Radiochemical methods

1. Radiochemical methods • Evaluation of radiation in samples • Alpha • Beta • Gamma • Three main methods • Neutron activation • Tracer • Isotope dilution • Natural radiation • Rn

2. A Brief History • 1895-Roentgen discovers x-rays • 1896-Becquerel discovers that uranium salts and crystals emit radiation that penetrate solids • 1898-Curie concludes that the uranium rays are an atomic property and introduces concept of “radioactivity.” Determines that thorium also is radioactive and isolates polonium and radium. • 1899-Rutheford finds that there are different types of radioactivity--, , and  rays--and that they absorb after passing through different thicknesses of aluminum

3. Rutherford’s Experiment: the Effect of an Electric Field on -, -, and -radiation http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch23/history.html

4. Types of Decay 1.  decay (occurs among the heavier elements) 2.  decay 3. Positron emission 4. Electron capture 5. Spontaneous fission

5. -decay changes mass of atom by 4 units -decay barely changes mass of atom at all Naturally Occurring Radioactive Substances Elements with atomic number greater than 83 (bismuth) are radioactive

6. Uranium (4n+2) Series Friedlander & Kennedy, p.8

7. Half Lives N/No=1/2=e-t ln(1/2)=-t1/2 ln 2= t1/2 t1/2=(ln 2)/ A=N Rate of decay of 131I as a function of time.

8. The radioactive process is a subatomic change within the atom • The probability of disintegration of a particular atom of a radioactive element in a specific time interval is independent of its past history and present circumstances • The probability of disintegration depends only on the length of the time interval. Probability of decay:p=Dt Probability of not decaying:1-p=1- Dt

9. Statistics of Radioactive Decay Statistics of Radioactive Decay 1-p=1-Dt=probability that atom will survive Dt (1- Dt)n=probability that atom will survive n intervals of t nDt=t, therefore (1-  Dt)n =(1-  t/n)n Since limn∞(1+x/n)n=ex, (1- t/n)n=e-t, the limiting value. Considering No atoms, the fraction remaining unchanged after time t is N/No= e-t N=Noe-t where  is the decay constant In practicality, activity (A) is used instead of the number of atoms (N). A= ct, where c is the detection coefficient, so A=Aoe-t

10. Half-life calculation • For an isotope the initial count rate was 890 Bq • After 180 minutes the count rate was found to be 750 Bq • What is the half-life of the isotope • 750=890exp(-l*180 min) • 750/890=exp(-l*180 min) • ln(750/890)= -l*180 min • -0.171/180 min= -l • 9.5E-4 min-1=l=ln2/t1/2 • t1/2=ln2/9.5E-4=729.6 min

11. Data With Random Fluctuations • Number of counts recorded per minute not uniform • calculate arithmetic mean (median may also be used) • from small number of observations, trying to estimate results of infinite number of measurements (parent population) • Standard Deviation (x) • moments of distribution: • squaring standard deviation yields variance (x2) • second moment, n=2 • normal distribution law describes distribution of experimental results with random errors:

12. P(x)dx is probability of observing a value of x in interval xx+dx • estimation of variance: • standard deviation also expressed as percentage of average of data • called coefficient of variability • Precision of Average Value • measure of reliability is variance of mean (variance/No) • Rejection of Data • consider magnitude of deviation and number of observations made • rejection of deviations from mean that are equal or greater than the observation in question have a probability of occurrence less than 1/(2No)

13. Radioactivity as Statistical Phenomenon • Binomial Distribution for Radioactive Disintegrations • probability W(m) of obtaining m disintegrations in time t from No original radioactive atoms • probability of atom not decaying in time t, 1-p, is (N/No)=e-t, where N is number of atoms that survive in time interval t and No is initial number of atoms • Time Intervals between Disintegrations • probability of time interval having value between t and t+d:

14. where 1-p=q • Average Disintegration Rate • for radioactive disintegration--if n=No and p=1-e-t--average number M of atoms disintegrating in time t is M=No(1-e-t); for small t, M=Not and disintegration R=M/t=No , which corresponds to -dN/dt=N • Expected Standard Deviation • if reasonably large number m of counts obtained, m may be used in place of M for purpose of evaluating 

15. Notation • Number of nucleons (except in reactions involving creation or annihilation of antinucleons), charge, energy, momentum, angular momentum, statistics, and parity conserved • Q is the energy of the reaction • positive Q corresponds to energy release, negative Q to energy absorption • Q terms given per nucleus transformed Shorthand:

