CHAPTER 1 Radioelements, Isotopes & Radionuclides
This chapter gives an overview needed to better understand ionizing radiation, i.e., radiation that has sufficient energy to remove electrons from atoms.
The Atom
Matter has mass and takes up space. Atoms are the basic building blocks of matter. Everything is made of atoms.
The ancient Greeks once thought that atoms were the smallest pieces of matter, and that they were indivisible. We now know that even atoms are made up of smaller
Engineering Aspects of Food Irradiation 1 Radioelements, Isotopes & Radionuclides
pieces. In these activities, we will learn how to build atoms from these parts. Atoms have a nucleus and electrons. Only protons and neutrons are in the nucleus.
Nucleus - the core of the atom, containing protons and neutrons is the nucleus.
protons (carry positive charge)
neutrons (carry no charge)
electrons are small (carry a negative charge and circle the nucleus)
Electrons cannot live in the nucleus. ELECTRONS SPIN IN SHELLS around the nucleus. As you know, ELECTRONS are always moving, spinning very quickly around the NUCLEUS. As the electrons spin they can move in any direction, as long as they stay in their shell. Any direction you can imagine; upwards, down- wards, sidewards, electrons can move that way. Scientists use letters to name the orbitals/shells around a nucleus. They use the letters “k, l, m, n, o, p, and q”. The “k”shell is the one closest to the nucleus and “q” is the furthest away.
You know that the nucleus is positive and that electrons are negative. This means that the electrons and the nucleus are attracted to each other. This is how an atom is held together.
Ions: Ions are charged particles, produced when an atom gains or loses one or more electrons. Ionization is likely to occur when an atom has a partially occupied outer electron energy level. Ionization is especially likely if the complete atom has only 1 or 2 electrons in its outermost energy level, or if it is only 1 or 2 electrons away from completing the full occupation of the energy level.
2 Engineering Aspects of Food Irradiation Radioelements, Isotopes & Radionuclides
For example, both hydrogen and sodium have only one electron in their outermost electron level. They are both likely to release the single electron in that ring. This will give the atom an imbalance between the number of electrons and the number of protons. Since they have more protons than electrons, they now have a net positive charge and are considered to be positive ions. [This is shown by placing a plus sign + next to the symbol for the element.]
Chlorine, on the other hand, has 7 electrons in its outermost electron level. Chlorine is likely to 'grab' an extra electron -- assuming one is available-- to become a nega- tively charged ion [symbolized by a negative sign - next to the symbol for the ele- ment.]
The diagram below shows the ionization of a hydrogen atom. In the space below the diagram, show the ionization of sodium and chlorine.
Glossary:
Alpha decay: Alpha decay is one process that unstable atoms can use to try to become more stable. During alpha decay, an atom's nucleus sheds two protons and two neutrons in a little packet that scientists call an alpha particle.
Since an atom loses two protons during alpha decay, it changes from one element to another. For example, after undergoing alpha decay, an atom of Uranium (with 92 protons) becomes an atom of Thorium (with 90 protons).
Engineering Aspects of Food Irradiation 3 Radioelements, Isotopes & Radionuclides
Alpha particle: An alpha particle is a fast moving packet containing two protons and two neutrons (a helium nucleus). Alpha particles carry a charge of +2 and strongly interact with matter. Produced during alpha decay, alpha particles can travel only a few inches through air and can be easily stopped with a sheet of paper.
Atomic number: The atomic number is equal to the number of protons in an atom's nucleus. The atomic number determines which element an atom is. For example, any atom that contains exactly 47 protons in its nucleus is an atom of silver.
4 Engineering Aspects of Food Irradiation Radioelements, Isotopes & Radionuclides
Beta decay: Beta decay is one process that unstable atoms can use to become more stable. There are two types of beta decay, beta-minus and beta-plus.
