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LABORATORY EXERCISES IN NUCLEAR CHEMISTRY I.
General Principles
RUSSELL R. WILLIAMS, JR., WILLIAM H. HAMILL, and ROBERT H. SCHULER University of Notre Dame, Notre Dame, Indiana
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of the most commendable accomplishments of preparation of active materials, problems having conthe Atomic Energy Commission and its employees has siderable instructional value. For this reason, and bebeen the efficient-produotion and distribution of radio- cause of certain other advantages which will be a p isotopes. This programis mak'mg a great contribution parent later, we have centered our attention upon the to the progress of science by placing in the hands of use of procedures which are largely self-contained. Neutron Capture. Radioactive isotopes are produced qualified scientists a research tool of very wide applicability. The full utilization of this opportunity in the by a variety of nuclear reactions (5). One of the most years to come *ill depend to a considerable extent upon efficient and convenient is the capture of a slow neutron the integration of pertinent subject material into the by a stable nucleus as exemplified by the equation training programs of onr schools and laboratories. nAu"' + n r p A ~ ' D p Y The laboratory course in physical chemistry usually Stable nucleus Neutron Unstable nucleus Gamma ray (1) given in the third or fourth college year is one appropriate occasion for introduction of some basic material in The resulting nucleus, having a mass number one unit greater than its progenitor may be an unstable comhinanuclear chemistry. Since the capacity of such courses tion of protons and neutrons which decays by beta is already strained, any proposed experiments must be particle emission. The exoergic nature of the neutron severely limited and carefully planned. In addition, capture process is attested to by the emission of one or they must not require excessive investment in equipmore quanta of gamma radiation for a total of several ment or care. million electron volts per capture. With these points in mind, we are presenting here a Neutrons are conveniently generated according to group of experiments exemplifying some of the basic the reaction operations in nuclear chemistry. The present article ,BeQ .He4(ar) ,CLz+ a1 (2) will review some of the important principles involved. Succeeding articles will offer more detailed discussion of Radium provides an essentially permanent source of lahoratory procedures in radioactivity determinations, alpha particles and in an intimate mixture with berylpreparation of radioactive samples, some applications to lium gives rise to the above process. One gram of chemical problems, and several other experiments. radium in equilibrium with its shorter-lived decay The material is intended to be used a t the advanced products emits more than 10" alpha particles per secundergraduate or beginning graduate level in college ond. Only a fraction of these produce neutrons and a trainmg. The time available and the previous training one-gram radium-beryllium neutron source can he exof the students involved will determine the selections pected to yield about lo7 neutrons per second. These and modifications to be made. have considerable kinetic energy and must be slowed down, or moderated, to thermal velocities in order to rePREPARATION AND CHARACTERISTICS OF act efficiently with stable nuclei according to equation RADIOACTIVE TRACERS (1). The moderation is accomplished by repeated A few radioactive isotopes suitable for chemical ex- collision with atomic nuclei around the source and simperiments occur in nature, but they are confined to the ple dynamical considerations indicate that hydrogen, elements heavier than mercury. Radioactive isotopes with its almost identical mass, will be the most efficient of lead and bismuth may be isolated from spent radon moderator. A few centimeters of water or ~araffin tubes and have been previously suggested as being around the source will considerably enhance the extent suitable for instructional purposes ( I ) . In addition a of activation. large number of radioactive isotopes are prepared and The sample to be activated may be mixed with or disdistributed by the Atomic Energy Commission a t very solved in the moderator or simply inserted a t a favorreasonable prices @). However, both of thew sources able position. It may be an element having several of radioactive materials by-pass to a considerable extent stable isotopes, only one of which forms the desired the chemical and physical problems involved in the unstable isotope. Since the rate of neutron capture
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+
210
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APRIL. 1949
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-
211
will be proportional to the number of stable nuclei available a correction must be made for the fractional abundance of the isotope of interest. The capture rate will also be proportional to the slow neutron flux, the proportionality constant being known as the capture cross section. The value of this quantity is a characteristic of each individual isotope. Radioactive Decay. An unstable nucleus formed by neutron capture usually has a higher neutron-proton ratio than its stable isobars, and therefore frequently decays by beta particle emission as exemplified by the equation rrAu'S8
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-16
+ wHglq8
-XN
d = A N
(4)
(5)
is the quantity usually observed or computed. Equation (4) may be integrated to yield A = Aae-At or Ln A = In Aa - X t
(3)
