radioelements, isotopes & radionuclides

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 AtomMatter 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

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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.

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.

protons (carry positive charge)

electrons are small (carry a negative

neutrons (carry no charge)

charge and circle the nucleus)

Engineering Aspects of Food Irradiation


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).



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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.



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.



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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.



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

(EQ 1)

where κ = Plank’s constant/2 = 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

aoκ2

mke2------------ 0.529 10 10–× meters= =

π



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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.



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


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.



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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.



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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.



Particle Data


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.



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Particle Data


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.

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.

TABLE 1. Particle Data

Name Symbol Mass Charge SpinUp 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



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’.



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S y m b o l E le m e n t A to m ic # S y m b o l E l e m e n t A to m ic #Ac Actinium 89 Md Mendelevium 101Al Aluminum 13 Hg Mercury 80Am Americium 95 Mo Molybdenum 42Sb Antimony 51 Ns Neilsborium 107Ar Argon 18 Nd Neodymium 60As Arsenic 33 Ne Neon 10At Astatine 85 Np Neptunium 93Ba Barium 56 Ni Nickel 28Bk Berkelium 97 Nb Niobium 41Be Beryllium 4 N Nitrogen 7Bi Bismuth 83 No Nobelium 102B Boron 5 5 Os Osmian 76Br Bromine 35 O Oxygen 8Cd Cadmium 48 Pd Palladium 46Ca Calcium 20 P Phosporus 15Cf Californium 98 Pt Platinum 78C Carbon 6 Pu Plutonium 94Ce Cerium 58 Po Polonium 84Cs Cesium 55 K Potassium 19Cl Chlorine 24 Pr Praseodymium 59Cr Chromium 17 Pm Promethium 61Co Cobalt 27 Pa Protactinium 91Cu Copper 29 Ra Radium 88Cm Curium 96 Rn Radon 86Dy Dysprosium 66 Re Rhenium 75Es Einsteinium 99 Rh Rhodium 45Er Erbium 68 Rb Rubidium 37Eu Europium 63 Ru Ruthenium 44Fm Fermium 100 Rf Rutherfordium 104F Flourine 9 Sm Samarium 62Fr Francium 87 Sc Scandium 21Gd Gadolinium 64 Sg Seaborgium 106Ga Gallium 31 Se Selenium 34Ge Germanium 32 Si Silicon 14Au Gold 79 Ag Silver 47Hf Hafnium 72 Na Sodium 11Ha Hahnium 105 Sr Strontium 38Hs Hassium 108 S Sulfur 16Hi Helium 2 Ta Tantalum 73Ho Holmium 67 Tc Technetium 43H Hydrogen 1 Te Tellurium 52In Indium 49 Tb Terbium 65I Iodine 53 Tl Thalium 81Ir Iridium 77 Th Thorium 90Fe Iron 26 Tm Thulium 69Kr Krypton 36 Sn Tin 50La Lanthanum 57 Ti Titanium 22Lr Lawrencium 103 W Tungsten 74Pb Lead 82 82 U Uranium 92Li Lithium 3 V Vanadium 23Lu Lutetium 71 Xi Xenon 54Mg Magnesium 12 Yb Ytterbium 70Mn Manganese 25 Yb Yttrium 39Mt Meitnerium 109 Zn Zinc 30

Zr Zirconiun 40



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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.

Avogadro Number: N0 = 6.023x1023

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:

?

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 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:

C O2 CO2→+

2 15.9994× 31.9988g=



(EQ 2)

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:

(EQ 3)

Since Avogadro’s number of molecules occupies 22.4 L at STP, the volume of CO2 at STP is:

(EQ 4)

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 the pressures, 760/752. Therefore, the volume of CO2 made from 2.3 g of C at 20oC and 752 torr is:

(EQ 5)

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-

y 2.312.0----------

32.0× 6.13g= =

N 2.312.0---------- 6.02 1023×× 1.15 1023×= =

VCO2

1.15 1023×6.02 1023×---------------------------

22.4× 4.28L= =

V20 C 752T,( ) 4.28 293273---------

760752---------

4.64L= =



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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:

(EQ 6)

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

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

λ cν---=

510− 210110−210−310−410− 1 310 41010

gamma rays

X-raysultraviolet

infrared

thermal radiation

microwave

visible

violet

blue

gree

nye

llow

red

λ (µm)



observed wavelength, λ, in the hydrogen spectrum. His formula is equivalent to the following:

(EQ 7)

Figure 2: Balmer series of lines in the spectrum of atomic hydrogen

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

. 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.

