IAEA International Atomic Energy Agency IAEA PGEC Pre-Study Materials Health Physics Fundamentals

IAEAInternational Atomic Energy Agency

IAEA PGEC Pre-Study Materials

Health PhysicsFundamentals

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Table of Contents

Topic Slide

Mass, Charge and Energy …………………3Atomic Structure……………………….…..18Radioactive Decay…………………….….. 44Activity and the Decay Equation….……. 71Interactions with Matter…………….……. 92Quantities and Units……………..……….124Time, Distance and Shielding.………… 146Radiation Detection ……………..……… 164Sources of Radiation ……………..……. 202Solutions to Problems ………….……….219

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MASS, CHARGEAND ENERGY

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Mass

Mass is basically a measure of theamount of matter in an object.

The more mass an object has, the harder it is to move, so physicistssay that mass is a measure of theresistance an object has to changes in its velocity.

All objects have mass, from large things to very small subatomic particles.

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Mass

Mass is different from weight.

Weight is a measure of the gravitational force of the earth on an object. Weight can be zero if no gravitational force is acting, but mass can never be zero.

Typical units for mass are grams (g) or kilograms (kg).

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Charge

• Electric charge is a fundamental property of matter that causes it to experience a force when near other electrically charged matter. Electric charge can be either positive or negative.

• Positively charged objects and negatively charged objects experience an attractive force. But two objects with the same charge experience a repulsive force.

• The unit of electric charge is the coulomb (C).

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Energy

Energy is the capacity of a physical system to perform work on another system.

Energy exists in several forms such as potential energy, kinetic energy, mechanical energy, electrical energy, heat, and light.

http://en.wikipedia.org/wiki/File:Plasma-lamp_2.jpg

http://en.wikipedia.org/wiki/File:Springs_009.jpg

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Types of Energy

Potential Energy is stored energy. For example, when a spring is stretched to the left, it exerts a force to the right so as to return to its original, unstretched position. Similarly, when a mass is lifted up, the force of gravity will act so as to bring it back down.

The action of stretching the spring or lifting the mass requires energy.

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• The kinetic energy of an object is the energy that it possesses due to its motion.

• It is defined as the work required to accelerate a body of a given mass from rest to a certain velocity.

Types of Energy

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• Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space.

• It has no charge or mass, but possesses both electric and magnetic field components.

• Examples of electromagnetic radiation include radio waves, visible light, and x-rays.

Types of Energy

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Energy Units

• Energy is measured using several units. Units of energy include joules, electron volts (eV), and ergs.

• In the field of radiation protection, the unit eV is used extensively. The eV is a very small energy unit (only about 1.6E-19 joules) that can be used to describe the energy of elementary particles like photons and electrons.

• Typically, you will see energy values expressed as kiloelectron volts (keV) or megaelectron volts (MeV).

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Mass – Energy Relationship

The mass of an object can also be thought of as a measure of its energy content. In other words, mass and energy are equivalent. Albert Einstein proposed this mass–energy equivalence in 1905 and described it by the famous equation:

E = mc2

where m is the mass of an object at rest and c is the speed of light in a vacuum.

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Mass – Energy Relationship

• Using the mass-energy relationship, we can measure the mass of objects in units of energy.

• In physics, a particle’s “rest” mass is typically given in units of electron-volts or eV.

• The rest mass of a particle is just the energy equivalent of the matter making up the particle, and does not include the particle’s kinetic energy (the energy of its motion).

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Conservation of Mass & Energy

• According to the laws of conservation of mass and energy, the total mass or energy of a closed system remains constant, although mass or energy in the system may change into another form.

• An example of this is the detonation of a nuclear weapon,where mass transforms into energy, like the visible light(electromagnetic radiation) shown in the picture.

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• Electromagnetic radiation exhibits properties of waves (e.g., frequency and wavelength), and particles (e.g., momentum).

• Because of this wave-particle duality, physicists use both waves and particles to represent electromagnetic radiation.

• The elementary particle used to represent a discrete quantity of electromagnetic radiation is the photon, which is commonly used in the field of Health Physics.

Electromagnetic Radiation

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• Photons are created through various physical processes (like radioactive decay or the acceleration of charged particles, both of which will be discussed later).

