Fundamentals of Nuclear and Radiochemistry

1. Fundamentals of Nuclear and Radiochemistry Moses Attrep, Jr. Los Alamos, New Mexico LA-UR 03335

2. 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.

3. Topics • 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

4. Organizing the Elements—The Periodic Table of the Elements • The elements are organized primarily by means of their electronic configuration/chemical prosperities.

6. 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

7. 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.

8. Chart of the NuclidesInformation 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

9. 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.

10. 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.

12. 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.

13. Binding Energy per Nucleon Light nuclides Stable nuclides

14. 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.

15. 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

16. 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.

17. 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

18. Conservation Laws and Radioactive Decay • 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)

21. Calculation of Decay Energy Qα(MeV) = -931.5(MZ-2 + MHe - MZ) 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.

22. Calculate the Alpha Decay Energy for Uranium-238 Qα = -931.5(234.043583 + 4.002604 - 238.050770) = 4.269 MeV

26. 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.

28. Summary of Major Decay Processes A X = starting nuclide Y Y = final nuclide after decay β- Z+1 N -1 Z = number of protons A N = number of neutrons X A = N + Z Mass Number Z N β+ or EC α A Y Z-1 N +1 A-4 Y Z-2 N -2

30. 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.)

32. 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.

33. 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.

34. 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.

35. 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.

36. 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 = λ N 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).

37. 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

40. Another Graphic Representation of Radioactive Decay

41. 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. Equations for Multi-Member Decay Series

42. Solution for Parent-Progeny Relationship N2 = [λ2/(λ2 - λ1)] N1o (e-λ1t – e-λ2t) + N2oe-λ2t

43. Uranium Ores Tobernite (Cu(UO2)2(PO4)2.12H2O) Pitchblende (U3O8)

46. When a Radioactive Decay is Not Linear (when plotted on semi-log)

47. Non Linear Decay Graphs • Multiple independent components • Series of two (or more) related radioactive species