During beta-minus decay, a neutron in an atom's nucleus turns into a proton, an electron and an antineutrino. The electron and antineutrino fly away from the nucleus, which now has one more proton than it started with. Since an atom gains a proton during beta-minus decay, it changes from one element to another. For exam- ple, after undergoing beta-minus decay, an atom of carbon (with 6 protons) becomes an atom of nitrogen (with 7 protons).
During beta-plus decay, a proton in an atom's nucleus turns into a neutron, a positron and a neutrino. The positron and neutrino fly away from the nucleus, which now has one less proton than it started with. Since an atom loses a proton during beta-plus decay, it changes from one element to another. For example, after undergoing beta-plus decay, an atom of carbon (with 6 protons) becomes an atom of boron (with 5 protons).
Although the numbers of protons and neutrons in an atom's nucleus change during beta decay, the total number of particles (protons + neutrons) remains the same.
Engineering Aspects of Food Irradiation 5 Radioelements, Isotopes & Radionuclides
Beta particles: Ejected from the nucleus during beta decay, a beta particle is a fast moving electron or positron, depending on the type on beta decay involved. Beta particles can travel a few feet through air and can be stopped with a few sheets of aluminum foil.
6 Engineering Aspects of Food Irradiation Radioelements, Isotopes & Radionuclides
Bohr Radius: The size of a ground state hydrogen atom as calculated by Niels Bohr using a mix of classical physics and quantum mechanics. The Bohr Radius is given by the following formula
κ2 × –10 ao ==------0 . 5 2 9 1 0 meters (EQ 1) mke2 where κ = Plank’s constant/2π = 1.055x10-34 Joule-seconds; m = mass of electron = 9.109x10-31 kg; k = Coulomb’s constant = 8.988x109 J-m/C2; and e = electron charge = 1.602x10-19
Cyclotron: A cyclotron is a machine used to accelerate charged particles to high energies. The first cyclotron was built by Ernest Orlando Lawrence and his gradu- ate student, M. Stanley Livingston, at the University of California, Berkley, in the early 1930's.
A cyclotron consists of two D-shaped cavities sandwiched between two electro- magnets. A radioactive source is placed in the center of the cyclotron and the elec- tromagnets are turned on. The radioactive source emits charged particles. It just so happens that a magnetic field can bend the path of a charged particle so, if every- thing is just right, the charged particle will circle around inside the D-shaped cavi- ties. However, this doesn't accelerate the particle. In order to do that, the two D- shaped cavities have to be hooked up to a radio wave generator. This generator gives one cavity a positive charge and the other cavity a negative charge. After a moment, the radio wave generator switches the charges on the cavities. The charges keep switching back and forth as long as the radio wave generator is on. It is this switching of charges that accelerates the particle.
Let's say that we have an alpha particle inside our cyclotron. Alpha particles have a charge of +2, so their paths can bent by magnetic fields. As an alpha particle goes around the cyclotron, it crosses the gap between the two D-shaped cavities. If the charge on the cavity in front of the alpha particle is negative and the charge on the cavity in back of it is positive, the alpha particle is pulled forward (remember that opposite charges attract while like charges repel). This just accelerated the alpha particle! The particle travels through one cavity and again comes to the gap. With luck, the radio wave generator has changed the charges on the cavities in time, so the alpha particle once again sees a negative charge in front of it and a positive charge in back of it and is again pulled forward. As long as the timing is right, the alpha particle will always see a negative charge in front of it and a positive charge
Engineering Aspects of Food Irradiation 7 Radioelements, Isotopes & Radionuclides
in back of it when it crosses the gap between cavities. This is how a cyclotron accelerates particles!
Unfortunately, there's one more thing to worry about. The faster a charged particle moves, the less it is affected by a magnetic field. So, as particles speed up in a cyclotron, they spiral outwards. This makes it easy to get the particles out of the cyclotron, but also puts a limit on the amount of acceleration they can undergo.
Deuterium: Discovered in 1932 by Harold C. Urey, deuterium is a stable isotope of the element hydrogen. An atom of deuterium consists of one proton, one neutron and one electron. About.015% of natural hydrogen is composed of deuterium.