16. Energetics • Q may even be calculated if the masses of involved nuclei are not known • if the product nucleus is radioactive and decays back to the initial nucleus with known decay energy • The Q of a rxn is not necessarily equal to the needed kinetic energy of the bombarding particles for the rxn to occur • nucleus conservation of momentum requires that some of the particles’ kinetic energy be retained by the products as kinetic energy • the fraction of the bombarding particle’s kinetic energy that’s retained as kinetic energy of the products becomes smaller with increasing mass of the target nucleus

17. Barriers for Charged Particles • Coulomb repulsion between charged bombarding particles and the nucleus • repulsion increases with decreasing distance of separation until charged particle comes within range of nuclear forces of the nucleus • gives rise to the previously discussed potential barrier of height Vc • probability of tunneling through barrier drops rapidly as energy of particle decreases • Coulomb barriers affect charged particles both entering and leaving the nucleus • charged particles emitted from nuclei have considerable kinetic energies (greater than 1 MeV)

18. Neutrons • Since neutrons carry no charge, not opposed by Coulomb barrier • thermal neutrons have particularly high probabilities for reaction with target nuclei • fast neutrons lose energy in collisions with protons, repeated collisions reduce the energy to the thermal range, and such slow neutrons show large capture cross sections

19. Cross Sections The probability of a nuclear process is generally expressed in terms of a cross section  that has the dimensions of an area. • Originates from simple picture that probability for reaction between nucleus and impinging particle is proportional to the cross-sectional target area presented by the nucleus • doesn’t hold for charged particles that have to overcome Coulomb barriers or for slow neutrons • Total cross section for collision with fast particle is never greater than twice the geometrical cross-sectional area of the nucleus • 10-24 cm2=1 barn

20. For a beam of particles striking a thin target--one in which the beam is attenuated only infinitesimally--the cross section for a particular process is defined: When a sample is embedded in a uniform flux of particles incident on it from all direction, such as in a nuclear reactor, the cross section is defined: Ri= # of processes of type under consideration occurring in the target per unit time I= # of incident particles per unit time n= # of nuclei/cm3 x=target thickness (cm) =flux of particles/cm2/sec N=number of nuclei contained in sample

21. Target Preparation • Reactor Irradiations • sample containers exposed in high-flux reactors must be carefully chosen, with regard to neutron flux, ambient temperature, and length of irradiation • thermal stability of substance to be irradiated must be considered • cooling and buildup of of dangerous pressures unless provisions for venting or catalytically recombining gases • self-shielding of materials with high neutron cross sections

22. Thick-Target Accelerator Experiments • thick target is one in which incident bombarding particles are appreciably degraded in energy • major problem in cyclotron irradiations for radionuclide products is cooling • energy dissipation in target can become large • cooling by water, He gas, cold bath, etc. • Requirements for Thin Targets • used for measurement of reaction cross section • energy degradation of bombarding particle in passage through target won’t cause significant change in cross section • need to suppress secondary reactions caused by particles produced in primary interactions, if products of secondary reactions interfere with measurement

23. Techniques for Preparation of Thin Targets • commercially available foils that are suitable • vacuum evaporation • cathodic sputtering for deposition of small amounts of material with high efficiency • electrodeposition • nearly quantitative, so suitable for use with enriched isotopes • molecular plating, which is electrodeposition of molecular species from organic solvents • thermal decomposition of gases on hot surfaces • sedimentation • useful if uniformity criteria are not too stringent

24. Measurement of Target Thickness • desirable to know thickness of target and its uniformity • weighing accurately measured area • measurements on several neighboring areas can give idea of uniformity on larger scale • methods based on absorption of  and  particles • monoenergetic  particles or low energy  particles used • well-collimated monoenergetic  beam can be detected by high-resolution spectrometer • shift of spectral line to lower energy when foil is interposed is a measure of average foil thickness and line broadening can give information on nonuniformities • Rutherford scattering • requires measurement of primary-beam and scattered-beam intensities and knowledge of beam energy and scattering angle

25. Target Chemistry • Identification, isolation, purification of nuclides produced in nuclear reactions • Comparison with Ordinary Analytical Practice • time factor introduced by short half lives of species • high yields not always that important • high chemical purity may not be required, but radioactive purity usually required • Hazards Encountered with Radioactive Materials • even at low activity levels, person carrying out separation received dangerous doses unless protected by shielding or distance • especially in the case of -ray emitters

