Page 50 - Radiochemistry and nuclear chemistry

Nuclei, Isotopes and Isotope Separation 39

2.9. Exercises

2.1. How many atoms of 235U exist in 1 kg of uranium oxide, U30 s, made of natural uranium?
2.2. What is the atomic fraction of deuterium in water with the mole fraction of 0.81 for H20, 0.18 for HDO,
and 0.01 for D20?
2.3. The translational energy of one mole of gas is given by 3/2RT, which corresponds to an average thermal
molecular velocity v (the root mean square velocity), while the most probable velocity v'- vr(0.67) v.
(a) What is the most probable velocity of a helium atom at 800~
(b) What voltage would be required to accelerate an 0~-particle to the same velocity?
2.4. A Nier type mass spectrometer has a fixed radius of curvature of 5 cm and a magnetic field of 3000 G; 1
G = 10 -4 T. At what accelerating voltage will a Na + ion be brought to focus at the ion collector?
2.5. In a Dempster type (constant B and V) mass spectrograph utilizing 180 ~ degree focusing, the ions 12C + and
llBH+ are recorded simultaneously, the latter ion having a slightly larger orbit diameter. The separation between
the lines recorded on the photographic plate is 0.0143 cm and the orbit diameter for the 12C+ ion is 20 cm. What
is the atomic mass of liB?
2.6. When the rotational quantum number n r goes from 0 to 1 in H35C1, it is accompanied by the absorption of
light with a wave number of 20.6 cm -l. From this it is possible to calculate the interatomic distance between
hydrogen and chlorine in the molecules. What is this distance?
2.7. In one mole of a gas at STP (standard temperature and pressure, i.e. 0oc and 1 arm) a small fraction of the
molecules have a kinetic energy _ 15kT. (a) How many such molecules are there, and (b) what would their
temperature be if they could be isolated?
2.8. In an investigation the isotope ratio lSo/160 was found to be 2.045 • 10 -3 for fresh water and 2.127 •
10 -3 for carbon dioxide in the atmosphere. Calculate the equilibrium constant (mole fractions!) for the reaction
H2180(l)+CO2(g) = H20(I)+C 180 160(g )

2.9. How many ideal stages in an ordinary cascade are required at an 0t = 6 to produce water in which 10% of
the hydrogen is deuterium?
2.10. In a distillation column with total reflux, l~ is enriched through exchange distillation of BF30(C2H5) 2 from
the natural value of 20 atom % to a product containing 95 % l~ The packed column has a length of 5 m and a
diameter of 3 cm. What is the approximate height of a theoretical stage if the enrichment factor is 0.026?
2.11. A gas centrifuge plant is set up in order to enrich UF 6 of natural isotopic composition in 235U. The
centrifuges, which each have a length of 100 cm and a diameter of 20 cm, rotate at 40000 rpm. The gas
temperature is 70oC.
(a) Prove that the separation factor 0~ in (2.47) can be approximated by e 6 according to (2.58) when the product
flow is very small compared to the waste flow, and ot is not far from 1.
(b) Using this approximation, what is the theoretical separation factor for one unit?
(c) Assuming that the enrichment factor obtained with the centrifuge is only 70% of the theoretical one, what
number of units would be required in series in order to achieve UF 6 with 3 % 235U?
2.12. How much separative work is needed in order to produce 1 kg of uranium containing 4 % 235U from a feed
of natural uranium and leaving 0.25 % in the tail?

2.10. Literature

J. M. MCCRE^, On the Isotopic Chemistry of Carbonates and a Paleotemperature Scale, J. Chem. Phys. 18 (1950)
849.
J. BmGELEISEN, Isotopes, Ann. Rev. Nucl. Sci. 2 (1953) 221.
G. H. CLEWL~'r, Chemical separation of stable isotopes, Ann. Rev. Nucl. Sci. 1 (1954) 293.
A. P. V~OGRADOV, Bull. Acad. Sci. U.S.S.R. 3 (1954) 3.
S. EPSTEIN, quoted by A. P. V~OGRADOV.
T. F. JOHNS, Isotope separation by multistage methods, Progr. Nucl. Phys. (ed. O. R. Frisch) 6 (1957) 1.