Page 135 - Radiochemistry and nuclear chemistry

Radionuclides in Nature 121

5.11. Exercises

5.1. Cosmic-ray irradiation of the atmosphere yields 0.036 1~ atoms cm -2 s -l. If this l~ is rapidly carried
down into sea water, which is assumed to have a volume of 1.4 x 10 Is m 3, what will the equilibrium radioactivity
of l~ in 1 m 3 sea water be? The earth's surface area is 510 x 106 km 2.
5.2. In Greenland ice the l~ radioactivity has been measured to be 0.0184 dpm m -3. How old is this ice if it
was formed out of water in equilibrium with cosmic-ray l~ (see previous question)?
5.3. The CO 2 in the atmosphere is in exchange with carbon in living organisms, humus, dissolved organic
compounds, and carbonate in the sea water, the latter being the main reservoir (88 %) of all exchangeable carbon.
The amount of such exchangeable carbon is estimated to be 7.9 gcm -2 of the earth. When cosmic-ray produced
14C is mixed into this exchangeable carbon, what will the specific activity become?
5.4. On the label of a bottle of cognac bought in 1976 it is stated that the cognac is over 20 years old. An
analysis showed a tritium content of 80 TU. Discuss the trustworthiness of the statement.
5.5. 0.11 cm 3 helium gas at NTP was isolated from 100 g of uranium mineral containing 5 ppm uranium. How
old is the mineral ?
5.6. A mineral was found to contain 39. I g K and 87.2 x 10 -6 liter Ar at NTP. How old is the mineral?
5.7. A uranium mineral was found to contain the lead isotopes 2~ :~b, and 2~ in the ratio 1:1087:388,
as determined with a mass spectrometer. Estimate the age of the mineral.
5.8. The heat flow from the earth's crust is 0.060 W m -2. The mean thickness of the crust is 17 km and the
earth's radius is 6371 km. The average concentration of uranium, thorium, and potassium in granite is estimated
to be 4 ppm (by weight) 18 ppm, and 3.6 %, reSl~ectively. Assuming that 7 % by volume of the crust is made up
of granite (feldspar + quartz, density 2.6 g cm-~), what will the heat flow at the earth's surface be from each of
these elements? Assume/~-heat as 1/3 Ensx; for a-decay assume E,~ = Q~. Each 4~ decay by the EC-branch
emits one 1.46 MeV 3'. Discuss the results.
5.9. A 1 GW 9 nuclear power station uses annually about 30 t uranium enriched to 3 % 235U. (a) How much
natural uranium has been produced to keep it running? Assume waste stream from isotope separation plant to
contain 0.3 % ~35U. Co) How much low grade ore (assume 0.06 % uranium) must be mined, if the uranium recovery
efficiency in the process is 70%?
5.10. The assumed uranium resources in Japan are 4 kt, in Argentina 12 kt and in France 48 kt U30 s. How many
1 GW e reactor years can these uranium amounts sustain in each country at the uranium consumption rate (a) of
the previous exercise?

5.12. Literature

E. K. HYDE, Natural Radioactivity of the Heavy Elements: A Comprehensive Review, Univ. of California Radiation
Laboratory, Report UCRL-10612.
W. F. Lmnv, Radiocarbon Dating, University of Chicago Press, 1956.
C. E. IUNGE, Air Chemistry and Radioactivity, Academic Press, 1963.
H. CILM(;, S. L. MILLER, and G. J. WASSERBURG (Eds.), Isotopic and Cosmic Chemistry, North-Holland, 1963.
E. I. HAMILTON and L. H. AHRENS, Applied Geochronology, Academic Press, 1965.
B. KEISCH, Dating works of art through their natural radioactivity: improvements and applications, Science 160
(1968) 413.
D. YORK and R. M. FARQUHAR, The Earth's Age and Geochronology, Pergamon Press, 1972.
P. K. KUROD^, Fossil nuclear reactor and plutonium-244 in the early history of the solar system. In IAEA, The
Oklo-phenomenon, Vienna, 1976.
Ionizing Radiation: Sources and Biological Effects, United Nations 1982.
P. S. ZURER, Archeological Chemistry, Chem. & Eng. News Febr. 21, 1983, p.21.
P. J. D. LLOYD, p. 772 in T. Lo, M. BAIRD and C. HANSON, (Eds.), Handbook of Solvent Extraction, J. Wiley
& Sons 1983.
G. FAURE, Principles oflsotope Geology, 2nd Ed. ] Wiley & Sons 1986.
M. EISENnUD, Environmental Radioactivity, 3rd Ed., Academic Press 1987.
M. A. GEYH and H. SCHLEICHER, Absolute Age Determination, Springer-Verlag 1990.