26. Carriers • inactive material isotopic with radioactive transmutation product added to act as carrier for active material • amount of radioactive material produced in nuclear reaction is often very small • hold-back carriers are added for radionuclides that one does not wish to carry along with the product of interest • “washing-out” method • extreme purification attainable by repeated removal of impurities via successive fresh portions of carrier • for added inactive material to serve as carrier for active substance, the two must be in same chemical form

27. Specific Activity (activity per unit weight) • desired specific activity often deciding criterion in choosing quantity of carrier to be used • analytical technique to be used is also a factor • use nonisotopic carrier in first stages of separation to prepare samples of high specific activities • Precipitation • difficulties arise from carrying down of other materials • “scavengers” so effective as precipitates that they are used to deliberately carry down foreign substances in trace amounts • useful for radionuclide capable of existence in two oxidation states

28. Ion Exchange • one of the most useful techniques for radiochemical separations • solution containing ions to be separated is run through column of finely divided resins • synthetic organic resins used as both cation and anion exchangers • most popular ion-exchange resins are crosslinked polystyrenes • ionic species may be adsorbed together on column and separated by use of eluting solutions differing in composition from original input solution • rates with which different ionic species move down column differ because stabilities of both resin compounds and complexes vary from ion to ion • anion exchange faster than cation exchange because larger flow rates can be used

29. Chromatographic Methods • paper chromatography • thin-layer chromatography • electrochromatography • extraction chromatography • Solvent Extraction • some elements may be selectively extracted from aqueous solution into organic solvent • partition coefficients nearly independent of concentration down to tracer concentrations • compounds that from chelate complexes with inorganic ions important • usually soluble in nonpolar solvents • pH dependence • may leach active product out of solid target material

30. Volatilization • exploitation of differences in vapor pressure for radiochemical separations • removal of radioactive rare gases from aqueous solutions or melts by sweeping with inert gas • often gives clean separations • Electrochemical Methods • electrolysis or electrochemical deposition used to either plate out active material of interest or plate out other substances, leaving active material in solution • when using tracer concentrations, measured potential E may deviate from standard potential Eo, according to Nernst Equation: E=Eo-(RT)/(nF) lnQ • chemical displacement may be used for separation of carrier-free substances from bulk impurities

31. Transport Techniques • rapid and efficient transport of reaction products from accelerator or reactor to measuring instrument or apparatus for chemical separations important • pneumatic transfer • tube and carrier (rabbit) which is moved through it by application of vacuum or pressure • recoil energy imparted by nuclear reaction or radioactive decay may be used to separate reaction products physically from target and transport them • helium-jet method Friedlander & Kennedy, p.302

32. Preparation of Samples for Activity Measurements • Attainment of suitable and reproducible geometrical arrangement and scattering and absorption of radiations • Choice of Counting Arrangement • radiations emitted by substance and available measuring equipment among determining factors regarding form in which samples are measured • -emitters counted in form of thin depositsand placed in proportional counter or ionization chamber • liquid scintillation counters used for -emitters • counting efficiencies very high • solid samples used •  counting performed in well-type scintillation counter

33. Backscattering, Self-Scattering, Self-Absorption • in measurement of activities, samples usually mounted on thick supports of low-Z material to achieve reproducibility; also assayed in same geometry • self-scattering negligible for sample approx. 1 mg cm-2 thick • when thicker samples used, advisable to standardize thickness or prepare empirical calibration curve for different thicknesses • self-absorption and self-scattering depend on -particle energy, chemical form of sample, and geometrical arrangement of sample and detector • highest precision achieved with nearly weightless samples mounted on essentially weightless plastic films and assayed in 4 counter • “infinitely thick” samples should be used if sepcific activity--rather than total activity--of sample is of interest

34. Useful Sample-Mounting Techniques • choice depends on type of measurement, total and specific activity, physical and chemical properties of radioelement, thickness and degree of uniformity, need for quantitative of semiquantitative transfer, etc. • evaporation of solution to dryness in shallow cup • leaves nonuniform deposit • precipitation followed by filtration and drying gives more uniform deposits • centrifugation into demountable bottoms of specially constructed centrifuge tubes