Deuteron: The nucleus of a deuterium atom. A deuteron consists of one proton and one neutron.
8 Engineering Aspects of Food Irradiation Radioelements, Isotopes & Radionuclides
Electrons: Electrons are negatively charged particles that circle the atom's nucleus. Electrons were discovered by J. J. Thomson in 1897.
.
Particle Data
Symbol Mass Lifetime Charge Spin
e-.511 MeV stable -1 1/2
Gluons: Gluons are the particles responsible for binding quarks to each other.
Particle Data
Symbol Mass Lifetime Charge Spin g 0 stable 0 1
Half-life: The half-life describes the amount of time needed for half of a sample of unstable atoms or particles to undergo decay. Thallium-208, for example, decays into lead-208 with a half-life of 3.05 minutes. This means that half of a sample of thallium-208 will decay into lead-208 over the course of 3.05 minutes.
Scientists can not predict when a particular atom or particle will decay. They only know that, on average, half of a sample will decay during the span of one half-life.
Engineering Aspects of Food Irradiation 9 Radioelements, Isotopes & Radionuclides
10 Engineering Aspects of Food Irradiation Radioelements, Isotopes & Radionuclides
Helius: In Greek mythology, Helius was god of the sun. Helius drove his chariot across the sky each day to provide daylight and returned home each night on the river Oceanus in an enormous golden cup to hide the light.
Isotope: Atoms that have the same number of protons but different numbers of neu- trons are called isotopes. The element hydrogen, for example, has three known iso- topes: protium, deuterium and tritium.
Liquid Nitrogen: The liquid state of the element nitrogen. Liquid nitrogen freezes at 63 K (-346°F) and boils at 77.2 K (-320.44°F) under standard atmospheric pressure. The white mist seen in the photograph is fog created by cooling the water vapor present in the air below the dew point.
Engineering Aspects of Food Irradiation 11 Radioelements, Isotopes & Radionuclides
Neutrons: Neutrons are uncharged particles found within atomic nuclei. Neutrons were discovered by James Chadwick in 1932. Experiments done at the Stanford Linear Accelerator Center in the late 1960's and early 1970's showed that neutrons are made from other particles called quarks. Neutrons are made from one 'up' quark and two 'down' quarks.
Particle Data
Symbol Mass Lifetime Charge Spin Quark Content n 939.6 MeV in nuclei: stable 0 1/2 udd free: 15 min
Positron: The antimatter counterpart of the electron, positrons were discovered in 1932 by Carl Anderson while observing cosmic ray showers.
12 Engineering Aspects of Food Irradiation Radioelements, Isotopes & Radionuclides
Particle Data
Symbol Mass Lifetime Charge Spin
e+ .511 MeV stable +1 1/2
Protons: Protons are positively charged particles found within atomic nuclei. Pro- tons were discovered by Ernest Rutherford in experiments conducted between the years 1911 and 1919. Experiments done at the Stanford Linear Accelerator Center in the late 1960's and early 1970's showed that protons are made from other parti- cles called quarks. Protons are made from two 'up' quarks and one 'down' quark.
Particle Data
Symbol Mass Lifetime Charge Spin Quark Content p 938.3 MeV > 1032 years +1 1/2 udd
Positrom: The antimatter counterpart of the electron, positrons were discovered in 1932 by Carl Anderson while observing cosmic ray showers.
Engineering Aspects of Food Irradiation 13 Radioelements, Isotopes & Radionuclides
Particle Data
Symbol Mass Lifetime Charge Spin
e+.511 MeV stable +1 1/2
Quarks: Quarks are believed to be one of the basic building blocks of matter. Quarks were first discovered in experiments done at the Stanford Linear Accelera- tor Center in the late 1960's and early 1970's.
Three families of quarks are known to exist. Each family contains two quarks. The first family consists of Up and Down quarks, the quarks that join together to form protons and neutrons. The second family consists of Strange and Charm quarks and only exist at high energies. The third family consists of Top and Bottom quarks and only exist at very high energies. The Top quark was finally discovered in 1995 at the Fermi National Accelerator Laboratory.
