edited by
EDWARD K. MELLON
network
Florida State University Tallahassee, FL 32306-3006
Nuclear Reactions versus Inorganic Reactions And the Winner Is... Judy Godfrey Warner Robins Senior High School, Warner Robins, GA 31 099 Ron McLachlan Mount DeSales High School, Macon, GA 31213 Charles H. Atwood Mercer University, Macon, GA 31207 Nuclear reactions are analogous to inorganic reactions: They are basically driven by the same thermodynamic and kinetic considerations. The common physical transformations of molecules are also possible in nuclei, but under more extreme conditions. These analogies can be used by teachers to successfully introduce nuclear phenomena and reaction dynamics to high school students. This paper will give the basic information and analogies needed to include nuclear chemistry in their basic cumculum. Unlike other Reactivity Network papers, this paper cannot ~rovidemany classroom demonstrations because most high schools do not have nuclear reactors or particle accelerators. Hopefully, many of the analogies will appeal to the students'knowledge of the everyday world and to the "Gosh, Gee Whiz!" instincts that most students have. First we cover nuclear reactions, then their thermodynamics, and finally their kinetics. Hopefully, the relative simplicity of nuclear reactions, compared to inorganic reactions, will convince teachers to introduce more nuclear chemistry. Basics of Nuclear Reactions Terminology First students must know isoto~eterminolow because it will be used to show how nucleaf reactions proceed. They and determine must be able to intermet isoto~e - svmbols . the numbers of proto& and neutrons present in a given nucleus. For example, the symbol 4Ga provides the following information. The element is Ca.
There are 20 protons in the nucleus. (Atomic number Z = 20.) The sum of the number of protons and neutrons is 48. (Mass
numberA = 48). Thus, the number of neutrons is 28 (48 - 20 = 28). (Neutron numberN = 28). What Changes? Students must also learn that nuclear reactions are very different from chemical reactions in a key asped: Nuclear This paper was presented at the 198th National Meeting of the American Chemical Society;Miami Beach, FL; September 11, 1989.
reactions transmute or change elements. A chemical reaction is shown in eq 1in which two elements, Hz and 02, rearrange to form a new molecule, HzO. A nuclear reaction is shown in eq 2 in which the same two elements, in monatomic form, H and 0 , are transformed into two new elements, N and He.
This difference should be emphasized to help students distinguish between chemical and nuclear reactions. Energy lnvolved Another vital difference between nuclear and chemical reactions is the level of energy involved in each reaction type. In chemical reactions, energy differences between reactants and products are usually a few hundred kilojoules (kJ). For example, the formation of Hz0 (g) from Hz(g)and Oz(g)in eq 1releases 483.6 kJ. (This reaction is explosive under the right conditions.) Nuclear reactions, on the other hand, involve energy differences of hundreds of millions of kJ. For example, eq 2 releases 3.838 x 10' kJ. Thus, mica1 chemical reactions are about 1,000,000times less rneigetic than typical nuclearrcactions. Even the most cxothrmm~rchemical reactions are ahout 100,000 times less energetic. There are two reasons for this difference. The first, that nuclei operate in an environment that is much more energetic than the chemical world will be discussed in detail later. The second, the Coulomb barrier will now be considered. The Coulomb Barrier Most nuclear reactions require that two positively charged species (i.e., two nuclei) come into close proximity so that they may exchange parts (protons, neutrons, etc.) and complete the reaction. These like-charged species repel one another with a force called the Coulomb barrier, and a nuclear reaction can not occur unless the nuclei are given enough kinetic energyto overcome it. For lighter nuclei, the magnitude of the Coulomb bamer is about 2 million el=Volume 68 Number 10 October 1991
819
tmn volts (2 MeV or 2 x 10' kJ); for heavier nuclei, it is hundreds of MeV. You can easilv demonstrate this force to students with two annular mabmets and a dowel stick. Place the magnets on the dowel stick with like odes facinr!one another. Thev will "float" in the air as the mutual-repulsion of thecr magnetic poles causes a physical separation ( I ) . Figure 1follows the potential energy changes involved in nuclear and chemical reactions. Itjuxtaposes two graphs that have similar shapes hut very different energy scales: the familiar chemical reaction potential and a nuclear reaction potential. Supplying the Energy Chemical reactions can occur in beakers through the mixing and heating of solutions, gases, ete., because chemical reaction energetics are low. Nuclear reactions require much more energy, but some do wcur spontaneously in nature: within stars, within natural reactors such as the Oklo mine in Gabon (21, cosmic-rayinduced reactions in the air and soil, and natural radioactivity. Most nuclear reactions studied, however, must be initiated with nuclear reactors or particle accelerators. In chemical reactions, a Bunsen burner can be used to give the reactants enough kinetic energy to overcome the activation energy E. (Fig. 1) and start them down the potential energy slope to yield products. In nuclear reactions, nuclear particle accelerators are needed to give nuclei enough energy to overcome the Coulomb barrier E, (Fig. 1).