1λ--- RH

122----- 1

n2-----–

=

•A8000

•A7000

•A6000

•A5000

•A4000

n=3 n=4 5 6 7...

3647 Aserieslimit

Red Yellow Green BlueViolet

Ultraviolot

n ∞→



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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:

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.:

are isotones with N = 124.Hydrogen has three isotopes:

all of which occur naturally. Deuterium, , is stable; tritium, , is radioactive.

Fluorine has only a single naturally occurring isotope, ; 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:

Chlorine is found to have two naturally occurring isotopes, , which is 76%

abundant, and , 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:

H11 H2

1 and U23892;;

Pb20682 and Hg204

80;;

H11 H2

1 H31;;

H21 H3

1

F199

Cl3517

Cl3717



Taking the weighted average of the atomic weights of the two isotopes, we find for the atomic weight of Cl:

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

atomic number) and the mass number are used. For example, is carbon with the mass number 14 and atomic number 6. The atomic number can be omitted

because it is known by the symbol. 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:

(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

0.76 34.97 0.24 36.97×+× 35.45=

C146

C14

Cβ 0.156MeV( ) N14→14



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• 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 TransmutationOn 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,



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 EnergiesThe 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



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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:

(EQ 9)

The most important contribution is the volume energy:

(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:

(EQ 11)

where ac is a constant = 0.585 MeV and Z the atomic number. A1/3 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:

(EQ 12)

where aF is a constant = 13.1 MeV and A2/3 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:

(EQ 13)

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:

EB Ev Ec EF Es Eg+ + + +=

Ev avA=

Ec acZ Z 1–( )

A--------------------–=

EF aFA2 3⁄–=

Es asA 2Z–( )

A---------------------

2–=



(EQ 14)

The value of δ 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 A (Eg = 0) and two parabolas for even mass numbers A (Eg = +δ).

Figure 3: Binding energy with odd mass numbers.

Eg

δ A Z,( )…even even–0…even odd odd even–,–

δ A Z,( )…ood– odd–

=

��

Z

Bind

ing

Ener

gy E

B[M

eV]



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Nuclide MassesThe mass number A is equal to the number of nucleons, A = P + N, and is always an integer. The nuclide mass M, on the other hand, is the exact mass of the nuclides in universal atomic mass units u, and the atomic mass is the mean of the nuclide masses of the stable nuclides in their natural abundance.

The basis of the atomic mass unit u is the mass of the carbon isotope C-12: M(C-12) = 12.000000. Nuclide masses and atomic masses include the mass of the elec-trons of the neutral atom: M = mass of the nucleus +Zme, where me the mass of one

electron in atomic mass units u. One atomic mass unit is 1.660566 x 10-24g (1/N0 =

1/6.03x1023).

The mass m of particles traveling with very high velocities increases as the velocity approaches the velocity of light c:

(EQ 15)

where m0 is the mass of the particle at rest and v its velocity. Eq(15) was derived by Eistein in his theory of relativity. Another result of this theory is the equivalence of mass and energy:

(EQ 16)

Since 1 u = 1.660566x10-24 g and c = 2.997925x10-8 m/s, 1 u is equivalent to 1.49244x10-10 J. The energy units mainly used in nuclear science are eV, (the energy gained by an electron passing in vacuum a potential of 1 V; 1 eV = 1.60219x10-19 J), keV and MeV. So,

1 u = 931.5 MeV

On the basis of the proton-neutron model of atomic nuclei, the following equation can be written for the mass of a nuclide:

(EQ 17)

mm0

1 v c⁄( )2–-----------------------------=

E mc2=

M ZMH NMn δM–+=



where MH is the nuclide mass of H-1 and comprises the mass of one proton as well as that of one electron. Mn is the mass of the neutron in atomic mass units, and δM is the mass effect. It is due to the fact that the binding energy EB of the nucleons according to Eq(16) results in a decrease in the mass compared with the sum of the masses of the individual particles. The effect of the binding energy of the electrons is very small with respect to the binding energy of the nucleons and can be neglected.

Application of Eq(16) gives:

(EQ 18)

If EB is divided by A, the mean binding energy per nucleon is obtained, which is a measure of the stability of the nucleus:

(EQ 19)

Physical Properties of Nuclei

Diameter

The diameters of atoms vary between about 0.8x10-10 and 3.0x10-10 m and the diameters of nuclei are in the range of about 0.3x10-14 to 1.6x10-14 m. The radius of an atomic nucleus can be described by the equation:

(EQ 20)

where r0 = 1.33 fm (femtometers) (1 fm = 10-15 m) is a constant and A the mass number.

