Transcript Chap. 1 (Introduction), Chap. 2 (Components and Circuits)

Radiochemical methods
• Evaluation of radiation in samples
 Alpha
 Beta
 Gamma
• Three main methods
 Neutron activation
 Tracer
Isotope dilution
 Natural radiation
Rn
21-1
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
21-2
Rutherford’s Experiment: the Effect of an
Electric Field on -, -, and -radiation
21-3
http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch23/history.html
Types of Decay
1.  decay (occurs among the heavier elements)
226
88
Ra Rn   Energy
222
86
4
2
2.  decay
131
53

I 131
Xe


  Energy
54
3. Positron emission
22
11
Na Ne     Energy

22
10
4. Electron capture
26
13
Al    Mg   Energy

26
12
5. Spontaneous fission
Cf  Xe Ru 4 n  Energy
252
98
140
54
108
44
1
0
21-4
Naturally Occurring
Radioactive Substances
Elements with atomic number greater than
83 (bismuth) are radioactive
Series
uranium
thorium
actinium
Parent
238
U
232
Th
235
U
End Product Formula
206
Pb
4n+2
208
Pb
4n
207
Pb
4n+3
• -decay changes mass of atom by 4 units
• -decay barely changes mass of atom at all
21-5
Uranium (4n+2) Series
21-6
Friedlander & Kennedy, p.8
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.
21-7
• 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
21-8
StatisticsofofRadioactive
Radioactive Decay
Statistics
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
21-9
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(-*180 min)
750/890=exp(-*180 min)
ln(750/890)= -*180 min
-0.171/180 min= -
9.5E4 min-1 ==ln2/t1/2
t1/2=ln2/9.5E-4=729.6 min
21-10
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) 1 N
n


i=1 xi  xt
o
• Standard Deviation (x)
 moments of distribution:
No
  x  xt 2 
P( x)dx =
exp
dx

2
2 x2
 2 x 
1
 squaring standard deviation yields variance (x2)
second moment, n=2
 normal distribution law describes distribution of
experimental results with random errors:
21-11
 P(x)dx is probability of observing a value of x in interval
xx+dx
1
N
2
2


x =
x x

i =1 i
 estimation of variance:
N 1
o
o
 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
21-12
probability of occurrence less than 1/(2No)
Radioactivity as Statistical
Phenomenon
• Binomial Distribution for Radioactive Disintegrations
 probability W(m) of obtaining m disintegrations in
time t from No original radioactive atoms
No!
W (m) =
p m (1  p) No m
( N o  m)!m!
 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
21-13
and t+d:
P(t )dt = Noe N t dt
o
• Average Disintegration Rate
n!
W (r ) =
p r q nr
(n  r )!r!
np = r =0 rW (r ) = r
 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
where 1-p=q
r =n
• Expected Standard Deviation
 = N o (1  e  t )e  t = Met
Sincein counting practicet is generallysm all,  = M
 if reasonably large number m of counts obtained, m may be
used in place of M for purpose of evaluating 
m
Rt
R
R = m / t;  R =
=
=
t
t
t
21-14
Notation
14
7
N  He O H  Q
4
2
Shorthand:
17
8
14
1
1
N ( , p)17O
• 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
21-15
Energetics
E = Mc
2
• 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
21-16
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)
21-17
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
21-18
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
21-19
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:
Ri = Inx i
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 = N i
Ri= # of processes of type under consideration occurring in the target
per unit time
I= # of incident particles per unit
=flux of particles/cm2/sec
time
N=number of nuclei contained in
n= # of nuclei/cm3
sample
21-20
x=target thickness (cm)
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
21-21
• 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
21-22
• 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
21-23
• 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 scatteredbeam intensities and knowledge of beam energy and
scattering angle
21-24
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
21-25
• 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
21-26
• 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
21-27
oxidation states
• 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
21-28
• 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
21-29
• 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
21-30
carrier-free substances from bulk impurities
• 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
21-31
Friedlander & Kennedy, p.302
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
21-32
• 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 cm2 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
21-33
interest
• 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
21-34
• “Weightless” Sources
 extremely thin sources required for  and  spectrometry
and for 4 counting
 to prevent broadening of lines in -particle or conversionelectron 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 21-35
carry
daughter atoms onto nearby catcher plate
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
21-36
• 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
21-37
 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
Friedlander & Kennedy, p.310
21-38
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
21-39
 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
21-40
Friedlander & Kennedy, p.317
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
21-41
• 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 massseparated 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
21-42
• 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
21-43