Me69 "YrnbB,
Figure 2. Mass distribution of products from the neutron-induced fission of '"u. Each pair of dots whose sum is about 230 represents one reaction channel. (Thisfigure is adapted from ref 23with permission of the author.) Balancing the Charge
E,= activation energy AHcxn=
reaction enthalpy
Chemical equations are balanced when the number of atoms of each element is the same on both (reactant and product) sides of the equation because the kinds of atoms and the numbers of each kind are conserved. Nuclear equations can not be balanced by this method because the kinds of atoms are changed by the nuclear reaction. However, the total charge of the system and the total of the mass numbers are conserved. For example, in eq 2 the reactant side contains nine protons (one in the hydrogen nucleus and eight in the oxygen) and 10 neutrons (from 'iO ). On the ~roductside this same number of orotons and neutrons is bistributed as seven protons and gght neutrons in N, and two ~rotonsand two neutrons in He. Thus. both the total charge and the total mass are conserved,' and eq 2 is a balanced nuclear equation.
I Reaction Coordinates
Pathways
Separation Distance Between The Two Nuclei Figure 1. A comparison of potential energy diagrams for a chemical reaction (top)and a nuclear reaction (bottom).Note the difference in potential energy scale. In the bottom diagram, the separation decreases from left to right. 820
Journal of Chemical Education
Chemical reactions do not always travel a single pathway For example, a given set of reactants can yield different mixtures of products under exactly the same reaction conditions, due to a variety of reaction pathways. All of us have seen this, probably in organic lab, wheneveryone else obtained a yield above 80%,but we obtained only lo%,with lots of some other product. Nuclear chemists and physicists see something similar in their own work. The individual reaction pathways are called reaction channels, and fission is an example of a reaction that has many. For example, the fission of U !:' by a neutron can populate many different reaction channels. Two are shown in eqs 3 and 4.
Amore complete picture of the possible reaction channels for the fission of Zi%J by neutrons is shown in Figure 2. One reaction channel is represented by any pair of dots whose mass numbers yield 236 when added. For example, the reaction channel of eq 3 is indicated by the dots a t masses 142 and 92; eq 4 a t masses 148 and 85. The largest percent yields on this graph are still less than lo%, reflecting the low yields for any particular reaction channel. This observation was important in the history and evolution of nuclear chemistry. For many years physicists studied fission reactions without really understanding what they were seeing. Enrico Fermi was given the 1938 Nobel Prize in physics for supposedly producing heavier elements from uranium by neutron-induced reactions (3). The products were really neutron-induced fission products present in such small amounts and in such a complex mixture that they were difficult to sort. About a year after Fermi received the award, Otto Hahn and Fritz Strassman (two of the first nuclear chemists), with the guidance of physicist Lise Meitner, determined that fission was the primary reaction when neutrons bombarded uranium (3,41. After their discovery more chemists were invited to join physicists in this new and exciting field to study the fissioning of uranium (5,6).Thus, nuclear chemistry was born. Advanced Analogies We also suggest two more analogies that are more advanced. They help students further understand that nuclear phenomena are not so unusual.
Quantum Numbers Describing electron states in atoms by quantum numbers is a basic part of high school curricula. The same quantum numbers can also be used to describe the states of protons and neutrons, but we need a set for each. Since there are more neutrons than protons in the heavier nuclei, higher quantum numbers must be used. These higher numbers will exceed those used to describe the familiar energy levels ofelectrons. Ihr example, in thr heaviest ntoms known, the electrons only fill the f orhitals. However, some nuclei have more than i26 neutrons. To describe them we must use orbitals in g, h, i, and j sublevels.
which the rest of the star rebounds, thus starting the supernova explosion (8-101. Thermodynamics and Energetics The thermodynamic quantities that predict spontaneity for a chemical reaction (AH, AS, and AG) also can be determined for nuclear reactions. However, only one of them is really important.
