21-1

Radiochemical methods

• Evaluation of radiation in samples Alpha Beta Gamma

• Three main methods Neutron activation Tracer

Isotope dilution Natural radiation

Rn

21-2

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

21-3

Rutherford’s Experiment: the Effect of an Electric Field on -, -, and -radiation

http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch23/history.html

21-4

1. decay (occurs among the heavier elements)

2. decay

3. Positron emission

4. Electron capture

5. Spontaneous fission

Types of Decay

EnergyRnRa 42

22286

22688

EnergyXeI 13154

13153

EnergyNeNa 2210

2211

EnergyMgAl 2612

2613

EnergynRuXeCf 10

10844

14054

25298 4

21-5

Naturally Occurring Radioactive Substances

Series Parent End Product Formulauranium 238U 206Pb 4n+2thorium 232Th 208Pb 4nactinium 235U 207Pb 4n+3

-decay changes mass of atom by 4 units -decay barely changes mass of atom at all

Elements with atomic number greater than 83 (bismuth) are radioactive

21-6

Uranium (4n+2) Series

Friedlander & Kennedy, p.8

21-7

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.

21-8

• 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=t

Probability of not decaying: 1-p=1- t

21-9

1-p=1-t=probability that atom will survive t

(1- t)n=probability that atom will survive n intervals of t

nt=t, therefore (1- t)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

Statistics of Radioactive Decay

N=Noe-t where is the decay constant

In practicality, activity (A) is used instead of the number of atoms (N).

A= ct, where c is the detection coefficient, so A=Aoe-t

Statistics of Radioactive Decay

21-10

Half-life calculation

• For an isotope the initial count rate was 890 Bq After 180 minutes the count rate was found

to be 750 BqWhat is the half-life of the isotope750=890exp(-*180 min)750/890=exp(-*180 min) ln(750/890)= -*180 min -0.171/180 min= -min-1=ln2/t1/2

t1/2=ln2/9.5E-4=729.6 min

21-11

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=2normal distribution law describes distribution of

experimental results with random errors:

oN

i

nti

o

xxN 1

1

dx

xxdxxP

x

t

x

2

2

2 2exp

2

1)(

21-12

P(x)dx is probability of observing a value of x in interval xx+dx

estimation of variance:

standard deviation also expressed as percentage of average of datacalled coefficient of variability

• Precision of Average Value

measure of reliability is variance of mean (variance/No)

• Rejection of Dataconsider magnitude of deviation and number of observations

maderejection of deviations from mean that are equal or

greater than the observation in question have a probability of occurrence less than 1/(2No)

oN

i io

x xxN 1

22

1

1

21-13

Radioactivity as Statistical Phenomenon

• Binomial Distribution for Radioactive Disintegrationsprobability 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 Disintegrationsprobability of time interval having value between t

and t+d:

mNm

o

o oppmmN

NmW

)1(

!)!(

!)(

dteNdttP tNo

o )(

21-14

• 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=Not 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

nr

r

rnr

rrrWnp

qprrn

nrW

0)(

!)!(

!)(

where 1-p=q

MsmallgenerallyistpracticecountinginSince

MeeeN ttto

,

)1(

tt

t

t

mtm

RRR R ;/

21-15

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 reactionpositive Q corresponds to energy release, negative Q to

energy absorptionQ terms given per nucleus transformed

QHOHeN 11

178

42

147

Shorthand: OpN 1714 ),(

21-16

Energetics

• Q may even be calculated if the masses of involved nuclei are not knownif 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 occurnucleus conservation of momentum requires that some of

the particles’ kinetic energy be retained by the products as kinetic energythe 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

2McE

21-17

Barriers for Charged Particles

• Coulomb repulsion between charged bombarding particles and the nucleusrepulsion 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 nucleuscharged particles emitted from nuclei have

considerable kinetic energies (greater than 1 MeV)

21-18

Neutrons

• Since neutrons carry no charge, not opposed by Coulomb barrierthermal neutrons have particularly high probabilities

for reaction with target nucleifast 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

21-19

Cross Sections

• Originates from simple picture that probability for reaction between nucleus and impinging particle is proportional to the cross-sectional target area presented by the nucleusdoesn’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 nucleus10-24 cm2=1 barn

The probability of a nuclear process is generally expressed in terms of a cross section that has the dimensions of an area.

21-20

ii NR

ii InxR

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:

=flux of particles/cm2/sec

N=number of nuclei contained in sample

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)

21-21

Target Preparation

• Reactor Irradiationssample 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 consideredcooling and buildup of of dangerous pressures

unless provisions for venting or catalytically recombining gases

self-shielding of materials with high neutron cross sections

21-22

• Thick-Target Accelerator Experimentsthick target is one in which incident bombarding

particles are appreciably degraded in energymajor problem in cyclotron irradiations for

radionuclide products is coolingenergy dissipation in target can become largecooling by water, He gas, cold bath, etc.