• Photons are created with a broad spectrum of energies. A photon’s energy is directly proportional to its measured wavelength.

Electromagnetic Spectrum

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Electromagnetic Spectrum

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ATOMICSTRUCTURE

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The Atom

The atom is the basic structure from which all matter is composed of. Atoms cannot be seen with the human eye, but we often represent them with a model like the one shown here.

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Bohr’s Atomic Model

The Bohr atomic model (named after Danish physicist Neils Bohr) is widely used to describe atomic structure.

The Bohr atom includes a dense core composed of tightly packed particles, called the nucleus.

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Nucleus

Subatomic particles known as protons and neutrons compose the nucleus of the atom.

The number of the particles in the nucleus determines the elemental identity of the atom and its density.

Protons and neutrons have essentially the same mass (about 1.67E-27 kg).

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Protons

Protons have a single positive charge, and are found inside the nucleus of the atom.

Atoms of each element in the periodic table have a unique number of protons.

Proton number never changes for any given element. For example, oxygen always has 8 protons.

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Neutrons

Neutrons are the other particle found in the nucleus of an atom. Unlike protons, however, neutrons carry no electrical charge and are thus electrically "neutral."

Atoms of a given element do not always contain the same number of neutrons (more on this later).

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Electrons

Smaller particles, known as electrons, are found outside of the nucleus.

According to the Bohr model, electrons can only occupy certain orbits within “shells” around the nucleus.electrons

inner shell

outer shell

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Electrons

Electrons are particles with a single negative charge. We can think of electrons as orbiting around the nucleus, similar to moons orbiting around a planet.

The mass of the electron is almost 2000 times smaller than the mass of protons or neutrons (0.911E-30 kg).

The sharing or exchange of electrons between atoms forms chemical bonds which is how molecules and compounds are formed.

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Electrostatic Forces within the Atom

• Since electrons are negatively charged and protons are positively charged, they attract via electrostatic forces. This force is what “holds” electrons around the positively charged nucleus.

• Conversely, the positive protons within the nucleus experience electrostatic repulsion. However, the protons within a nucleus are close enough together so that strong nuclear forces can overcome this electrostatic repulsion (more on this later).

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Electron Binding Energy

• Binding energy is the energy required to “pull” an electron away from it’s positively charged nucleus

• Recall that electrons exist in discrete “shells” around the nucleus. Electrons found in the different shells have different binding energies.

binding energy

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Electron Shells

• The shells are designated by letters (K, L, M, N…) where K, the shell closest to the nucleus, has the largest binding energy, so the K electron is the most tightly bound.

• There are a maximum number of electrons in each shell: 2 in K shell, 8 in L shell, etc.

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Shell Hydrogen Tungsten

K -13.5

-69,500

L -3.4 -11,280

M -1.5 -2,810

N -0.9 -588

O -0.54

-73

Electron Binding Energy

(Binding Energy in eV)

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Binding Energy

10

30

40

506070

100

80

90

110

20

50 60 70 80 90 10010 20 30 400

0

Atomic Number (Z)

Bin

din

g E

ner

gy

(keV

)

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Particle Symbol Mass (kg) Energy (MeV) Charge

Proton p 1.672E-27 938.2 +1

Neutron n 1.675E-27 939.2 0

Electron e 0.911E-30 0.511 -1

Review: Parts of the Atom

Here, an energy is given for each particle since mass and energy are interchangeable as discussed earlier. The energy shown is considered the energy required to create a given particle with no kinetic energy (i.e., it’s “rest mass”).

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Atomic Mass Unit (amu)

Where 1 amu is approximately equal to1.6605 x 10-24 grams

Because atoms are so small, scientists defined the atomic mass unit (amu) to measure their mass. The amu is based on the Carbon-12 atom:

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The atomic mass of the proton and the neutron in amu are approximately:

Proton = 1.6726 x 10-24 grams = 1.0073 amuNeutron = 1.6749 x 10-24 grams = 1.0087 amu

Thus, the neutron is just a little heavier than the proton.

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The atomic mass of the electron in amu is approximately:

Electron = 9.1094 x 10-28 grams = 0.00055 amu

Thus, the electron has a much smaller mass than either the proton or the neutron, 1837 times smaller or about 2000 times smaller.

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Elements

The number of protons in an atom dictate what element that atom is.