AH and Q Whether a chemical reacton is exothermic can be determined by the sign on AH,, which is calculated using the AH7 values of the reactants and products. For example, the value of -241.8 kJ/mol for the AH7 of Hz0 (g) indicates that 241.8 kJlmol of energy is needed to break 1mole of H,O (g) into one mole of Hz (g) and one mole of Oz(g).The negative sign indicates that the combustion of CH4is an exothermic reaction. CH,
+
20, ->
CO,
+ 2H20
(5)
Whether a nuclear reaction is exothermic can be determined by calculating the Q value, using the difference in the masses of the reactants and products, where mass is converted to energy according to Einstein's famous equation, E = me2. Atomic masses, expressed in atomic mass units (amu's), are given for the following reaction.
atomic masses
2.01410
3.01605
4.00260
1.00866
Q = ((4.00260+ 1.00866)- (2.01410+ 3.01605))amu = (-0.01889 smu) (931.48MeVlamu)
(8) (9)
=-I730 MeV
Phase Transitions The second analogy common to chemistry is that nuclei, like molecules, undergo phase transitions. It is very common to see substances, such as water, change from solid to liquid to gas. Nuclei also change phases, but obviously under much more rigorous conditions. In 1939, Niels Bohr and John Wheeler first proposed the liquid drop model (71 that appropriately described nuclei. A nucleus at room temperature is seen as analogous to a liquid drop, because it both rotates and vibrates. If a nucleus has its internal temperature raised high enough, it will emit particles to lower its internal energy. Obviously, this cannot be done with a Bunsen burner. However, nuclear particle accelerators, which can collide nuclei that have high kinetic energy, can raise the internal nuclear temperatures enough to cause them to emit neutrons, then protons. Neutrons are emitted first because, for them, there is no Coulomb barrier to overcome, making them energetically easier to remove. For nuclei, a n extremely rigid or "solid" phase occurs only a t extremely high pressure and density, such as in the center ofa star initiatingasupernovaexplosion. As the star collapses under its own mass, having exhausted its fuel supply, the interior density can exceed 2 x loL4glcm3. The nuclei are squeezed so tightly that they are literally on top of one another. They form a n incredibly rigid core from
The negative sign on the product of eq 9 tells us that this reaction is exothermic. For many years nuclear chemists and physicists have used the convention that Q values are determined by subtracting product masses from reactant masses. In the above calculation a chemistry convention was used. Reactant masses were subtracted from product masses. When looking up data in nuclear chemistry textbooks, it is good to keep these conventions in mind. In the nuclear physics convention, the reaction of eq 7 has a positive sign for the Q value, indicating an exothermic reaction. Atomic masses may be found in the appendices of nuclear chemistry texts. The most complete table is given in ref 13 (11-13). There is another very significant difference between the calculation of the Q value and AH,,. While G H , is determined for one mole of reactants, the Q value is determined for one reaction. Also note the conversion from m u ' s to the energy unit MeV. For chemists the energy unit kJ is more familiar than MeV. Converting the 17.60 MeV of eq 7 to kJ is done by first converting one reaction to one mole of reactions. Then convert MeV to J, then J to kJ.
Volume 68 Number 10 October 1991
821
Obviously this reaction is very exothermic by chemical standards. Entropy
Now that a comparison of AHand Q has been established, he used to understand the diminished contribution of entropy (AS)to free energy (AG)in nuclear reactions. The equation that relates free energy to enthalpy and entropy was derived by Gibbs (eq 13). For nuclear reactions, Q is substituted for AH (eq 14). it can -. - - --
AG = Q - TAS (for nuclear reactions)
(14)
For entropy to play a significant role in a chemical reaction, AH must be about the same order of magnitude as TAS. Thus, AH and AS "compete" to determine whether a reaction occurs spontaneously. From the previous discussion it should be obvious that for nuclear reactions Q is much, much larger than AH, thus dominating the TAS term. Gibbs equation can then be approximated as AG = Q. There is another reason that entropy is less important in nuclear reactions than in chemical ones. Entropy is essentially a statistical phenomenon. Many particles must be involved for AS to be significant. There is a big difference in the way that nuclear reactions and chemical reactions are performed. Chemical reactions occur when moles (or significant fractions of moles) of atoms are mixed. Nuclear reactions, on the other hand, occur essentially when one nucleus impinges on another. This fact was driven home by the discovery of element 109 in which a single nucleus of this element was made after several weeks of experimentation (14). Since Q values are large and few nuclei are involved for most nuclear reactions, we can safely ignore the contribution ofAS to spontaneity, which is determined primarily by the Q value once the nuclei have sufficient energy to overcome the Coulomb barrier. This simplification obviously does not apply when many moles of nuclei are reacting, such as in the cores of stars or in reactions involving many protons or neutrons (15).An example of the latter reaction type is the reaction of Ar with Au, for which AS is significant (16,171.