TABLE 1. Particle Data
Name Symbol Mass Charge Spin Up u 3 MeV +2/3 1/2 Down d 6 MeV -1/3 1/2 Charm c 1300 MeV +2/3 1/2 Strange s 100 MeV -1/3 1/2 Top t 175000 MeV +2/3 1/2 Bottom b 4300 MeV -1/3 1/2
Tritium: Discovered in 1934, tritium is an unstable isotope of the element hydro- gen. An atom of tritium consists of one proton, two neutrons and one electron. Tri- tium is radioactive and has a half-life of about 12.5 years.
14 Engineering Aspects of Food Irradiation Radioelements, Isotopes & Radionuclides
Bremsstrahlung (‘braking radiation’): continuous X-rays. X-rays are produced when a beam of electrons strikes a target. The electrons lose most of their energy in collisions with atomic electrons in the target, causing ionization and excitation of atoms. In addition, they can be sharply deflected in the vicinity of the atomic nuclei, thereby losing energy by irradiation X-ray photons. A single electron can emit X-ray photon having any energy up to its own kinetic energy. As a result, a monoenergetic beam of electrons produces a continuous spectrum of X-rays with photons energies up to the value of the beam energy. The continuous X-rays are also called Bremsstrahlung or ‘braking radiation’.
Engineering Aspects of Food Irradiation 15 Radioelements, Isotopes & Radionuclides
Symbol Element Atomic # Symbol Element Atomic # Ac Actinium 89 Md Mendelevium 101 Al Alum i num 13 Hg M ercury 80 Am Am ericium 95 Mo Molybdenum 42 Sb Antim ony 51 Ns Neilsborium 107 Ar Argon 18 Nd Neodym ium 60 As Arsenic 33 Ne Neon 10 At Astatine 85 Np Neptuni um 93 Ba Barium 56 Ni Nickel 28 Bk Berkelium 97 Nb Niobium 41 Be Beryllium 4 N Nitrogen 7 Bi Bism uth83NoNobelium 102 BBoron 5 5 Os Osm ian 76 Br Brom ine 35 O O xy gen 8 Cd Cadm ium 48 Pd Palladium 46 Ca Calci um 20 P P hosporus 15 Cf Californium 98 Pt Plati num 78 CCarbon 6 P u P lutoni um 94 Ce Cerium 58 Po Poloni um 84 Cs Cesi um 55 KP otassium 19 Cl Chlorine 24 Pr Praseodym ium 59 Cr Chrom i um 17 P m P rom ethium 61 Co Cobalt 27 Pa P rotactinium 91 Cu Copper 29 Ra Radium 88 Cm Curium 96 Rn Radon 86 Dy Dysprosi um 66 Re R heni um 75 Es Einstei ni um 99 Rh R hodi um 45 Er Erbium 68 Rb Rubidium 37 Eu Europi um 63 R u R utheni um 44 Fm Ferm ium 100 Rf Rutherfordium 104 FFlourine 9 Sm Sam arium 62 Fr Francium 87 Sc S candium 21 Gd Gadolinium 64 Sg Seaborgium 106 Ga Gallium 31 Se Selenium 34 Ge Germ anium 32 S i S i li con 14 Au Gold 79 Ag S ilver 47 Hf Hafni um 72 Na S odium 11 Ha Hahni um 105 S r S trontium 38 Hs Hassi um 108 S S ulfur 16 Hi Helium 2 Ta Tantalum 73 Ho Holm ium 67 Tc Technetium 43 HHydrogen 1 Te Tellurium 52 In Indium 49 Tb Terbium 65 I Iodine 53 Tl Thalium 81 Ir Iridium 77 Th Thorium 90 Fe Iron 26 Tm Thulium 69 Kr Krypton 36 Sn Tin 50 La Lanthanum 57 Ti Ti tanium 22 Lr Lawrencium 103 W Tungsten 74 Pb Lead 82 82 U Uranium 92 Li Lithi um 3 V V anadi um 23 Lu Luteti um 71 Xi Xenon 54 Mg Magnesium 12 Yb Ytterbium 70 Mn Manganese 25 Yb Yttrium 39 Mt Meitneri um 109 Zn Zi nc 30 Zr Zi rconi un 40
16 Engineering Aspects of Food Irradiation Radioelements, Isotopes & Radionuclides
Engineering Aspects of Food Irradiation 17 Radioelements, Isotopes & Radionuclides
Atomic Nature of Matter
Gay-Lussac law of combining volumes of gases: the volumes of gases that enter into chemical combination with one another are in the ratio of simple whole num- bers when all volumes are measured under the same conditions of pressure and temperature.