δMEB

c2------ ZMH NMn M–+= =

EBA------ c2

A---- ZMH NMn M–+( )=

rN r0A1 3⁄=



30

Density

The charge distribution (distribution of the protons) is practically constant in the interior of the nucleus and decreases near its surface, as shown in Figure 4.

Figure 4: Charge distribution in nuclei (c= half-density radius; d = skin thick-ness)

The layer of decreasing density is about 2.5 fm, independently of the atomic num-ber. The distribution of the neutrons is assumed to be approximately the same as that of the protons. Then the mass distribution in the nucleus is also the same as the charge distribution. The density of nuclear matter is the interior of the nuclei is given by:

(EQ 21)

Radius, R

Rel

ativ

e ch

arge

den

sity

1.0

00

c

d

0.5

ρ A43---πrN

3N0

--------------------- 143---r0

3N0

----------------- 2 1014 gcm3---------×≈= =



Nuclear ForcesStrong Interaction: The nucleon-nucleon interaction becomes effective only at distance less than 2.4 fm. The interaction is very strong, resulting in a high negative potential of about 50 MeV and a very small equilibrium distance of about 0.6 fm.

The Coulomb repulsion energy Ec between two protons is given by:

(EQ 22)

where e is the electric charge of a proton, ε0 the electric field constant, and r the dis-tance apart within the nucleus. Since r = 3 fm, Ec is about 0.5 MeV. The repulsion energy is small compared with the mean binding energy of about 8 MeV. For a greater number of protons the total repulsion energy increases according to:

(EQ 23)

where r is the effective distance between the protons, which can be set equal to the radius of the nucleus. Whereas the nuclear forces strive for saturation, the Coulomb repulsion energy between protons increases continuously with the atomic number Z, causing the instability of heavy nuclei with high atomic numbers.

Weak Interaction: Nuclear forces are due to the strong interaction between nucle-ons. Besides the strong interaction, weak interaction and electromagnetic interac-tion are important for nuclei and elementary particles. Weak interaction also has a limited range, of the order of some femtometers. It is responsible for β-decay pro-cesses.

Electromagnetic Interaction: Electromagnetic interaction is observed for all parti-cles carrying electromagnetic field (charged particles such as protons and neutral particles with a magnetic momentum such as neutrons). Electromagnetic interac-tion is also responsible for chemical bonding. As weak and electromagnetic interac-tions have some common features, they are assumed to have a common origin.

Gravitation Interaction: The fourth kind of interaction is gravitation, the range of which is extremely large. Gravitation is responsible for gravity and the motion of the planets. The four fundamental types of interaction are summarized in Table 2.According to quantum theory, virtual mediating particles are responsible for the

Ece2

4πε0r--------------=

Ec35---Z Z 1–( ) e2

4πε0r--------------=



32

interactions, e.g. exchange of gluons for strong interaction and exchange of photons for electromagnetic interaction.

Nuclear MomentumThe hyperfine structure of atomic spectra that is observed under the influence of an external magnetic field is due to the interaction of electrons and nuclei. This hyper-fine structure may be caused by: (a) different masses of the atoms (if the element contains two or more isotopes) which represents an isotope effect and/or (b) the interaction of the magnetic momenta of the lectrons and the nuclei (if the latter have an angular momentum) which proof the existence of a nuclear angular momentum.

The nuclear angular momentum is measure in units of κ/2π, as well as the angular momentum of an electron, a proton or a neutron, which is 1/2 κ/2π, for each of these particles. It is a vector of magnitude

where I is the quantum number of the nuclear angular momentum, called the nuclear spin. Nuclei with even mass numbers A have integral nuclear spins, I = 0, 1, 2,., whereas nuclei with odd numbers have half-numbered nuclear spins, I = 1/2, 3/2, 5/2,... Even-even nuclei in the ground state always have I = 0. Odd-odd nuclei have an integral spin, in most cases I = 0.; and even-odd and odd-even nuclei have half-numbered spins varying between I = 1/2 and I = 11/2. It is assumed that pro-tons and neutrons compensate their spins in pairs. The main contribution to the nuclear spins come from the last unpaired nucleon.

TABLE 2. The four fundamental types of interactions

Type of Interaction Mediating particle Relative force constantStrong Gluon 1

Electromagnetic Photon 10-2

Weak Boson (Z, W-,W+) 10-5

Gravitation Graviton 10-40

I I 1+( ) κ2π------



The nuclear angular momentum originates from the individual angular momenta of the nucleons, which have two contributions, spin angular momenta and orbital angular momenta, which are due to the spin and orbital motions, respectively, of the

nuclei. The spin angular momenta of the nucleons as well as their orbital angular

momenta are vectors. With respect to the interaction of particles in a system, two cases may be distinguished:

• The interaction of the individual and of each particle is strong compared with the interaction between the particles, i.e., the spin-orbital coupling is strong. The resulting angular momentum of each particle is calculated according to the rules of vector addition:

(EQ 24)

and the angular momenta of the system is given by:

(EQ 25)

where is the angular momentum. This kind of coupling is called jj coupling.