amount of energy required to break one mole of ?H nuclei into one mole of protons and one mole of neutrons. This is called the binding energy of the '?H nucleus, and it is the nuclear analog of AH? for molecules. When we consider the binding energies of all the elements, we see a trend. The binding energy steadily increases until the heavier nuclei (e.g., 2:4P~)reach values like 1.81 x lo3 MeV or 1.74 x 10" kJ1mol per nuclei. This is not too surprising because it should take more energy to hold together a larger nucleus. Binding Energy per Nucleon
This approximate increase in binding energy with increasing mass also helps us determine which nuclei are the most stable. Divide the binding energy or the mass defect by the mass numberA of a given nucleus. This is commonly called the binding energy per nucleon. (Protons and neutrons are collectivelycalled nucleons.)In effect, the binding energy per nucleon tells the energy required to remove a single proton or neutron from a nucleus. The most stable nuclei are those in which the individual protons and neutrons are bound the strongest. Consider two apple trees. One is very large with many apples, but not every apple is firmly attached. The second tree is smaller with fewer apples, but each apple requires considerable effort to remove. If the total enerm needed to remove all apples from each tree is determinex the larger tree would reauire more enerm s i m ~ l v because it has more apples. But &ch tree is more likeiito withstand a wind storm with its apples still attached? The small tree is hardier because the applesare more f m l y attached. Figure 3 graphically depicts the relative stability of nuclei across the periodic chart. It plots mass defect per nucleon vs. mass number, showing the systematics of nuclear stability. The nuclei at the top of this curve have the highest mass defect per nucleon, and are thus the most stable in nature. They are the nuclei with A = 56, with @e being the most stable. Heavier nuclei like 2$qU and 2$4P~,aa well as lighter nuclei, have a lower mass defect per nucleon and are less thermodynamically stable. It is easy to see why both fission and fusion nan be exothermic.
Binding Energy
Another thermodynamic concept, binding energy, is needed to explain the thermodynamics of fission and fusion-two good examples of nuclear reactions that are thermodynamically driven. Fission is the splitting of one heavy nucleus into two lighter nuclei. Fusion is the joining or the meltineof two lieht nuclei to form a heavier nucleus. The term ' ' m h v $ isised literally: the temperaturesare such that the two nuclei actually melt together, just as two snowflakes can melt together to forma water droplet. Every nucleus is held together by the strong nuclear force whose energy is derived from converting the mass of individual protons and neutrons to energy. For example, the experimentally determined masses of protons and neutrons when not bound in a nucleus are 1.00783and 1.00867 amu. We might expect the mass of the fH nucleus, with its one proton and one neutron, to be the sum of the unbound masses (2.01650 amu), but it is experimentally measured to be2.01410 amu, or 0.00240 amu less. When this"missing mass" or mass defect is converted to energy, we get 2.24 MeV per nucleus (2.16 x lo8 kJ/mol of nuclei), or the 822
Journal of Chemical Education
C
MASS DEFECT CURVE FOR NUCLEI
u W
0 ,-
0
50
100 150 MASS NUMBER
200
250
Figure 3. Mass defect per nucleon vs. mass number, across the periodic chart, showing the relative stability of all nuclei. Note that the maximum is at about 56, with a peak at 4.
