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All matter is composed of elements and all elements are composed of atoms. The atom contains a nucleus consisting of protons and neutrons with electrons revolving in circular and elliptical orbits about the nucleus. Electrons carry a negative charge, protons carry positive charge, and the neutrons have no electrical charge. An atom normally has one electron in orbit for each proton in the nucleus, leaving the atom electrically neutral.
A
The atomic structure of an element is denoted as X
Z
where:
Each individual arrangement of protons and neutrons is referred to as a Nuclide. Nuclides which have the same number of protons are called Isotopes. Shown below are examples of isotopes of Hydrogen:
Many nuclides, but not all, are unstable or "radioactive". In the above examples, only tritium is radioactive. Radioactivity is defined as the spontaneous disintegration of unstable nuclei with the resulting emission of radiation that results in the formation of new nuclei. Stability of the nucleus is related to its ratio of neutrons to protons. For low atomic numbered elements, approximately equal numbers of neutrons and protons in the nucleus are necessary for stability. For elements of higher atomic number, the ratio rises to approximately 1.6 to 1. As a nuclide departs from this stable ratio, changes in the nucleus occur which tend to bring the product to a more stable arrangement. This approach to stability is accomplished by one or more of 5 "radioactive decay modes".
The energy of the ejected beta particle is characteristic of each nuclide and is one criterion used for identification purposes. In general, the average energy per particle is about 1/3 of the maximum energy.
The generalized atomic equation for beta decay is as follows:
A A
X ---> Y + 
- + v X = Original (parent) atom
Z Z+1 Y = New (daughter) atom
- = Beta particle (electron)
v = Neutrino
Examples of Beta decay:
3 3
H -> He + 0.0186 MeV --max MeV = 1 million electron volts
1 2 - max = maximum beta particle energy
14 14
C -> N + 0.156 MeV -max
6 7
The positron behaves exactly as an electron except that when the positron comes in contact with a free electron, the two particles combine and are annihilated. This gives rise to two gamma rays whose energies correspond to the rest mass equivalence of the particles (0.511 MeV/gamma). See page 13 for a description of annihilation radiation.
The generalized atomic equation for positron decay is as follows:
A A
X -> Y + + + v + = positron (positive electron)
Z Z-1
Example of Positron decay:
19 19
Ne -> F + 2.22 MeV - + v
10 9
The generalized atomic equation for electron capture is:
A A
X + e -> Y + X-rays + v e = electron
Z Z-1
Example of electron capture decay:
54 54
Mn + e -> Cr + 0.835 MeV X-rays + v
25 24
The generalized atomic equation for alpha decay is:
A A-4 4
X -> Y + 
= He (Helium nucleus)
Z Z-2 2
Example of alpha decay:
210 206
Po -> Pb + 5.3 MeV
84 82
Nuclear transition can occur after beta decay, positron decay, electron capture and alpha decay.
Example of radionuclides that undergo nuclear transition are shown below:
60 60
Co -> Ni + 0.318 MeV - + 1.17 MeV
; + 1.33 MeV
27 28
= gamma ray
22 22
Na -> Ne + 0.546 MeV + + 1.27 MeV
11 10
125 125
I -> Te + 0.035 MeV (6.67%) + X-rays
53 52
226 222
Ra -> Rn + 4.78 MeV (93.4%) + 4.59 (5.7%) + 0.186 MeV + X-rays
88 86
The Chart of The Nuclides (Appendix I) list all known nuclides and is a useful reference for radioactive decay and energy data.
).
This constant
is defined as the instantaneous fraction of atoms decaying per unit time. Each
radioactive nuclide has its own characteristic decay constant.
The instantaneous time rate of change of the number of atoms, N, for a radionuclide is given by:
dN = - N
dt
If we started with No radioactive atoms at some time t=0, the number of atoms at some other time Nt, can be obtained by integrating:
The e-t term indicates that the radioactive atoms decay exponentially. This equation, is called the decay equation.
Nt = N 0e- t
If we were to substitute into the decay equation the time, T, it takes for the reduction of a quantity of radioactive atoms to half of the original, we get:
NT=1No
2
1No = Noe-1/2
2
1 = e-t 1/2
2
ln 1/2 = -T1/2 Therefore (ln 1/2=ln1-ln2; ln1=0)
Therefore -ln2 = -T1/2
T1/2=ln2 > (ln2=0.693)
Therefore = 0.693
T1/2
Thus, the decay constant, , can be calculated for any radioactive nuclide from its half-life.