• The interaction of the individuals and of each particle is weak compared with the interaction between the particles; i.e., the spin-orbital coupling is weak. Then the resultant spin angular momentum and the resultant orbital angular momentum are calculated first:

(EQ 26)

and the angular momentum of the system is given by:

(EQ 27)

This kind of coupling is called LS or Russel-Saunders coupling.

The jj coupling holds for the nucleons in nuclei and for electrons of heavy atoms, LS coupling for the lectrons of light and medium-heavy atoms. The term “nuclear spin” is correct for the spin momentum of a single nucleon, but is commonly used

si

Ii

si Ii

ji si Ii+=

Ii Σji=

ji

si Ii

S Σsi…and…L Σli= =

I S L+=



34

for the quantum number for the resultant angular momentum of a nucleus consist-ing of two or more nucleons.

The law of conservation of momentum is also valid for nuclear angular momenta.

Magnetic momentum: Rotation of a charged particle causes a magnetic momen-tum (dipole momentum). The magnetic momentum of an electron is:

(EQ 28)

where µ0 is the magnetic field constant, e the electrical elementary unit, and me the mass of an electron µB is called the Bohr magneton. The magnetic momentum of the nucleus is much smaller:

(EQ 29)

where mp is the mass of protons and µN is called the nuclear magneton. The mag-netic momentum of the proton is much greater than the calculated value (+2.7926 µB, parallel to the spin). The neutron has also a magnetic momentum (-1.9135 µN, antiparallel to the spin). the se values are explained by the inner structure of the proton and neutron. the magnetic momentum of a nucleus is also a vector:

(EQ 30)

where gI is the nuclear g factor. From Eq(30) you can see that all nuclei with nuclear spin I = 0 (even-even nuclei) have no magnetic momentum.

If the magnetic momentum of a nucleus is not zero, the nucleus performs a preces-sion with frequency ν0 (Larmor frequency) under the influence of an outer mag-netic field:

(EQ 31)

where B0 is the magnetic flux density. For B0 = 1 tesla, ν0 is 42.6x10-6 1/s, which is in the region of radiofrequencies. the nucleus may adopt 2I + 1 energy levels from each other by:

µBµ0eκ4πme------------- 1.1653 10 29–× Vsm= =

µNµ0eκ4πmp------------- 6.3466 10 33–× Vsm= =

µI gIIµN=

ν0gIµN

κ-----------B0=



(EQ 32)

By absorption or emission of photons of frequency:

(EQ 33)

which is identical to the Larmor frequency, the nucleus can pass from a certain energy level to a neighboring level. This process is known as nuclear magnetic res-onance (NMR).

Quadrupole momentum: many nuclei also have an electrical quadrupole momen-tum, which is a measure of the deviation of charge distribution from spherical sym-metry. the electrical quadrupole momentum is:

(EQ 34)

where a and b are the radii of an ellipsoid of revolution along the axis of symmetry and perpendicular to it, respectively, r is the mean radius, ∆r = a - b, and ∆r/r is a measure of the deformation. Q may be positive (a>b) or negative (a<b). Nuclides with I = 0 or 1/2 do not have an electrical quadrupole momentum; that means their nuclei have spherical symmetry.

∆E κν gIµNB0= =

νgIµN

κ-----------B0=

Q 25---Z a2 b2–( ) 4

5---Zr2∆r

r------= =



36

APPENDIX



RADIATION AND RADIOACTIVITY

Radiation is energy traveling in the form of particles or waves in bundles of energy called photons. Some everyday examples are microwaves used to cook food, radio waves for radio and television, light, and x-rays used in medicine.

Demonstration with Chart of Electromagnetic Spectrum

Radioactivity is a natural and spontaneous process by which the unstable atoms of an element emit or radiate excess energy in the form of particles or waves. These emissions are collectively called ionizing radiations. Depending on how the nucleus loses this excess energy either a lower energy atom of the same form will result, or a completely different nucleus and atom can be formed.

Ionization is a particular characteristic of the radiation produced when radioactive elements decay. These radiations are of such high energy that when they interact with materials, they can remove electrons from the atoms in the material. This effect is the reason why ionizing radiation is hazardous to health, and provides the means by which radiation can be detected.