Avogadro hypothesis: equal volumes of any gases at the same T and P contain the same number of molecules. The molecules of some gaseous elements could be comprised of two or more atoms of that element.
23 Avogadro Number: N0 = 6.023x10
A gram atomic weight of any element contains Avogadro’s number of atoms. A gram molecular weight of any gas also contains N0 molecules and occupies a vol- ume of 22.4136 L at standard T and P (0C = 273 K and 760 torr = 760 mm Hg). The modern scale of atomic and molecular weights is set by stipulating that a gram atomic weight of the carbon isotope, 12C, is exactly 12.000...g. A periodic chart, showing atomic numbers, atomic weights, densities, and other information about chemical elements, is shown on the appendix.
Example 1:
How many gram of oxygen combine with 2.3 g of carbon in the reaction:
→ CO+ 2 CO2 ?
How many molecules of CO2 are thus formed? How many liters of CO2 are formed at 20oC and 752 torr?
Answer:
In the given reaction, 1 atom of carbon combines with one molecule (2 atoms) of oxygen. From the atomic weights given in the periodic chart, it follows that 12.011 g of carbon reacts with 2× 15.9994 = 31.9988g of oxygen. Rounding of the 3 sig- nificant figures, letting y represent the number of grams of oxygen asked for, and taking simple proportions, we have:
18 Engineering Aspects of Food Irradiation Radioelements, Isotopes & Radionuclides
2.3 y ==------× 32.0 6.13g (EQ 2) 12.0
The number N of molecules of CO2 formed is equal to the number of atoms in 2.3 g of C, which is 2.3/12.0 times Avogadro’s number:
2.3 23 23 N ==------× 6.02× 10 1.15× 10 (EQ 3) 12.0
Since Avogadro’s number of molecules occupies 22.4 L at STP, the volume of CO2 at STP is:
× 23 1.15 10 × VCO ==------22.4 4.28L (EQ 4) 2 6.02× 1023
At the given higher temperature of 20oC = 293K, the volume is larger by the ratio of the absolute temperatures, 293/273; the volume is also increased by the ratio of o the pressures, 760/752. Therefore, the volume of CO2 made from 2.3 g of C at 20 C and 752 torr is:
293 760 V ==4.28 ------4.64L (EQ 5) 20()C, 752T 273 752
This would also be the volume of oxygen consumed in the reaction under the same conditions of temperature and pressure, since 1 molecule of oxygen is used to form 1 molecule of carbon dioxide.
All forms of matter emit radiation. For gases and semitransparent solids, such as glass and salt crystals at elevated temperatures, emission is a volumetric phenome- non. That is, radiation emerging from a finite volume of matter is the integrated effect of local emission throughout the volume. In most solids and liquids, radiation emitted from interior molecules is strongly absorbed by adjoining molecules. Accordingly, radiation that is emitted from a solid or a liquid originates from mole- cules that are within a distance approximate 1 µm from the exposed surface.