A = N
1 Curie = 3.7 X 1010 disintegrations per second (DPS)
= 3.7 X 1010 becquerels
or
1 Curie = 2.22 X 1012 disintegrations per minute (DPM)
The International System (SI) of units has defined the Becquerel (Bq) as the unit of activity, equal to 1 disintegration per second. The Becquerel is already in use in some parts of the world and will eventually replace the Curie.
Because the Curie is a very large quantity, fractions of the Curie are often used:
1 millicurie = (mCi) = 2.22 X 109 dpm = 10-3 Curies 1 microcurie = (µCi) = 2.22 X 106 dpm = 10-6 Curies 1 nanocurie = (nCi) = 2.22 X 103 dpm = 10-9 Curies 1 picocurie = (pCi) = 2.22 dpm = 10-12 Curies
Since radioactive material is measured in units of activity, the decay equation now takes the form:
A = Aoe-t
Where: A = Activity after some time t
Ao = Original activity of the sample
= The radioactivity decay constant equal to 0.693
T1/2
T1/2 = Half-life of isotope
t = Decay time
Note: The decay time and half-life must be expressed in the same units of time.
The transfer of energy from emitted radiations to matter occurs in two major ways: Ionization and Excitation.
Radiation can be classified into two groups:
Such particles capable of creating ion pairs in this manner are called ionizing radiation.
The term used to compare and relate the ionizing powers of different types of charged particles is called the "specific ionization" Specific ionization is defined as the number of ion pairs per unit path length formed by ionizing radiation in a medium:
Specific Ionization = # of ion pairs formed
cm of path
The specific ionization is dependent on the velocity of the charged particle (and therefore its energy), and the density of the absorbing material (the number of atoms available for ionization).
Because of its relatively large mass (2 neutrons and 2 protons), high electrical charge (+2) and low velocity, the specific ionization of an alpha particle is very high. That is, it creates many ion pairs in a very short path length. Because of this, it loses all of its energy in a very short distance. The range in air is only several centimeters even for the most energetic alpha particles.
Since the alpha particle has a very limited range in matter, it presents no external radiation hazard to man. Many alpha particles cannot penetrate the protective layer of skin. However, once inside the body, surrounded by living tissue, damage will be to the local area in which the alpha emitter is deposited. Thus, alpha emitters are an internal hazard and intake to the body must be prevented. (See Chapter IV, "Radiation Protection Techniques").
Beta particles, like alpha particles, lose their energy by ionization and excitation, but because of their small mass (1/7300 of an alpha) and lower charge (1/2 of that of an alpha) the interactions take place at less frequent intervals. Therefore, the beta particles do not produce as many ion pairs per centimeter of path as alpha particles, and thus, have a greater range in matter. The beta particle's range in matter depends on the energy and the composition of the material. (See Appendix III, "Penetration Ability of Beta Radiation").
Beta particles can interact with a nucleus of an element and give rise to X-rays by a method called Bremsstrahlung. Bremsstrahlung (German for "Breaking Radiation") occurs when high speed beta particles approaches the nucleus of an atom. The electrical interaction between the negative beta particle and the positively charged nucleus causes the beta particle to be deflected from its original path or stopped all together. Their stoppage or deflection results in a change in velocity of the beta particle with the emission of X- rays of various energies The likelihood of Bremsstrahlung production increases with increasing atomic number of the absorber. For this reason, beta shields are made from low atomic numbered material, like aluminum or plastics.
Beta particles require an energy of greater than 70 keV to penetrate the protective layer of the skin, and thus, are somewhat of an external hazard. The beta can also constitute an internal hazard. A beta particle has a greater range in tissue compared to an alpha particle due to its low specific ionization. The beta particle gives up less energy per unit volume of tissue and, therefore, is not as effective in causing damage as an alpha particle.
Since X and rays are chargeless, they do not interact by electrostatic forces as in the case of charged particles, which cause ionization of matter directly along their path of travel. However, X and gamma rays do have sufficient energy to release high energy secondary charged particles (electrons) from matter through one of three basic interactions:
The high speed electrons resulting from these interactions then cause ionization of the medium.
-ray photons** as well as other photons (such as light), whereby all of the energy of the photon is transferred to an inner shell electron (usually the K shell), ejecting it from the atom and leaving the atom with an inner shell vacancy. This shell vacancy creates an excitation energy which corresponds to the Binding Energy (BE) of the ejected photoelectron.
The Kinetic Energy (KE) of the photoelectron is equal to the energy of the X or -ray photo minus the BE of the electron ejected.