THE ATOM

A typical model of the atom is called the Bohr Model, in honor of Niels Bohr who proposed the structure in 1913. The Bohr atom consists of a central nucleus com-posed of neutrons and protons, which is surrounded by electrons which “orbit” around the nucleus.

Protons carry a positive charge of one and have a mass of about 1 atomic mass unit or amu (1 amu =1.7x10-27 kg, a very, very small number). Neutrons are electrically “neutral” and also have a mass of about 1 amu. In contrast electron carry a negative charge and have mass of only 0.00055 amu. The number of protons in a nucleus determines the element of the atom. For example, the number of protons in uranium is 92 and the number in neon is 10. The proton number is often referred to as Z.

Atoms with different numbers of protons are called elements, and are arranged in the periodic table with increasing Z.



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Atoms in nature are electrically neutral so the number of electrons orbiting the nucleus equals the number of protons in the nucleus.

Neutrons make up the remaining mass of the nucleus and provide a means to “glue” the protons in place. Without neutrons, the nucleus would split apart because the positive protons would repel each other. Elements can have nucleii with different numbers of neutrons in them. For example hydrogen, which normally only has one proton in the nucleus, can have a neutron added to its nucleus to from deuterium, ir have two neutrons added to create tritium, which is radioactive. Atoms of the same element which vary in neutron number are called isotopes. Some elements have many stable isotopes (tin has 10) while others have only one or two. We express isotopes with the nomenclature Neon-20 or 20Ne10, with twenty representing the total number of neutrons and protons in the atom, often referred to as A, and 10 rep-resenting the number of protons (Z).

Radionuclides can be arranged by A and Z in the chart of the nuclides (http://www2.bnl.gov/CoN/).

This is sort of like the periodic table of elements. A very good Web Periodic Table can be found at this site.

Alpha decay is a radioactive process in which a particle with two neutrons and two protons is ejected from the nucleus of a radioactive atom. The particle is identical to the nucleus of a helium atom.

ALPHA PARTICLES

Alpha decay only occurs in very heavy elements such as uranium, thorium and radium. The nuclei of these atoms are very “neutron rich” (i.e. have a lot more neu-trons in their nucleus than they do protons) which makes emission of the alpha par-ticle possible.

After an atom ejects an alpha particle, a new parent atom is formed which has two less neutrons and two less protons. Thus, when uranium-238 (which has a Z of 92) decays by alpha emission, thorium-234 is created (which has a Z of 90).



Because alpha particles contain two protons, they have a positive charge of two. Further, alpha particles are very heavy and very energetic compared to other com-mon types of radiation. These characteristics allow alpha particles to interact readily with materials they encounter, including air, causing many ionizations in a very short distance. Typical alpha particles will travel no more than a few centime-ters in air and are stopped by a sheet of paper.

THE BETA PARTICLE

Beta decay is a radioactive process in which an electron is emitted from the nucleus of a radioactive atom, along with an unusual particle called an antineutrino. The neutrino is an almost massless particle that carries away some of the energy from the decay process. Because this electron is from the nucleus of the atom, it is called a beta particle to distinguish it from the electrons which orbit the atom.

Like alpha decay, beta decay occurs in isotopes which are “neutron rich” (i.e. have a lot more neutrons in their nucleus than they do protons). Atoms which undergo beta decay are located below the line of stable elements on the chart of the nuclides, and are typically produced in nuclear reactors. When a nucleus ejects a beta parti-cle, one of the neutrons in the nucleus is transformed into a proton. Since the num-ber of protons in the nucleus has changed, a new daughter atom is formed which has one less neutron but one more proton than the parent. For example, when rhe-nium-187 decays (which has a Z of 75) by beta decay, osmium-187 is created (which has a Z of 76). Beta particles have a single negative charge and weigh only a small fraction of a neutron or proton. As a result, beta particles interact less readily with material than alpha particles. Depending on the beta particles energy (which depends on the radioactive atom), beta particles will travel up to several meters in air, and are stopped by thin layers of metal or plastic.

High energy betas that travel through water sometimes produce Cerenkov Radia-tion, which in turn produces the blue glow seen around fuel and reactors.

GAMMA RADIATION

After a decay reaction, the nucleus is often in an “excited” state. This means that the decay has resulted in producing a nucleus which still has excess energy to get



40

rid of. Rather than emitting another beta or alpha particle, this energy is lost by emitting a pulse of electromagnetic radiation called a gamma ray. The gamma ray is identical in nature to light or microwaves, but of very high energy.