We know that radiation originates due to emission by matter and that its subsequent transport does not require the presence of any matter. But what is the nature of this transport? One theory views radiation as the propagation of a collection of particles termed photons or quanta. Alternatively, radiation may be viewed as the propaga-
Engineering Aspects of Food Irradiation 19 Radioelements, Isotopes & Radionuclides
tion of electromagnetic waves. In any case we wish to attribute to radiation the stan- dard wave properties of frequency ν and wave length λ. For radiation propagating in a particular medium, the 2 properties are related by:
c λ = --- (EQ 6) ν
where c is the speed of light in the medium. For propagation in a vacuum, co = 2.998x108 m/s. The unit of wavelength is micrometer (µm) where 1 µm = 10-6m.
The complete electromagnetic spectrum is delineated in Figure 1. The short wave- length gamma rays, X-rays, and ultraviolet (UV) radiation are primarily of interest to the high-energy physicist and the nuclear engineer, while the long wavelength microwaves and radio waves are of concern of electrical engineer.
Figure 1: Spectrum of electromagnetic radiation
visible blue red violet yellow green
X-rays microwave ultraviolet
thermal radiation gamma rays
− − − − − 105 10 4 10 3 10 2 10 1 1 10 102 103 104 λ (µm)
Figure 2 shows the lines in the visible and near-ultraviolet spectrum of atomic hydrogen. The wavelength of visible light is between about 4000 C (violet) and 7500 C (red). In 1885 Balmer published an empirical formula that gives these
20 Engineering Aspects of Food Irradiation Radioelements, Isotopes & Radionuclides
observed wavelength, λ, in the hydrogen spectrum. His formula is equivalent to the following:
1 1 1 --- = R ----- – ----- (EQ 7) λ H2 2 2 n
Figure 2: Balmer series of lines in the spectrum of atomic hydrogen
3647 A series limit
n=3 n=4 5 6 7...
• • • • • 8000A 7000A 6000A 5000A 4000A
Red Yellow Green Blue Violet Ultraviolot
where RH = 109,678 1/cm is called the Rydberg constant for hydrogen and n = 3,4,5,... represents any integer greater than 2. When n = 3, Eq(7) gives λ = 6562 C; when n = 4, λ =4861 C; and so on. The series of lines, which continue to get closer together as n increases, converges to the limit λ = 3647 C in the ultraviolet as n → ∞ . Other series exist for hydrogen that can be described by replacing the 22 in Eq(7) by the square of other integers. These other series lie entirely in the ultravio- let or infrared portions of the electromagnetic spectrum.
Engineering Aspects of Food Irradiation 21 Radioelements, Isotopes & Radionuclides
The nucleus
The nucleus of an atomic number Z and mass number A (atomic weight) consists of Z protons and N = A-Z neutrons. The atomic masses of all individual atoms are nearly integers, and A gives the total number of nucleons (i.e. protons and neutrons) in the nucleus. A species of atom, characterized by its nuclear constitution - its val- ues of Z and A (or N) - is called nuclide.It is conveniently designated by writing the appropriate chemical symbol with a subscript giving Z and superscript given A. For example:
1 2 238 1H;1H; an d92 U
are nuclides. Nuclides of an element that have different A (or N) are called isotopes (in the same place). Nuclides having the same number of neurons are called iso- tones, e.g.:
206 204 ; 82Pb; an d80 H g
are isotones with N = 124.Hydrogen has three isotopes:
1 2 3 1H; 1H; 1H
2 3 all of which occur naturally. Deuterium, 1H , is stable; tritium, 1H , is radioactive. 19 Fluorine has only a single naturally occurring isotope, 9F ; all of its other isotopes are man made, radioactive, and short lived. The measured atomic weights of the elements reflect the relative abundance of isotopes found in nature, as for example.
Example 2:
35 Chlorine is found to have two naturally occurring isotopes, 17Cl , which is 76% 37 abundant, and 17Cl , 24% abundant. The atomic weights of the two isotopes are 34.97 and 36.97. Show that this isotopic composition accounts for the observed atomic weight of the element.
Answer:
22 Engineering Aspects of Food Irradiation Radioelements, Isotopes & Radionuclides
Taking the weighted average of the atomic weights of the two isotopes, we find for the atomic weight of Cl:
0.76× 34.97+ 0.24× 36.97 = 35.45 as observed.
