Fundamentals of Nuclear and
Radiochemistry
Moses Attrep, Jr.
Los Alamos, New Mexico
LA-UR 03335
Some Reference Texts
• G. Friedlander, J.W. Kennedy, E.S. Macias, and J.M.
Miller, Nuclear and Radiochemistry, 3rd edition, J.
Wiley and Sons, 1981
• G.R. Choppin and J. Rydberg, Nuclear Chemistry—
Theory and Applications, Pergamon Press, 1980
• W.D. Ehmann and D.E. Vance, Radiochemistry and
Nuclear Methods of Analysis, J. Wiley and Sons,
1991.
• B. Kahn, ed., Radioanalytical Chemistry, Springer,
2007 and M. Attrep and B. Kahn, Radioanalytical
Experiments, Springer, 2008.
Topics
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Chart of the Nuclides
Modes of Nuclear Transformation (Decay)
Radioactive Decay Rate Equations
Nuclear Reactions: (n,γ) and (n,f)
Nuclear Fission
Molybedum-99 (for Technetium-99m)
production
Organizing the Elements—The Periodic
Table of the Elements
• The elements are organized primarily by means of their
electronic configuration/chemical prosperities.
Organization of the
Chart of the Nuclides
• Nuclides are exhibited in each square
• Vertical axis represents the increase of
protons
• Horizontal axis represents the increase of
neutrons
• Each horizontal group are isotopes of that
element
Nuclide—term used to describe any nuclear species
Isotope—nuclides of the same element having different neutrons
Chart of the Nuclides
shows all the nuclides
known
There are several companies and/or
institutions that provide charts of this
type.
They use different types of color codes
and notations.
Essentially, they have most all the
same information.
The Chart of the Nuclides is an
essential tool for all working in the
fields of nuclear physics, nuclear
chemistry, radioanalytical chemistry,
nuclear forensics, etc.
It can be called the compilation of
most of the relevant nuclear data of
the nuclides.
Chart of the Nuclides
Information
Here are some of the many things that
the given for the nuclides in the Chart
of the Nuclides
Stable or Unstable
Isomeric states
Percent abundance of stable or long
lived naturally occurring nuclides
Mode of Decay
Energy of particular mode of decay
Energy of gamma ray emissions
Half-life of radioactive decay
Atomic mass
Cross section for thermal neutron
capture
Energy of transition for radioactive
nuclides
Spin and parity
Fission product
Fission yield
The Nucleus
• The nucleus is comprised of neutrons and
protons.
• The nature of the forces that hold the protons
and neutrons together is still not fully
understood.
• A popular theory of the nuclear forces that
hold the nuclear particles together is the
particle exchange theory.
The Nucleus (Continued)
• The nucleus is very small and compact.
• Most of the atomic mass of an atom is
concentrated in the nucleus.
• The diameter of the nucleus is 10-12 to 10-13
cm.
• The density of nuclear material is ~1014 g/cm3.
• The binding energy of a nucleus is the amount
of nuclear matter “used” to hold the particles
together.
Nuclear Stability
• A nuclide is stable if its atomic mass is less than
the sum of the masses of the products for a given
process. Mnuclide < ∑MZ + ∑MN
• That nuclear stability may be expressed in terms
of binding energy as related to nuclear volume,
nuclear surface, Columbic forces, symmetry, and
pairing of nucleons.
• Nuclides with the highest stability (greatest
binding energy) are those around A = 60.
Exception is helium-4.
A is the atomic mass number and is equal to the number of protons (Z) + number of
neutrons (N). Example: carbon-12 has 6 protons (Z) + 6 neutrons (N): A = 6+6 = 12.
Binding Energy per Nucleon
Light nuclides
Stable nuclides
Plot for stable nuclides
showing neutron to
proton ratio
Notice that the ratio of neutrons to
protons for the lighter elements is
essentially 1.
Past A = 20 the ratio of neutrons to
protons increases.
This structure or observation is seen
when you inspect the complete chart
of the nuclides.
This observation is also taken into
account in the semi-empirical binding
energy equations that describe the
nuclear stability of the nuclides.
Radioactive Transformations and
Observed Radiation Emanations
• Alpha particle (α) [an alpha particle is a helium
nucleus]
• Beta negative (negatron) (β-) [negative
electron]
• Positive electron (positron) (β+) [positive
electron—antimatter]
• Electron capture (EC), nucleus captures an
atomic electron
Radioactive Transformations and
Observed Radiation Emanations cont’d
• Gamma ray emission—electromagnetic
radiation that accompanies most other types
of transformations—origin is from the nucleus
• X-ray emission—electromagnetic radiation
that accompanies most other types of
transformations resulting from the atomic
electrons of the atom
• Isomeric transition (IT)—meta state nuclides
decays to its ground state.
