neglected and one b particle is assigned to each decay, the average energy of which is 0.1 pJ (The Q factor of the b radiation is 1.)

 

(15 scores)
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