The various kinds of atoms differing from each other by their atomic number or by their mass are called nuclides. The correct name of unstable (radioactive) nuclides is radionuclides, and the terms radioelements for unstable elements and radionu- clides for unstable nuclides are analogous. For identification, the symbol (or the 14 atomic number) and the mass number are used. For example, 6C is carbon with the mass number 14 and atomic number 6. The atomic number can be omitted because it is known by the symbol. 14C can also be written as C-14. For complete information, the kind and the energy of transmutation and the half-life may be also indicated:
14 14 Cβ()0.156MeV → N (EQ 8)
About 2800 nuclides are known. About 340 of these are found in nature and may be subdivided into four groups: (1) 258 are stable, (2) for 25 nuclides with atomic number Z < 80 radioactive decay has been reported, but not confirmed for 7 of these. Many exhibit extremely long half-lives (9 nuclides > 1016 years and 4 nuclides > 1020 years), and radioactivity has not been proved ambiguously. (3) Main sources of natural radioactivity comprising 46 nuclides are U-238, U-235 and Th-232 and their radioactive decay products. (4) Several radionuclides are continu- ously produced by the impact of cosmic radiation, and the main representatives of this group are C-14, Be-10, Be-7 and H-3. Radionuclides present in nature in extremely low concentration, such as Pu-244 and its decay products or products of expontaneous fission of U and Th, are not considered in this list. Radionuclides existing from the beginning, i.e., since the genesis of the elements, are called pri- mordial radionuclides. They comprise the radionuclides of group (2) and U-238, U- 235, Th-232 and Pu-244.
The following groups of nuclides can be distinguished: • Isotopes: Z = P equal • Isotones: N = A - Z equal
Engineering Aspects of Food Irradiation 23 Radioelements, Isotopes & Radionuclides
• Isobars: A = N + Z equal • Isodiaspheres: A - 2Z = N - Z equal
For certain nuclides, different physical properties (half-lives, mode of decay) are observed. They are due to different energetic states, the ground state and one or more metastable excited states of the same nuclide. These different states are called isomers or nuclear isomers. Because of the transition from the metastable excited states to the ground states is “forbidden”, they have their own half-lives, which vary between some milliseconds and many years. The excited states (isomers) either change in the ground state by emission of a γ-ray photon (isometric transition; IT) or transmutation to other nuclides by emission of α or β particles. Metastable excited states (isomers) are characterized by the suffix m behind the mass number A, for instance Co-60m and Co-60 or Ru-103m and Ru-103. Sometimes the ground state is indicated by the suffix g. About 400 nuclides are known to exist in metasta- ble states.
By comparison of the number of protons P and the number of neutrons N in stable nuclei, it is found that for light elements (small Z) N = P. With increasing atomic number Z, however, an increasing excess of neutrons is necessary to give stable nuclei. A - 2Z is a measure of the neutron excess. For He-4 the neutrons excess is zero. It is 3 for Sc-45, 11 for Y-89, 25 for La-139, and 43 for Bi-209. Thus, if in the chart of the nuclides the stable nuclides are connected by a mean line, this line starts from the origin with a slope of 1 and is bent smoothly towards the abscissa. This mean line is called the line of β stability.
Nuclides Stability and Transmutation
On the basis of the proton-neutron model of atomic nuclei the following combina- tions amy be distinguished: • P even, N eve (even-even nuclei) - very common, 158 nuclei • P even, N odd (eve-odd nuclei) - common, 53 nuclei • P odd, N even (odd-even nuclei) - common, 50 nuclei • P odd, N odd (odd-odd nuclei) - rare, only 6 nuclei (H-2, Li-6, B-10, N-14, V- 50, Ta-180)
This unequal distribution does not correspond to statistics. The high abundance of even-even nuclei indicates the high stability of this combination. On the other hand,
24 Engineering Aspects of Food Irradiation Radioelements, Isotopes & Radionuclides
odd-odd nuclei seem to be exceptions. Four of the stable odd-odd nuclei are very light.