If the X or -ray photon does not have sufficient energy to knock the inner shell electron loose, the reaction will not occur.
The resultant atom is now in an excited state and will decay to the ground state by emission of X-rays and fluorescent radiation with the total energy equal to the BE of the photoelectron. The energies of the secondary radiations are usually much lower than the primary X or -ray energies.
Application of the Photoelectric Effect
Gamma rays emitted from excited nuclei, and X-rays emitted from excited atoms, have discrete energy characteristics of the specific nuclides and elements, respectively. Thus, the energy of these or X photons can be used as "finger prints" to identify unknown nuclides and elements.
** A photon, as described by the Quantum Theory, is a "particle" or "quantum" that contains a discrete quantity of electromagnetic energy which travels at the speed of light, or 3 X 108 meters per second.
The primary loses part of its energy to the Compton electron which gets scattered at an angle from the original direction of the incident , while the compton scattered (') is scattered as an angle. In this process, the scattered photon and Compton electron share the energy of the incident .
The KE carried off by the Compton electron may be deposited locally (i.e., absorbed immediately by the surroundings). However, the energy carried off by the Compton scattered photon is not deposited locally. Therefore, this scattered photon can significantly contribute to the dose outside a shielding apparatus.
Application of the Compton Effect
Due to its characteristic peaks, the Compton Effect aids in the identification of unknown nuclides. However, in a detecting system, the Compton scattered electron can mask lower energy photons interacting by the photoelectric effect making interpretation of results difficult.
-ray passing close to a nucleus suddenly disappears and an electron and a positron appear in its place. This interaction must take place in the neighborhood of a nucleus to conserve momentum.
Since both particles are created from energy supplied by the incident photon, the process is energetically possible only if E or EX is greater than 1.02 MeV.
When the positron slows down (i.e., loses its KE), it will annihilate itself by combining with an electron. This produces two photons with an energy of 0.51 MeV each. This "annihilation radiation" represents the energy equivalent of the rest mass of two electrons which is converted to pure energy according to the principles of Einstein's theories, in particular, E = mc2; where
E = energy of two 0.51 MeV photons
m = the rest mass of two electrons (1/1840 amu)
c = the velocity of light (3 X 108 m/sec)
Applications of Pair Production
Again, due to characteristic peaks observed for various known nuclides, Pair Production is an aid is an aid in the identification of unknowns.
The gray (Gy) is the SI unit of absorbed dose. One gray is equal to an absorbed dose of 1 Joule/kilogram (100 rads).
The rad (radiation absorbed dose) is a measure of energy deposition in any medium by all types of radiation. The rad is equal to 100 ergs/gram.
The rem (radiation equivalent man) is a unit of dose equivalent used for radiation safety purposes. The rem is defined as the dose (in rads) multiplied by appropriate Quality Factor (QF). The Quality Factor is a term used to derive dose equivalent from absorbed dose and takes into account the different abilities of radiation types to cause damage in a biological system. Below is a table listing Quality Factors for various types of radiations:
The Sievert is the SI unit of any of the quantities expressed as dose equivalent. The dose equivalent in rems is equal to the absorbed dose in grays multiplied by the quality factor.
Quality Factor
Absorbed dose equal to a unit Quality dose
Quality dose
Radiation Factor equivalent *
X, or 1 1
Neutrons of unknown energies 10 0.1
Alpha particles 20 0.05
High-energy protons 10 0.1
Thus, the rem allows us to add doses of different radiation types to obtain total effective dose. * Absorbed dose in rad equal to 1 rem or the absorbed dose in gray equal to 1 sievert.
Example: What is an individual's dose equivalent from 10 mrad of gamma rays, 5 mrads of - particles and 10 mrads of neutrons? (m = milli = 1/1000)
Dose Equivalent = mrads X QF = mrems
Gamma dose equivalent = 10 x 1 = 10
Beta dose equivalent = 5 x 1 = 5
Neutron dose equiv. = 10 x 10 = 100
Total 115 mrems
The SI unit for dose equivalent is the Sievert (Sv) and is equal to 1 Joule/kg. 1 Sievert = 100 rem.
Multiple choice questions may have more than one correct response. Refer to Appendix IV for reference data.
,
is equal to:
- particles, and 5 mrad of fast neutron radiations would give an individual a dose equivalent of:
Name of Process Example
a)__________________________ _________________________
b)__________________________ _________________________
c)__________________________ _________________________
a)__________________________ _________________________
b)__________________________ _________________________
a) What is the value of its decay constant,
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