Like all forms of electromagnetic radiation, the gamma ray has no mass and no charge. Gamma rays interact with material by colliding with the electrons in the shells of atoms. They lose their energy slowly in material, being able to travel sig-nificant distances before stopping. Depending on their initial energy, gamma rays can travel from 1 to hundreds of meters in air and can easily go right through peo-ple.

It is important to note that most alpha and beta emitters also emit gamma rays as part of their decay process. However, their is no such thing as a “pure” gamma emitter. Important gamma emitters including technetium-99m which is used in nuclear medicine, and cesium-137 which is used for calibration of nuclear instru-ments.

X-RAYS

Over a century ago in 1895, Roentgen discovered the first example of ionizing radi-ation, x-rays. The key to Roentgens discovery was a device called a Crooke’s tube, which was a glass envelope under high vacuum, with a wire element at one end forming the cathode, and a heavy copper target at the other end forming the anode. When a high voltage was applied to the electrodes, electrons formed at the cathode would be pulled towards the anode and strike the copper with very high energy. Roentgen discovered that very penetrating radiations were produced from the anode, which he called x-rays.

X-ray production whenever electrons of high energy strike a heavy metal target, like tungsten or copper. When electrons hit this material, some of the electrons will approach the nucleus of the metal atoms where they are deflected because of there opposite charges (electrons are negative and the nucleus is positive, so the electrons are attracted to the nucleus). This deflection causes the energy of the electron to decrease, and this decrease in energy then results in forming an x-ray.

Medical x-ray machines in hospitals use the same principle as the Crooke’s Tube to produce x-rays. The most common x-ray machines use tungsten as there cathode, and have very precise electronics so the amount and energy of the x-ray produced is optimum for making images of bones and tissues in the body.



PROPERY OF RADIATION

Different radiations have different properties, as summarized below:

In summary, the most common types of radiation include alpha particles, beta and positron particles, gamma and x-rays, and neutrons. Alpha particles are heavy and doubly charged which cause them to lose their energy very quickly in matter. They can be shielded by a sheet of paper or the surface layer of our skin. Alpha particles are only considered hazardous to a persons health if an alpha emitting material is ingested or inhaled. Beta and positron particles are much smaller and only have one charge, which cause them to interact more slowly with material. They are effec-tively shielded by thin layers of metal or plastic and are again only considered haz-ardous if a beta emitter is ingested or inhaled.

Gamma emitters are associated with alpha, beta, and positron decay. X-Rays are produced either when electrons change orbits within an atom, or electrons from an external source are deflected around the nucleus of an atom. Both are forms of high energy electromagnetic radiation which interact lightly with matter. X-rays and gamma rays are best shielded by thick layers of lead or other dense material and are hazardous to people when they are external to the body.

Neutrons are neutral particles with approximately the same mass as a proton. Because they are neutral they react only weakly with material. They are an external hazard best shielded by thick layers of concrete. Neutron radiation will be dis-cussed in more detail in the discussion of nuclear power.

Radiation Type of Radiation

Mass (AMU)

Charge Shielding material

Alpha Particle 4 +2 Paper, skin, clothes

Beta Particle 1/1836 ±1 Plastic, glass, light metals

Gamma Electromag-netic Wave

0 0 Dense metal, concrete, Earth

Neutrons Particle 1 0 Water, concrete, polyethylene, oil



42

HALF-LIFE

Half-life is the time required for the quantity of a radioactive material to be reduced to one-half its original value.

All radionuclides have a particular half-life, some of which a very long, while other are extremely short. For example, uranium-238 has such a long half life, 4.5x109 years, that only a small fraction has decayed since the earth was formed. In con-trast, carbon-11 has a half-life of only 20 minutes. Since this nuclide has medical applications, it has to be created where it is being used so that enough will be present to conduct medical studies.

Here is a on-line calculator that will calculate the activity of some radionuclides at some time after it is formed.

RADIATION MEASUREMENT

When given a certain amount of radioactive material, it is customary to refer to the quantity based on its activity rather than its mass. The activity is simply the number of disintegrations or transformations the quantity of material undergoes in a given period of time.

The two most common units of activity are the Curie and the Becquerel. The Curie is named after Pierre Curie for his and his wife Marie's discovery of radium. One Curie is equal to 3.7x1010 disintegrations per second. A newer unit of activity if the Becquerel named for Henry Becquerel who is credited with the discovery of radio-activity. One Becquerel is equal to one disintegration per second.

It is obvious that the Curie is a very large amount of activity and the Becquerel is a very small amount. To make discussion of common amounts of radioactivity more convenient, we often talk in terms of milli and microCuries or kilo and MegaBec-querels.