While several other types of radioactive decay reactions are known our attention will be centered upon beta decay for two reasons: first, it is the most commonly observed type of decay following slow neutron capture, and second, it is comparatively easy to detect. On the other hand, alpha decay produces particles of very small penetrating power, and gamma rays are so very penetrating that they are not efficiently absorbed in detecting devices of reasonable mass. The beta particle is simply a very energetic electron created in the nuclear transformation of a neutron into a proton. It has a maximum energy characteristic of the,particular decay reaction and is detected by means of the ionization it produces in its passage through ma& ter. The penetration observed will be approximately proportional to the energy of the particle and may be exemplified by the statement that typical beta radiation will be half absorbed after passing through 25 to 50 cm. of air. In contrast, 5 to 7 cm. of air serve to completely absorb most alpha particles, while gamma rays may be only half nbsorbed by as much as 100 meters of air. At least one case of the decay reaction known as isomeric transition is available for student experiments. This decay involves no change in atomic or mass number but is rather a transition between two energy states of the same nucleus. The energy may be evolved as gamma radiation or by the mechanism of internal conversion. In the latter case an extra-nuclear electron, usually from the K or L shell, interacts with the nucleus and is ejected from the atom with the energy of the transition less the ionization potential of the electron concerned. Such conversion electrons are usually very weak and therefore difficult to detect but the decay product-the lower energy state of the nucleus-may also be unstable, decaying by beta particle emission. The loss of a K or L electron by the decaying atom will be followed by electronic transitions from higher levels and the emission of weak x-rays and electrons. This process, known as an Auger shower, will leave the product atom with several valence electrons missing and has an important effect on the chemical future of the atom. Rate Equations. Radioactive decay follows the wellknown first-order rate law, which may be written in differential form as follows:
dN = dl
where N is the number of unstable nuclei a t time t and X is the characteristic decay constant. The value of X is independent of ordinary variables such as pressure, temperature, and state of chemical combmation. Smce radioactive elements are ordinarily detected and measured through the radiations emitted in the decay process, the activity A, related to N by the equation
(6)
where A. is the activity when t = 0. The second form indicates the convenience of using a semilogarithmic method of graphical analysis in activity-time measurements as illustrated in Figure 1, Curve A. It is customary to report radioactive decay rate measurements in terms of the half-life, tl/,, which may be defined as the time required for the activity to decrease by a factor of This quantity is related t o the decay constant through the equation
The half-life is a characteristic of the individual unstable isotopes and values from a few microseconds to billions of years have been observed and measured. For laboratory experiments, values from a few minutes to a few days are most suitable. The rate of formation of unstable nuclei by slow neutron capture will be proportional to the number of target atoms n and the slow neutron flux 4. The proportionality constant u is the capture cross section and has the
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I
1.0
1.5
2 0
I
2.5
3.0
TIME (IN MULTIPLES O F TL/4 F1gu.o 1. Activity a. e Fvnction of Tima Curve A , decay of a single radioactive species; Curve B, grovth of activity due to formation of a single radioaotive species at a constant rate: Curve C, growth and decay of daughter activity formed from an undetected parent whose half-life is four times that of the daughter.
JOURNAL OF CHEMICAL EDUCATION
for the unstable isotope, e-"I = 'jZ, and. the activity has reached one-half its saturation value. Curve B in Figure 1 shows the relative activity obtained a t the end of various bombardment periods. Note that this curve is equivalent to the difference between an exponential decay, such as Curve A, and the asymptote representing iE = cn+ - AN (8) the stationary state. dt It occasionally happens that a single radioactive deThe integrated form of this equation, when no unstable cay does not give rise to a stable nucleus, but to a nunuclei am present a t zero time is clear configuration which decays still further with its own characteristic period. The two differential equations describing the net rate of change of the two isotopes are or in tern of activity, rather than number of unstable dN2 = A,N1 - A&$ d N 1 = -AINI, atoms, (12) dimension of area. During an activation of finite duwtion some of the unstable nuclei will decay according to equation (4) and the differential equation for the dependence of the number of unstable nuclei N on the activation period t is as follows:
dl
A
=
&(l - e-u)
(10)
This relation indicates that for long activation periods a limiting activity given by A = on+
(11)
is attained. i. e.. a "stationarv state" has been achieved where the rate of formation is equal to the rate of decay. For an activation period correspondimg to one half-life
dt
where the subscripts 1and 2 refer to parent and daughter, respectively. The integrated form of these equations, describing the activity of the second member of the series as a function of time, is
where A,O and Azorepresent the activity of the parent and daughter a t t = 0. Note that when h i