For an uncharged atom, the number of electrons equals the number of protons.

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• The number of protons in the nucleus is called the atomic number, Z, which determines the element.

• The number of neutrons in the nucleus is the neutron number.

• The atomic mass, A, is the sum of neutrons and protons in the nucleus.

Carbon-14 is shown above, which is commonly written:

C-14 or 14C

Nuclear Notation

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Isotopes

Atoms of an element that have a different number of neutrons are called isotopes of that element.

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Isotope Example: Carbon

The number of protons and electrons remains the same for each isotope of carbon, but the number of neutrons varies. Note that two isotopes are stable and one is radioactive.

Carbon 12Stable

Carbon 13Stable

Carbon 14Unstable (Radioactive)

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Isotopes

There exist many different isotopes among the known elements.

Most have more neutrons than protons. Some are stable, but many are radioactive.

equal number of protons and neutrons

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Isotopes

long rangeelectrostatic

forces

short range strongnuclear forces

p

p

n

As seen in the previous slide, most isotopes have more neutrons than protons.

The more protons, the more repulsive the forces in the nucleus become.

Neutrons exert a stabilizing nuclear force to counteract the repulsion of the positively charged protons.

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Stable Nuclides

Line of stability

In this graph, the dotted line represents the stable nuclides.

For heavier nuclei, more neutrons are required relative to the number of protons to balance the long range repulsive electrostatic forces.

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Stable and Unstable Nuclides

Too manyneutrons

for stability

Too manyprotons

for stability

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SAMPLE PROBLEM 1

(Solution at end of presentation)

1. What positively charges particles are found in the nucleus of an atom?

2. Is binding energy higher or lower for the innermost electron shells?

3. What is the radioactive isotope of hydrogen?

4. Which isotope has more neutrons: carbon-12 or carbon-14?

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RADIOACTIVEDECAY

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Radioactive Decay

• Radioactive Decay is characterized by spontaneous changes in the nucleus of an unstable atom

• Decay is accompanied by a release of energy, either particulate or electromagnetic, or both

• May result in the formation of new elements (either stable or unstable)

• Nuclear instability is related either to the neutron-to-proton ratio in the nucleus, or the nucleus having excess energy

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Radioactive Decay

There are several decay mechanisms that allow an unstable nucleus to become more stable or to shed excess energy:

• Alpha particle decay• Beta particle decay• Positron decay• Electron capture • Gamma ray emission• Internal conversion

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Alpha Particle Decay (a++)

• Emission of a highly energetic helium nucleus (2 protons and 2 neutrons) from the nucleus of a radioactive atom

• Occurs when the atom’s neutron to proton ratio is too low

• Results in a decay product whose atomic number is 2 less than the parent and whose atomic mass is 4 less than the parent

• Alpha particles have a double positive charge

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Alpha Particle Decay

(Alpha particle has charge of +2)

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Alpha Particle Decay

• Alpha particles are monoenergetic. This means that every alpha particle released during the decay of a given radionuclide will have the same kinetic energy.

• Most alpha particles are emitted with kinetic energy on the order of several MeV (see examples below).

Isotope Half-Life Alpha Energy

(MeV)

210 Po 138.4 days 5.30433

222 Rn 3.823 days 5.48948

241 Am 432.2 years5.5445,

5.48556, 5.44280

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Alpha Decay Example

• 226Ra decays by alpha emission

• When an atom of 226Ra decays, its atomic mass decreases by 4 and its atomic number decreases by 2

• The element changes from radium to radon:

226Ra 222Rn + 4He

• In this example, every alpha released from the decay of Ra-226 has an energy of approximately 4.8 MeV.

28688

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Beta Particle Decay (b-)

• Emission of a beta particle (b) from the nucleus of a radioactive atom. Beta particles are identical to electrons in terms of mass and charge.

• Occurs when neutron to proton ratio is too high (i.e., a surplus of neutrons.)

• Essentially, a neutron within the nucleus transforms into a proton, an electron, and another particle called an antineutrino:

n p+ + e- + n

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Beta Particle Decay

In the example above, radioactive C-14 decays via beta decay to stable N-14. In the process, an electron (beta particle) and an antineutrino are emitted. The two emitted particles share the energy that is released from the decay.