Radiation is often measured in one of these three units, depending on what is being measured and why. In international units, these would be Coulombs/kg for roent-gen, Grays for rads and Seiverts for rem.



GAS FILLED DETECTOR

Since we cannot see, smell or taste radiation, we are dependent on instruments to indicate the presence of ionizing radiation.

The most common type of instrument is a gas filled radiation detector. This instru-ment works on the principle that as radiation passes through air or a specific gas, ionization of the molecules in the air occur. When a high voltage is placed between two areas of the gas filled space, the positive ions will be attracted to the negative side of the detector (the cathode) and the free electrons will travel to the positive side (the anode). These charges are collected by the anode and cathode which then form a very small current in the wires going to the detector. By placing a very sen-sitive current measuring device between the wires from the cathode and anode, the small current measured and displayed as a signal. The more radiation which enters the chamber, the more current displayed by the instrument.

Many types of gas-filled detectors exist, but the two most common are the ion chamber used for measuring large amounts of radiation and the Geiger-Muller or GM detector used to measure very small amounts of radiation.

The second most common type of radiation detecting instrument is the scintillation detector. The basic principle behind this instrument is the use of a special material which glows or “scintillates” when radiation interacts with it. The most common type of material is a type of salt called sodium-iodide. The light produced from the scintillation process is reflected through a clear window where it interacts with device called a photomultiplier tube.

SODIUM IODIDE DETECTOR

The first part of the photomultiplier tube is made of another special material called a photocathode. The photocathode has the unique characteristic of producing elec-trons when light strikes its surface. These electrons are then pulled towards a series of plates called dynodes through the application of a positive high voltage. When electrons from the photocathode hit the first dynode, several electrons are produced for each initial electron hitting its surface. This “bunch” of electrons is then pulled towards the next dynode, where more electron “multiplication” occurs. The sequence continues until the last dynode is reached, where the electron pulse is now millions of times larger then it was at the beginning of the tube. At this point the



44

electrons are collected by an anode at the end of the tube forming an electronic pulse. The pulse is then detected and displayed by a special instrument.

Scintillation detectors are very sensitive radiation instruments and are used for spe-cial environmental surveys and as laboratory instruments.

ACCELERATOR

What are accelerators used for?

Quite simply, accelerators give high energy to subatomic particles, which then col-lide with targets. Out of this interaction come many other subatomic particles that pass into detectors. From the information gathered in the detectors, physicists can determine properties of the particles and their interactions.

The higher the energy of the accelerated particles, the more closely we can probe the structure of matter. For that reason a major goal of researchers is to produce higher and higher particle energies.

Accelerator: A device (i.e., machine) used to produce high-energy high-speed beams of charged particles, such as electrons, protons, or heavy ions, for research in high-energy and nuclear physics, synchrotron radiation research, medical therapies, and some industrial applications. The accelerator at SLAC is an electron accelera-tor.

El;ectron accelerator: Electrons carry electrical charge and successful manipulation of electrons allows electronic devices to function. The picture and text on the video terminal in front of you is caused by electrons being accelerated and focused onto the inside of the screen, where a phosphor absorbs the electrons and light is pro-duced. A television screen is a simple, low-energy example of an electron accelera-tor. A typical medical electron accelerator used in medical radiation therapy is about 1000 times more powerful than a color television set, while the electron accelerator at SLAC is about 2,000,000 times more powerful than a color TV. One example of an electron accelerator used in radiotherapy is the Clinac, manufactured by Varian Associates in Palo Alto, CA

How many kinds of accelerators are there?



Particle accelerators come in two basic designs, linear (linac) and circular (synchro-tron). The accelerator at SLAC is a linac.

The longer a linac is, the higher the energy of the particles it can produce. A syn-chrotron achieves high energy by circulating particles many times before they hit their targets.

Linacs are used in medicine as well as high energy physics research. How does the SLAC linac work? Check it out!

How do they work?

Your TV set or computer monitor contains the components of an accelerator. As you might suspect, operating an accelerator as large as the linac at SLAC is a chal-lenging task. To learn more about the SLAC linear accelerator structural compo-nents and experimental facilities, select a link below.

Accelerator Components

• Beam Switch Yard • Damping Rings • Electron Gun • Klystrons • Linac • Positron Production



46


THE CYCLOTRON

The cyclotron is a particle accelerator conceived by Ernest O. Lawrence in 1929, and developed, with this colleagues and students at the University of California in the 1930s. (For a short pictorial history, see The Development of the Cyclotron at LBNL.)