Less Common Spontaneous Nuclear
Transformations
• Spontaneous fission—a heavy nucleus
spontaneously breaking up into two smaller
nuclides
• Delayed neutron emission—unstable nuclide
that emits a neutron—observed in certain
fission products
• Double Beta Decay—rare decay process where
two beta particles are emitted simultaneously
Conservation Laws and Radioactive
Decay
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Total energy of the process must be constant
Linear momentum must be conserved
Total charge must be constant
Mass number (A) must be constant
Nuclear angular momentum must be
conserved: orbital movement of individual
nucleons and intrinsic spin of nucleons are
combined as the nuclear spin quantum
number (ΔI)
Calculation of Decay Energy
Q (MeV) = -931.5(MZ-2 + MHe - MZ)
α
MeV = millions of electron volts. Nuclear energies are express
primarily in electron volts.
Unlike chemical expressions of energy where negative energies are spontaneous,
positive energies in nuclear expressions are spontaneous reactions.
931.5 MeV is equivalent to 1 atomic mass unit (amu) of matter.
Calculate the Alpha Decay Energy for
Uranium-238
Qα = -931.5(234.043583 + 4.002604 - 238.050770)
= 4.269 MeV
Auger electrons are atomic electrons (K or L) emitted when absorbed by x-rays emitted during
process. Bremstrahlung is continuous sprectrum of electromagnetic radiation of very low intensity
emitted in EC process.
Summary of Major Decay Processes
A
Y
Z+1 N -1
β-
Z = number of protons
A
Z
α
X = starting nuclide
Y = final nuclide after decay
N = number of neutrons
A=N+Z
Mass Number
X
N
β+ or EC
A
Z-1
A-4
Z-2
Y
N -2
Y
N +1
Gamma Ray Transitions
• Gamma ray transitions are allowed or
forbidden as determined by (a) spin
changes between energy states (ΔI) and
parity changes (ΔΠ)
• Gamma ray transitions are characterized
by electric and magnetic multipoles (E1, E2,
M1, etc.)
Spontaneous Fission
U-238 → FP1 + FP2 + 2-3 neutrons
Fission Products (FP) will be put into two classes: light mass (A~ 90) and heavy mass
A ~ 140. The amount of energy released is 100 and 200 MeV.
A kilogram of U-238 will have only about 70 fissions per second compared to 45
billion alpha disintegrations/sec.
Look up the alpha and SF half lives of U-238.
Radioactive Decay or
Transformation
• It is expressed as an exponential law in the
same form as any mono-molecular
reaction.
• Generally, the rate of decay cannot be
altered by temperature, chemical change,
pressure, gravitational, magnetic or
electrical fields.
• Radioactive decay can be treated in terms
of probabilities.
A Statistical Approach to Radioactivity
In 1905 E. von Schweidler approached radioactive transformation process as a
probability problem.
A particular atom capable of disintegrating in a time interval Δt is independent of its
past history and present circumstances. It depends only on the length of the time
interval Δt.
For sufficiently short intervals of time the probability (p) is proportional to Δt.
Thus, p = Δt where λ s the proportionality constant characteristic of the particular
radioactive atom.
The probability that the particular atom will not decay in the same time interval Δt is 1 –
p and is equal to 1 - Δt.
Thus the probability that an atom will n time intervals is (1 - Δt)n.
A Statistical Approach to Radioactivity--continued
If enough of these time intervals are taken to a longer time such that n Δt = t, the
total time, the survival probability is thus (1 – λt/n)n.
The probability that the atom will remain unchanged (not decay)after time t is just
the
value of this quantity when Δt is made infinitely small. In other words, it is the
limit obtained when of (1 – λt/n)n as n approaches infinity.
[Recall that ex = lim(1 + x/n)n as n→∞.]
If many atoms are considered, No, initially then the fraction remaining unchanged
after time t becomes N/No = e-λt, where N is the number of unchanged atoms at
time t.
This is the exponential law of decay.
Equations for Radioactive Decay
There are two primary relationships that describe the rates
of decay. The first is the rate of transformation or decay is
equal to the number of radioactive atoms times the decay
constant.
A α N
or A = kN or
A = λN
Where A is the activity or rate of decay, N is the number of
radioactive atoms at that time, and λ or k is the decay
constant. λ is equal to ln2/t1/2 where t1/2 is the half life (the
time required for ½ of the initial number of atoms to decay).