Beta( )

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• Unlike alpha particles, beta particles are emitted with a continuous spectrum of energies up to a definite maximum.

• The energy that is released is shared between the beta particle and the antineutrino that are created. The antineutrino normally carries away the majority of the energy.

• The antineutrino that is released has no charge, and has very little mass, so it is not a radiation safety concern.

Beta Energy Spectrum

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Rel

ativ

e N

o. o

f B

eta

Par

ticle

s

Kinetic Energy (keV)

Emax = 156 keVEav ≈ 50 keV

Beta Energy Spectrum for Carbon-14

Beta Energy Spectrum

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Average Beta Energy

The average energy of the beta particles emitted is about one-third of the maximum allowable energy:

Eave = Emax1

3

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Positron Decay (b+)

• Nucleus emits a positron (beta particle whose charge is positive)

• Occurs when neutron to proton ratio is too low

• Essentially, a proton within the nucleus transforms into a neutron, an electron, and a neutrino:

p+ n + e+ + n

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Positron Decay

In the example above, radioactive C-10 decays to stable B-10. In the process, a positron and a neutrino are emitted. As with beta decay, the two emitted particles share the energy that is released.

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A positron is the antiparticle to an electron.

When a particle and its antiparticle collide, especially at low energies, a phenomenon known as annihilation will occur.

Annihilation means that the particle/antiparticle pair interact in such a way that they are transformed into pure energy.

Positron Annihilation

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Positron Annihilation

In the case of positron annihilation, two photons are created.

The photons are each created with an energy of 511 keV, which is the rest mass of the electron and positron.

This means that the total energy of the system is conserved.

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Orbital Electron Capture

• Another mechanism of radioactive decay, also called “K Capture”

• Occurs when the neutron to proton ratio is too low

• One of the orbital electrons is captured by the nucleus, and interacts with a proton to form a neutron:

e- + p+ n

• This form of decay competes with positron decay

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In the example below, radioactive C-11 decays to stable B-11 through capture of an electron. The resulting B-11 has one more neutron than the parent C-11, and any excess energy is given to a neutrino that is created in the process.

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• Since electron capture creates an electron vacancy in the innermost shell, the atom is left in an unbalanced or excited energy state.

• In order to reach a stable state, the atom will fill this vacancy with an electron from another shell.

• When an electron moves from one shell to another, the difference in energy is released as a photon, called a characteristic x-ray.

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characteristicx-rays

Characteristic X-rays

electron capture

• The x-rays that are emitted from orbital electron transitions have discrete energies that are characteristic of that element.

• These x-rays are typically low energy (on the order of a few to several keV).

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Gamma Ray Emission

• Gamma rays are electromagnetic radiation (photons) emitted from an excited nucleus, typically following alpha or beta decay. The gamma rays rid the nucleus of its excess energy.

• In some situations, the excited nucleus doesn’t immediately emit the gamma ray following decay. It can take fractions of a second to several minutes. These radionuclides are referred to as metastable (e.g., 99mTc).

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• Gamma rays are typically more energetic than characteristic x-rays, and can have energies of several MeV.

• Gamma rays are monoenergetic. Their characteristic energies can be used to identify a radionuclide.

Gamma Ray Emission

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Gamma Rays vs. X-rays

Difference between x-rays and gamma rays

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Internal Conversion

• Internal Conversion is an alternative process by which an excited nucleus can rid itself of excess energy

• Can be pictured as the nucleus emitting a gamma ray which interacts with an orbital electron. The gamma ray then disappears after giving all of its energy to the electron, and the electron is ejected from the atom

• Characteristic x-rays are emitted as other electrons fill the vacancies left by the conversion electrons

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Internal Conversion

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Summary of Radioactive Decay Mechanisms

DecayMode

Characteristicsof Parent

Radionuclide

Change in Atomic

Number (Z)

Change inAtomic Mass Comments

Alpha Neutron Poor -2 -4 Alphas Monoenergetic

Beta Neutron Rich +1 0 Beta Energy Spectrum

Positron Neutron Poor -1 0 Positron Energy Spectrum

ElectronCapture

Neutron Poor -1 0K-Capture;

Characteristic X-rays Emitted

GammaExcited

Energy StateNone None Gammas Monoenergetic

Internal Conversion

Excited Energy State

None NoneEjects Orbital Electrons; characteristic x-rays and Auger electrons emitted

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SAMPLE PROBLEM 2


1. What particulate form of radiation is identical to a helium nucleus?

2. If the neutron-to-proton ratio of a radioactive atom is too high, what means of radioactive decay will result?

3. Given: Strontium-90 decays via beta decay.

True or False: For every decay of Sr-90, we would measure beta particles that were emitted with the same kinetic energy.