• Requirements for Thin Targetsused 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

21-23

• Techniques for Preparation of Thin Targetscommercially available foils that are suitablevacuum evaporationcathodic sputtering for deposition of small amounts

of material with high efficiencyelectrodeposition

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 surfacessedimentation

useful if uniformity criteria are not too stringent

21-24

• 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 particlesmonoenergetic particles or low energy particles usedwell-collimated monoenergetic beam can be detected by

high-resolution spectrometershift 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 scatteringrequires measurement of primary-beam and scattered-

beam intensities and knowledge of beam energy and scattering angle

21-25

Target Chemistry

• Identification, isolation, purification of nuclides produced in nuclear reactions

• Comparison with Ordinary Analytical Practicetime factor introduced by short half lives of specieshigh yields not always that importanthigh 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 distanceespecially in the case of -ray emitters

21-26

• Carriersinactive material isotopic with radioactive

transmutation product added to act as carrier for active materialamount of radioactive material produced in

nuclear reaction is often very smallhold-back carriers are added for radionuclides that

one does not wish to carry along with the product of interest

“washing-out” methodextreme 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

21-27

• Specific Activity (activity per unit weight)desired specific activity often deciding criterion in

choosing quantity of carrier to be usedanalytical technique to be used is also a factor

use nonisotopic carrier in first stages of separation to prepare samples of high specific activities

• Precipitationdifficulties 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

21-28

• Ion Exchangeone of the most useful techniques for radiochemical

separationssolution containing ions to be separated is run through

column of finely divided resinssynthetic organic resins used as both cation and

anion exchangersmost popular ion-exchange resins are crosslinked

polystyrenesionic species may be adsorbed together on column and

separated by use of eluting solutions differing in composition from original input solutionrates 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

21-29

• Chromatographic Methodspaper chromatographythin-layer chromatographyelectrochromatographyextraction chromatography

• Solvent Extractionsome elements may be selectively extracted from

aqueous solution into organic solventpartition coefficients nearly independent of

concentration down to tracer concentrationscompounds that from chelate complexes with

inorganic ions importantusually soluble in nonpolar solventspH dependence

may leach active product out of solid target material

21-30

• Volatilizationexploitation of differences in vapor pressure for

radiochemical separationsremoval of radioactive rare gases from aqueous

solutions or melts by sweeping with inert gasoften gives clean separations

• Electrochemical Methodselectrolysis 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

21-31

• Transport Techniquesrapid and efficient transport of reaction products from

accelerator or reactor to measuring instrument or apparatus for chemical separations important

pneumatic transfertube and carrier (rabbit) which is moved through

it by application of vacuum or pressurerecoil 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

21-32

Preparation of Samples for Activity Measurements

• Attainment of suitable and reproducible geometrical arrangement and scattering and absorption of radiations

• Choice of Counting Arrangementradiations 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 -emitterscounting efficiencies very highsolid samples used

counting performed in well-type scintillation counter

21-33

• Backscattering, Self-Scattering, Self-Absorptionin 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 thickwhen 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

21-34

• Useful Sample-Mounting Techniqueschoice 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 cupleaves nonuniform depositprecipitation followed by filtration and drying

gives more uniform depositscentrifugation into demountable bottoms of specially

constructed centrifuge tubes

21-35

• “Weightless” Sourcesextremely thin sources required for and spectrometry

and for 4 countingto 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 sourcedistorts spectrum, so conducting film should be

usedif 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

21-36

Determination of Half Lives• Long Half Lives

activity A=cN may not change measurably in time available for observationN=-dN/dt=A/c, where c is the detection coefficientessentially a measurement of specific activitymost accurate for emitters

disintegration rate sometimes obtained from measurement of equal disintegration rate of daughter in secular equilibrium

use of differential measurementscompare, 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

21-37

• Intermediate Half Lives (second to years)measure activity with appropriate instrument, plot logA

vs. time, and half life found by inspectionmeasure 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 Livesmore sophisticated techniques and procedures required as

half life to be determined grows shortertime 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

21-38

distribution of time intervals between formation and decay of active atom observed experimentally instead of decay rate of collection of radioactive atomsdistribution described by exponential decay lawnecessary to have signal at time that decaying state is

formed and at time that state decaysresult is exponential decay

Doppler shift of -ray energy used to determine lifetime of short-lived -ray emitter

Friedlander & Kennedy, p.310

21-39

Decay Scheme Studies• Complete Decay scheme

all modes of decay of nuclideenergies and transition rates of radiations sequence in which radiations are emittedmeasurable half lives of intermediate statesall quantum numbers, particularly spins and parities, of

all energy levels involved in the decay• Survey of Techniques

half life must be establisheddecay 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

21-40

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

21-41

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 deflectionvelocity obtained from time-of-flight measurement

21-42

• 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 ratiosuse focusing mass spectrograph of moderately high

resolutiondetermination 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 productsuse of mass spectrometers and isotope separators

ionization of recoiling products on hitting hot metal wallfor cross section determinations, identification of new

isotopes, half-life measurements, and mass determinations

21-43

• In-Beam Gamma-ray Spectroscopyproducts of nuclear reactions generally formed in excited

statesin-beam measurements of rays may contribute

importantly to nuclear spectroscopydetection devices basically the same

Ge(Li) detectors play dominant rolebackground problems may be cut down by

coincidences between beam pulse and -ray pulsemultidetector arrays useful in studying complex reactions

in which several or many particles and rays are emittedmore 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