Equations for Radioactive Decay
The previous equation can be developed into another useful form that
describes the rate of decay or number of atoms present at two different
times.
N = No e-λt
Where N is the number of radioactive atoms at any time t and No is the
number that was present initially. The equation can also be expressed with
activities (A and Ao):
A = Ao e-λt
Another Graphic Representation
of Radioactive Decay
Equations for Multi-Member Decay Series
Relationship of activities (number of atoms) when there are two
(or more) members such as that in the uranium-238 series.
A → B → C → etc.
The general solution to know the amount of any member is given by the
Bateman equation. Let Nn represent the number of atoms present of the nth
member of a series of radioactive series at any time t.
Nn = C1e-λ1t + C2 e-λ2t + . . . . . . Cn e-λnt
C1 = (λ1λ2 …… λn-1) N1o/(λ2 - λ1) (λ3 - λ1) …..(λn - λ1)
C2 = (λ1λ2 …… λn-1) N1o/(λ1 - λ2) (λ3 - λ2) …..(λn - λ2)
and so on.
Solution for Parent-Progeny
Relationship
N2 = [λ2/(λ2 - λ1)] N1o (e-λ1t – e-λ2t) +
N2oe-λ2t
Uranium Ores
Pitchblende (U3O8)
Tobernite (Cu(UO2)2(PO4)2.12H2O)
When a Radioactive Decay is Not
Linear (when plotted on semi-log)
Non Linear Decay Graphs
• Multiple independent components
• Series of two (or more) related radioactive
species
Nuclear Fission
Important Events Leading to the Discovery of Fission and the Concept of the
the Nuclear Bomb
Discovery of the neutron
Chadwick 1932
Discovery of fission
Hahn and Strassmann
1938
Lisa Meitner gives the process
the name “fission” and realizes
the large amount of energy released.
Leo Szilard files patent in England
for nuclear bomb.
Scientists in Germany, US, etc. realize
potential for bomb.
Implicit understanding of
nuclear criticality and large
amount of energy available.
Nuclear reactor
concept realized.
NEUTRON INDUCED NUCLEAR FISSION
n
10-15 sec
Target
nucleus
Primary fission
fragments + neutrons
10-11 sec
γ emission
Long-lived and/or
stable fission products
β- and γ decays
Primary fission products
Asymmetric Fission
100-200 MeV energy release per fission
FPs are neutron-rich
Fission Products
• Fission products are “neutron rich” therefore
they are all negatron (negative beta) emitters.
• The initial fission products formed are very
short lived.
• There are two fission products for each
fission one “light” and one “heavy”.
• The products are formed asymmetrically
because of nuclear shell properties and
columbic repulsion.
Major Fissile Nuclides
• U-235 –Naturally occurring in uranium
ores
• Pu-239—Must be made from the neutron
capture by U-238
Fission Yield Curves
Some Useful Equations for Irradiation Experiments
A = NΦσ(1 – e-λt)
A = activity (disintegrations per unit time) of the species being produced
at any time of the irradiation
N = number of target atoms
Φ = flux of neutrons (neutrons per second per cm2)
σ = cross for the reaction (cm2)
λ = decay constant for species being produced = 0.693/t1/2
t = length of the irradiation
Rate (R) of production of a species atoms per unit time
A fission product when a fissile material is being irradiated
R = NΦσY
Y is the fission yield
Number of atoms produced for a particular fission product when a fissile
material is being irradiated:
Nfp = Rt = NΦσYt
How Are Fission Products
Measured
• A fissile material is
prepared for irradiation
• Irradiated in a nuclear
reactor where neutron
energy is characterized
• Same is removed,
allowed to “cool”, and
dissolved
• An aliquot is taken for
analysis
• Carrier is added and
chemistry is performed
• Sample is prepared for
counting
• Sample is counted
• Data analyzed
• Disintegrations per
minute or atoms are
reported
The Radiochemical Analysis
• Purpose is to isolate a radioactive
nuclide(s) of an element in a pure form for
quantitative analysis
• The amount of the radioactive nuclide will
be measured by radioactive measurements
(detectors)
• Methods commonly use classical inorganic
chemical separation steps to isolate, purify
and prepare the sample for counting
Radiochemical Separation
Techniques
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Precipitation
Extraction
Ion Exchange
Oxidation state manipulation
Complex formation
Electrochemistry
Etc.
Determination of Fission Products
P.K.Kuroda, et al., Science 147, 1248-9 (1965)
Graph of Results
Technetium-99m
Some 15 or more chemical steps
later all performed in the hot cells…
Mo-99 → Tc-99m → Tc-99g