Alpha activity is preferably found for heavier elements, Z = P > 83 (Bi). Elements with even atomic numbers exhibit mainly β activity or electron capture. In the case of β decay or electron capture, the mass number A remains constant. Either a neu- tron is changed into a proton or a proton into a neutron. Thus, odd-odd nuclei are transformed into even-even nuclei - for instance, K-40 into Ar-40 or into Ca-40.
In finding nuclides of natural radioactivity, the Mattach rule proved to be very help- ful. It states that stable neighboring isobars do not exist (exceptions: A = 50, 180). In the following sequences of isobars, the middle one is radioactive: • Ar-40 K-40 Ca-40 • Ba-138 La-138 Ce-138 • Y-176 Lu-176 Hf-176
Detailed study of the chart of nuclides makes evident that for certain values of P and N a relatively large number of stable nuclides exist. These numbers are 2, 8, 20, 28, 50, 82 (126, only for N). The preference of these “magic numbers” is explained by the shell structure of the atomic nuclei (shell mode). It is assumed that in the nuclei the energy levels of protons and neutrons are arranged into shells, similar to the energy levels of electrons in the atoms. Magic proton numbers correspond to filled proton shells and magic neutron numbers to filled neutron shells. Because in the shell model each nucleon is considered to be an independent particle, this model is often called the independent particle model.
Nuclei Binding Energies
The high stability of closed shells (magic numbers) is also evident from the binding energies of the nucleons. Just below each magic number the binding energy of an additional proton or neutron is exceptionally high, and just above each magic num- ber it is exceptionally low, similar to the binding energies of an additional electron by a halogen atom or a noble gas atom, respectively.
Not all properties of the nuclei can be explained by the shell model. For calculation of binding energies and the description of nuclear reaction, in particular nuclear fis- sion, the drop model of the nucleus has been used successful. The model assumes that the nucleus behaves like a drop of a liquid, in which the nucleons correspond to
Engineering Aspects of Food Irradiation 25 Radioelements, Isotopes & Radionuclides
the molecules. Characteristic properties of such drop are cohesive forces, surface tension, and tendency to split if the drop becomes too big.
To calculate the binding energy (EB) of the nuclei, the semi-empirical equation is used:
EB = Ev ++Ec EF ++Es Eg (EQ 9)
The most important contribution is the volume energy:
Ev = avA (EQ 10)
where av is a constant = 14.1 MeV and A is the mass number. The mutual repulsion of the protons is taken into account by the Coulomb term Ec:
ZZ()– 1 E = –a ------(EQ 11) c c A
1/3 where ac is a constant = 0.585 MeV and Z the atomic number. A is a measure of the radius of the nucleus and therefore also the distance between the protons. With increasing surface energy a drop of water becomes more and more unsta- ble.Accordingly, in the drop model of the nucleus a surface energy term EF is sub- tracted:
23⁄ EF = –aFA (EQ 12)
2/3 where aF is a constant = 13.1 MeV and A is a measure fro the surface. Neutrons are necessary to build up stable nuclei. But the excess of neutrons diminishes the total energy of the nucleus. This contribution is called the symmetric energy Es:
()A – 2Z 2 E = –a ------(EQ 13) s s A
where as is a constant = 19.4 MeV. The relatively high stability of even-even nuclei is taken into account by a positive contribution of the total binding energy EB of the nuclei, and the relatively low stability of odd-odd nuclei by a negative contribution. The following values are taken for this odd-even energy:
26 Engineering Aspects of Food Irradiation Radioelements, Isotopes & Radionuclides
δ()…AZ, even– even E = … , (EQ 14) g 0 even– odd odd– even – δ()…AZ, ood – odd
δ The value of is equal to ag/A, where ag is a constant = 33 MeV.
EB plotted as function of Z will give parabolas, one parabola for odd mass numbers ) δ A (Eg = 0 and two parabolas for even mass numbers A (Eg = + ).
Figure 3: Binding energy with odd mass numbers.