LEO SZILARD National Physics Competition

FINAL 2000 Selecting Competition
 

1. What kind of processes can take place during reaction of 3He, 4He nuclei with thermal neutrons?

(5 scores)

(Problem of the Szilárd Competition in 2000, selecting competition)

Data: see the table

 

2. Environmental and health regulations determine when radioactive waste can be released to the draining system. For example the 32P isotope can be released only if its radioactivity does not exceed 20 MBq/m3. How long should a waste with activity level 8× 107 Bq/l be stored before release? The half-life of 32P is 14.3 days.

(5 scores)

(Problem of the Szilárd Competition in 2000, selecting competition)


3. If we have neutron and a -radiation of the same intensity and energy level which one is more dangerous from biological point of view?

(Problem of the Szilárd Competition in 2000, selecting competition)

(5 scores)

4. Let us have a pen dosimeter containing 5 cm3 air in normal conditions, with 1 pF capacity and charged to 1000 V. What is the absorbed dose if the voltage decreased to 900 V after the exposure?

(Problem of the Szilárd Competition in 2000, selecting competition)

(5 scores)

Data: Average ionisation energy of air is 6.88 aJ and let assume 1.3 kg/m3 as air density

(Problem of the Szilárd Competition in 2000, selecting competition)

 

5. According to the theory of Grand Unification the proton is not totally stable either, but decays to p 0-meson and positron with a long half-life. In an experiment 3300 tons of water was analysed for one year, but no events indicating proton decay were registered. Based on this experiment what lower limit can be given regarding the proton half-life?

(Problem of the Szilárd Competition in 2000, selecting competition)

(5 scores)

6. As a consequence of the Chernobyl nuclear accident in 1986 due to the radioactive contamination of the atmosphere, which effected Hungary as well the radioactivity of the air in our country increased by 1 Bq/m3 in average, mainly due to the 131I isotope with 8 days half-life time. Altogether how many grams of iodine entered the atmosphere of the country? How many grams of radioactive iodine was released from the damaged Chernobyl reactor if the released total radiation was 1018 Bq? We assume that 90 % of the radiation originated from the iodine.

(Problem of the Szilárd Competition in 2000, selecting competition)

(5 scores)

Data: Let us consider the height of the contaminated atmosphere 5 km and the territory of Hungary 105 km2.

 

7. We accelerate threefold ionised UF6 molecules with 5 kV potential and then through a little orifice lead them into a magnetic field with 1 T induction. The induction vector is perpendicular to the velocity.

  1. What will be the path of the ions? Describe the characteristic parameters of the ion paths for the 238U and 235U isotopes.
  2. This way the isotope 238U and 235U can be separated from each other. During the World War II the available ion sources in the USA could generate 1 mA ion currant. How long would have it taken to produce 1 kg pure 235U using this method?

(Problem of the Szilárd Competition in 2000, selecting competition)

(5 scores)

8. We know that the b decays resulting in increasing and decreasing atomic numbers occur with the atoms on the different sides of the atomic “energy valley”. That is why we would expect that there are no atoms, which can be both b -decay (increasing atomic number) and electron capture (decreasing atomic number). The 40K isotope is however a b -decaying isotope with 88 % probability, it decays with electron capture with 12 % probability. (There are other similar atoms as well not only the 40K.) How it could be possible?

(Problem of the Szilárd Competition in 2000, selecting competition)

(5 scores)

9. A laser releases an impulse with 20 J for 0,5 m s on 580 nm wavelength. We target this light to a Caesium sheet focusing onto a circle with 12 m m diameter. 90 % of the light is absorbed and 10 % is reflected.

  1. How many photons hit the metal sheet in this impulse?
  2. What pressure will be generated by the light ray?
  3. What will be the maximum velocity of the electrons released from the caesium sheet generated by the light?

Data: The ionisation energy of the electrons in the caesium is 0.3 aJ.

(Problem of the Szilárd Competition in 2000, selecting competition)

(5 scores)

10. In the nuclear power plants one of the methods used to measure neutron flux is the measurements made by the electron emission detectors. Such a detector consists of a wire made of 103Rh and placed in a stainless steel cylinder with 3 mm diameter. The wire and the cylinder are insulated from each other (See the figure). As an effect of the neutron irradiation b decay of 104Rh occurs in the wire and high energy b particles are released, which penetrate the insulation between the wire and the shell. Then the shell absorbs the b particles. By using an ammeter connected to the wire the current can be measured. (Notice that these detectors do not require separate power supply that is why they are called self-feeding detectors.)

  1. What is the radiation level of the Rh wire when the ammeter indicates 0.1 m A.
  2. How can it be possible that the ammeter indicates permanent current value for a long time although it should decrease according to the half-life of the radioactive materials?
  3. On the power level indicated in point a.) how many years would take the transformation of the 5 % of the originally existing 103Rh atoms?

Data: The half-life of the 104Rh is 42.3 s. The density of rhodium is 12400 kg/m3.

(Problem of the Szilárd Competition in 2000, selecting competition)

(5 scores)

TABLE

Nucleus

Mass (10-27 kg)

Half-life

Type of decay

neutron

1.6749543 .

1000 s

b -

1H

1.6726485 .

stable

  

2H

3.342727844

stable

  

3H

5.005622512

12.33 years

b -

3He

5.005589319

stable

  

4He

6.64296669 .

stable

  

5He

8.318722076

2× 10-21 s

a +n
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