35. “Weightless” Sources • extremely thin sources required for  and  spectrometry and for 4 counting • to prevent broadening of lines in -particle or conversion-electron spectra, to minimize distortions of  spectra, and to ensure almost 100% efficiency in 4 measurements • insulating film with radioactive source deposited on it may become highly charged as result of emission of charged particles from source • distorts spectrum, so conducting film should be used • if quantitative deposition of given amount of source material on thin backing required, evaporation of solution is method of choice • in preparation of radionuclides which are themselves formed by radioactive decay, recoil energy used to carry daughter atoms onto nearby catcher plate

36. Determination of Half Lives • Long Half Lives • activity A=cN may not change measurably in time available for observation • N=-dN/dt=A/c, where c is the detection coefficient • essentially a measurement of specific activity • most accurate for  emitters • disintegration rate sometimes obtained from measurement of equal disintegration rate of daughter in secular equilibrium • use of differential measurements • compare, as function of time, activity of sample having half life to be determined with that of sample with sufficiently long half life to be practically nondecaying • R=ce-t (where c is a constant), if decay constant of reference source is negligible relative to decay constant  of the unknown

37. Intermediate Half Lives (second to years) • measure activity with appropriate instrument, plot logA vs. time, and half life found by inspection • measure decay curves separately through several thicknesses of absorbing material to obtain data with some components relatively suppressed • for half lives of a few minutes or less, useful to transport radioactive sample by means of rabbit system • Short Half Lives • more sophisticated techniques and procedures required as half life to be determined grows shorter • time dependence of decay rate of active sample observed • lower limit determined by recovery time of detector, but practically by time required to transport sample from site of formation to detection system • utilizes fact that reaction imparts momentum to products

38. distribution of time intervals between formation and decay of active atom observed experimentally instead of decay rate of collection of radioactive atoms • distribution described by exponential decay law • necessary to have signal at time that decaying state is formed and at time that state decays • result is exponential decay • Doppler shift of -ray energy used to determine lifetime of short-lived -ray emitter Friedlander & Kennedy, p.310

39. Decay Scheme Studies • Complete Decay scheme • all modes of decay of nuclide • energies and transition rates of radiations • sequence in which radiations are emitted • measurable half lives of intermediate states • all quantum numbers, particularly spins and parities, of all energy levels involved in the decay • Survey of Techniques • half life must be established • decay modes identified by use of appropriately selected detectors for  and  particles, conversion electrons,  and X rays, and fission fragments • determination of energy spectra of radiations emitted involves use of energy-sensitive detection devices

40. sequence in which various radiations are emitted and existence of alternative decay paths determined by coincidence measurements • increased selectivity usually accompanied by decreased detection efficiency • Complex Decay Schemes Friedlander & Kennedy, p.317

41. In-Beam Nuclear-Reaction Studies (Measurements of what occurs within 10-1 s of reaction) • Particle Identification • angular and energy spectra of emitted particles and spatial and temporal correlations among them are important • requires simultaneous measurement of their specific ionization and at least two of the following: kinetic energy, momentum, and velocity • specific ionization dE/dx measured by allowing particles to pass through detector thin compared to their range, and recording energy deposited in detector • kinetic energy determined by stopping particles completely in detector • momentum measured by magnetic deflection • velocity obtained from time-of-flight measurement

42. On-Line Mass Separation • important tool in studies of fission, spallation, and heavy-ion reactions • separation of unslowed fission fragments according to their charge-to-mass ratios • use focusing mass spectrograph of moderately high resolution • determination of kinetic-energy spectra of mass-separated fission fragments and investigation such as dependence of fission yields along mass chain on kinetic energy • analysis of stopped reaction products • use of mass spectrometers and isotope separators • ionization of recoiling products on hitting hot metal wall • for cross section determinations, identification of new isotopes, half-life measurements, and mass determinations

43. In-Beam Gamma-ray Spectroscopy • products of nuclear reactions generally formed in excited states • in-beam measurements of  rays may contribute importantly to nuclear spectroscopy • detection devices basically the same • Ge(Li) detectors play dominant role • background problems may be cut down by coincidences between beam pulse and -ray pulse • multidetector arrays useful in studying complex reactions in which several or many particles and rays are emitted • more sophisticated instruments can simultaneously measure-ray multiplicity, individual -ray energies, total pulse height and associated -ray multiplicity, neutron multiplicity, -ray angular correlations, and delay times between various groups of  rays in each cascade