A cyclotron consisted of two large dipole magnets designed to produce a semi-cir-cular region of uniform magnetic field, pointing uniformly downward.

These were called Ds because of their D-shape. The two D's were placed back-to-back with their straight sides parallel but slightly separated.

An oscillating voltage was applied to produce an electric field across this gap. Par-ticles injected into the magnetic field region of a D trace out a semicircular path until they reach the gap. The electric field in the gap then accelerates the particles as they pass across it.

The particles now have higher energy so they follow a semi-circular path in the next D with larger radius and so reach the gap again. The electric field frequency must be just right so that the direction of the field has reversed by their time of arrival at the gap. The field in the gap accelerates them and they enter the first D



48

again. Thus the particles gain energy as they spiral around. The trick is that as they speed up, they trace a larger arc and so they always take the same time to reach the gap. This way a constant frequency electric field oscillation continues to always accelerate them across the gap. The limitation on the energy that can be reached in such a device depends on the size of the magnets that form the D's and the strength of their magnetic fields.

Once the synchrotron principle was developed (see below), it was found to be a much cheaper way to achieve high energy particles than the cyclotron and so the original cyclotron method is no longer used.

Synchrotron

A synchrotron (sometimes called a synchro-cyclotron) is a circular accelerator which has an electromagnetic resonant cavity (or perhaps a few placed at regular intervals around the ring) to accelerate the particles.

There are several circular accelerators at Fermi National Accelerator Laboratory. Particles pass through each cavity many times as they circulate around the ring, each time receiving a small acceleration, or increase in energy. When either the energy or the field strength changes so does the radius of the path of the particles.

Thus, as the particles increase in energy the strength of the magnetic field that is used to steer them must be changed with each turn to keep the particles moving in the same ring. The change in magnetic field must be carefully synchronized to the change in energy or the beam will be lost. Hence the name "synchrotron". The range of energies over which particles can be accelerated in a single ring is deter-mined by the range of field strength available with high precision from a particular set of magnets. To reach high energies, physicists sometimes use a sequence of dif-ferent size synchrotrons, each one feeding the next bigger one. Particles are often pre-accelerated before entering the first ring, using a small linear accelerator or other device.



Synchrotron Radiation

Synchrotron radiation is the name given to the electromagnetic radiation emitted by the charged particles circulating in a synchrotron. It occurs because the charged particles are accelerated (deflected) by the magnetic field from the dipole magnets to make the beam travel around the ring. Any accelerated charged particle produces some electromagnetic radiation.

The wavelength and intensity of the synchrotron radiation depends on the energy and type of the emitting particle. If all you are interested in is storing a high energy beam, then synchrotron radiation is a problem. The energy lost from the beam by this radiation effect must be restored by introducing accelerating cavities at one or more places in the ring, to give the particles a kick in energy every time they pass. The amount and energy of the radiation depends on the speed of the radiating parti-cles and the magnetic field strength. As the particle approaches the speed of light, the effect increases rapidly. The special relativity factor, gamma (, is the ratio of the energy of the particle to its rest mass-energy, mc2. The energy loss for a given elec-tron energy is proportional to ()3.

Dependence on Particle Type

For an 1.5 GeV electron in the SPEAR storage ring, gamma is approximately 3000. For a 50 GeV electron in the SLC arcs, gamma is approximately 100,000. Gamma is the ratio of the energy of the particle to its rest mass-energy, mc2. Thus, because a proton is so much more massive than an electron, a proton with 1 TeV = 1,000 GeV energy has a gamma factor of only 1,000. (1 TeV is the energy produced by the synchrotron at Fermilab). Thus synchrotron radiation is much greater for elec-trons than for equal energy protons. This is the reason why much higher energy synchrotrons can be built for protons than for electrons.



50

SSRL

At SPEAR, the synchrotron radiation has wavelengths from ultraviolet to x-ray, just the right scale to use it as a probe of the atomic and molecular scale structure of matter. The Stanford Synchrotron Radiation Laboratory at SLAC is devoted to studies using this powerful tool.

Storage Ring

A storage ring is the same thing as a synchrotron, except that it is designed just to keep the particles circulating at a constant energy for as long as possible, not to increase their energy any further. However, the particles must still pass through at least one accelerating cavity each time they circle the ring, just to compensate for the energy they lose to synchrotron radiation.

Two storage rings have been built at SLAC; SPEAR, a 3 GeV ring completed in the early 70's and PEP a 9 GeV ring completed in the early 80's. SPEAR is now used solely by SSRL while PEP is being rebuilt as a two-ring facility known as the B factory.



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radioelements, isotopes & radionuclides

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