Fission and Fusion
Radioactive Decay
Fission, the splitting of a heavy nucleus (A = 240) into two lighter pieces (e.g.,A = 142 and 921, is exothermic because the products are more thermodynamically stable. This pmcess is marked on Figure 3 to show the relative increase in stability Fusion, the process of melting nuclei together, can also he exothermic-for the light nuclei. This is also shown on Figure 3. In particular, notice the tremendous increase in stability that is possible for nuclei with A < 4. Reactions that fuse nuclei like f H and BH into $He (eq 7) are especially exothermic due to the large differences in stability. In fact, fusion reactions are the fuel of stars. Equation 7 shows the fission reaction that is the primary fuel source for stars during their longest evolutionary phase (8-10,181. Once the thermodvnamic driving forces behind fission and fusion are understood, we canhklude some interesting asoects of these two reactions in classroom discussion. The discovery of fission and the subsequent Manhattan Proje G t h a t ultimately led to the destruction of Hiroshima and Nagasaki--are fascinating historical subjects. Students can learn about many of the exciting scientific discoveries of this century and peer into the lives of great scientists such as Rutherford, Bohr, Fermi, and Einstein. They can also develop an impression of the way that science is actually done. This taste of the scientific method in action along with the truly international flavor of the endeavor can spark the students'interest. Agood source ofmaterial for this subject is provided by Rhodes (3). Another topic for discussion that will grab the students' attention is the development and use of nuclear power. This is rich ground not only for discussing scientific and technological matters but also for looking at science's impact on society. Other possible topics for discussion include how nuclear reactors operate (19, 201, the scientific basis of radioactive waste disposal and its possible longterm effects (20, 21), and the impact of nuclear accidents, such as the one at Chernobyl(22). Fusion also provides many discussion topics that will stimulate the students' interest. The development of the first thermonuclear weapons (H bombs) can be a practical starting point for discussion. A good, readable reference source for this information is Rhodes' book (3).After this initial discussion, current development of fusion reactors and their potential for power production can be introduced. This particular topic is full of material that generates thought-orovokingdiscussions.The students'imaginations c a n ti. &nulared just bv the ~dpathat people are trylng to burld and drblm mschmes that can withstand and contarn temperatureslhigher than the 10' T needed to overcome the Coulomb harrier for fusion reactions. A cursory introduction to this material is found in ref 20. Finally, fusion helps teachers introduce truly universal topics: stellar evolution, which is determined by the different reaction pathways for fusion (18), and our most recent opportunity to study stellar evolution, Supernova 1987A (8-10).
All nuclei that radioactively decay also obey first-order kinetics. Integration of eq 15 yields eqs 16 and 17. They show how the concentration of a chemical-or how the amount of a radioactive species-changes with time. They relate the initial amount No of a radioactive substance, which has radioactive decay constant k, to the amount N present after radioactive decay for time t .
N and No are expressed in one of two types of units: the mass of the nuclei or the number of nuclei. Some unit of time (e.g., second, day) is used to express t, and its reciprocal is used to express k. The value of k is unique to a particular radioactive nucleus, and thus can be used to identify it. As shown below, k is related to the half-life of radioactive decav. Equations 16 and 17 describe the exponential decay of a eiven soecies. The amount oresent at a piven time d e ~ e n d s the value of k a i d the i n the'amount initially period of time over which decay was observed. In Figure 4 the p- decay of 1g of fWS to aqC1 over time is diagrammed. The value of k is 0.2451hr. The left ordinate gives the number of grams of 7:s. The right ordinate gives the number of atoms. The right axis is not a linear scale. The amount of BES remaining after decay steadily decreases and ilsymptotically approaches 0. Figure 4 can also be used to determine the half-life ofthii decay, which is abbre\iatrd t r ? . Thii; is the time necessaly for 1'2 of rhe oricinal material to decav. The initial amount of QtSpresentwas 1.0 g. Thus, t l i z is the time a t which 0.5 g remains (after about 2.8 hr). Another tIiZhas elapsed when 0.25 g of tfS remains (after about 5.6 hr). Figure 4 shows a total of nearly 10 half-lives for QfS.
-
Kinetics of Nuclear Reactions To understand kinetics or reaction rates in nuclear chemistry, the students must become familiar with first-order reactions in which rate depends only on the concentration or amount of one species. For example, if the concentration is doubled, the reaction rate doubles. Mathematically this statement is written rate = k
[M
(15)
where k is the rate constant and [N] is the concentration of reactant N.
time (hrr.)
Figure 4. Exponential decay of 1 g of 3 8 to~ 3 8 ~ 1 as a function of time. The right ordinate does not have a linear scale. Volume 68 Number 10 October 1991
823
neutrons produced in the fission reaction can perpetuate the fission process, just as free radicals can drive polymerization reactions (Fig. 5). When the concentration of 2$qU or %QPuis so high that many of the neutrons produced initiate subsequent fission reactions, the reaction becomes explosive. This is the basic design behind the atomic weapons dropped on Hiroshima and Nagasaki. However, if the concentration of %$qUor 2 ~is p kept~low enough, the reaction proceeds below the explosive rate and can generate much heat. Nuclear power plants are designed to use this heat to ~roduceelectricitv. " In Droducine . ..electricitv. bv" nucleur p w w , fhe nuclear reactor iscontrolled by kinctlcs With nuclear reactlons, unllke chem~calreactlons. there is little or no need to mention the kinetics of reaction mechanisms. To truly understand a chemical reaction, we must know whether the reaction is first-order or secondorder with respect to one of the reactants, and whether the reaction is second- or third-order overall. Such subtleties are essentially ignored in nuclear reactions. This simplifies tremendously the understanding of nuclear reactions, as compared to inorganic reactions.
Figure 5. The chain reaction of the neutron-induced fission of %. To determine the relationship between k and t l l z , replace N with 112 and No with 1in eq 17 to obtain
For k = 0.2451/hr, the tm for the decay of to ffC1 is calculated to be 2.83 hr, which agrees with the value from Figure 4. Chain Reactions Students must understand frst-order kinetics and radioactive decay before we explain more complex processes, such as growth of radioactive species in nuclear reactors or accelerators. Then they can also learn the kinetics of decay chains, in which one radioactive nucleus decays into another, and so forth. Using simple assumptions and applying algebra appropriately, these processes are understood as simple extensions of first-order kinetics (11,IZ). Kinetics also helps us understand chemical chain reactions and their analogy in nuclear processes. In a chain reaction, one of the reaction products can sustain the reaction. For example, in the growth of polymers, molecules produced in intermediate steps have reactive centers that can extend the polymer chain. In free-radical reactions, additional free radicals are produced during intermediate steps. Some of these reactions continue along a t a nice, slow pace and give products such as polyethylene. However other free-radical reactions such as Hz + C12or Hz + O2 are highly exothermic. The large amount of heat coupled with the increasing concentration of free radicals causes the reaction rate to grow exponentially and the reaction becomes explosive.. An example of a chain reaction in a nuclear processs is the neutron-induced fission of '8gU (eqs 3,4) or 2;BPu. The
824
Journal of Chemical Education
Conclusion The study of nuclear chemistry has many analogies with the study of inorganicchemistry Students begin to see that their chemical intuition is an excellent stepping stone to understanding nuclear phenomena. Some aspects of nuclear reactions are actually simpler than their analogs in inorganic reactions. Most importantly, when teachers introduce nuclear reactions, thev introduce material that excites studmtsand generarcsenthusii~smfor understanding nature and science. This reason alone ~ustifiesteitchine nuclear chemistry at the high school levei. Acknowledgment The authors thankE. K. Mellon for his invitation to write this paper for the Reactivity Network and for his thoughtprovoking questions. We also thank N. R. Fletcher for insights into the statistical nature of entropy and its effect on nuclear reactions. Literature Cited 1. Vio1a.V.E., Jr J. Chem Edue
19T3,50,311316. Cowan, G. A. Sci Am 1976,235,3647. Rhodes. R.The Makina offheAfomicBomb:Slmon and Schuster: NewYork. 1986. Semin, R. L. J. ~ h e m . ~1969,66,373376. d ~ ~ . Steinbw,E.P. J.Chem. Educ L989.66.367372 6 8 2799Rd~ Se8bore.G. T. J. Cham. Educ 1989 ~ ~ ~ ~ , 7 . Bohr, Wheeler,J. A. Phya Reu. 1939,56,426. 8. Atwmd. C.H.J. C h . Educ 1990.67. 731-735 ; H. Chpmlam in Bri&l&.26. 423-426, 9. ~ t w o o dC. 10. W m r l w . S.E.: Weaver. T . Sci.Am. 1 9 8 9 . 2 6 1 . 3 2 4 .
2. 3. 4. 5. 6.
c.';
~
~~~~
Wapatra, A. H. Nucl. Phya A 1986,432. 1-54. Munzenberg, G. ot a1 Z.Phys. A 1982,309.89, Burmwa, A. Phys. Today 1987,40,2837. BeMch, G.; Dong, M.; McLerrsn. L.: Ruuskanen, v.;Sarkkinen, E. Phya. Rev. D, 1988.37.1202-1209. 17. Caernai. L. P.;Fai, G.;Westfall,G,D.Phys. F a C , 1988,38,2661-2685. 18. Viola,V.E., Jr. J. Cham. Educ 1980,667,uar. 19. Atwmd, C. H. 2YCDistilloia 1966.4, &8. 20. Atwmd, C. H.; Sheline,R. K . J Cham.Ed. 1983.66, 389393. 21. Hoffman", D. C.; Choppin,G. R. J. Chpm.Edue. 1986, m, 1059-1084. 22. Atwood, C. H. J. Cham. Edue 1988.65.1037-1041. 23. Choppin, G. R.; Erp~rimentolNuclear Chemistry: RenticeHall: Englwwd Cliffs, NJ, 1961: Appendix A, 204. 13. 14. 15. 16.
~
~