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ACTIVITY AND THEDECAY EQUATION

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1 Bq = 1 disintegration per second

Activity

Activity is the rate of disintegration of a radionuclide.

The SI unit for activity is the becquerel (Bq).

(or 1 “decay” per second)

(or 1 “transformation” per second)

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Multiples & Prefixes (Activity)

Multiple Prefix Abbreviation1 ------- Bq

1,000,000 Mega (M) MBq

1,000,000,000 Giga (G) GBq

1,000,000,000,000 Tera (T) TBq

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Activity Units

In some countries, special units are used to measure activity. The special unit for activity is the curie (Ci):

1 Ci = 3.7 x 1010 dps

And since 1 becquerel (Bq) = 1 dps,

1 Ci = 3.7 x 1010 Bq

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Activity = A = N

Where:

l = decay constantN = number of radioactive atomsA = activity in units of disintegrations

per second (dps or Bq)

Activity Equation

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Decay Constant

NOTE: Units on are

Typically or sec-1 or “per second”

1

time

1

sec

• The decay constant is denoted by l

• The decay constant is unique for each radionuclide

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Half-Life and Decay Constant

T½ = = 0.693

ln 2

• The half-life of a radionuclide (T1/2) is the time required for any amount of that radionuclide to decay to one-half of its initial activity.

• The relationship between half-life and the decay constant is:

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Half-Life

Radioactive decay is an exponential process as shown in the graph.

The rate of decay is determined by a radionuclide’s half-life.

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Half-Lives of Common Radionuclides

Radionuclide Half-Life

Phosphorus-32 14.3 days

Iridium-192 74 days

Cobalt-60 5.25 years

Caesium-137 30 years

Carbon-14 5760 years

Uranium-238 4.5 x 109 years

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Radioactive Decay Equation

A(t) = A0 e- t

Where:

A(t)= activity at any time, t A0 = the initial activity at time t = 0

If we know the initial activity of a given sample of radioactive material and we know its decay constant, we can use the following exponential equation to solve for activity in that sample at any time:

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SAMPLE PROBLEM 3

A vial contains 1E6 atoms of Cs-137. Cs-137 has a half-life of 30 years. After 15 years, how many atoms of Cs-137 remain?


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Specific Activity

Specific Activity is the activity of a radionuclide per unit mass.

SA = A/mass

SA = (0.693/T1/2)(N)

mass

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0.001 g 1 g 1,428,571 g

Amount in gramsof each isotope equaling one curieof activity

60Co27

226Ra88

NatU

Specific Activity Comparison

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Serial Decay

• Some radionuclides decay into progeny that are also radioactive. This is called serial decay.

• As seen within the U-238

series, decay occurs through different means – alpha, beta and gamma.

• Each nuclide within the series

has its own unique half-life, which can vary from fractions of a second to billions of years.

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Serial Decay and Equilibrium

• If you start out with a pure sample of a radionuclide that undergoes serial decay, its decay products will build up within the sample as time passes.

• This build up of decay products can result in different types of equilibrium with the parent radionuclide.

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Types of Equilibrium

Type of Equilibrium

Conditions of Equilibrium

Secular Half-life of parent much greater (>100 times) than that of decay products

Transient Half-life of parent only slightly greater (~10 times) than that of decay product

No Equilibrium

Half-life of parent less than that of progeny

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Secular Equilibrium

Parent Activity (AP)

Daughter Activity (AD)

AP = AD

~ 7 daughter half-lives

If the half-life of the parent is much longer then the daughter, the daughter activity builds up until it equals the parent activity.

At this point, we say the parent and the daughter are in secular equilibrium.

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One example of secular equilibrium occurs with strontium-90. Sr-90 decays with a half-life of 29 years. Its decay product is yttrium-90, which is also radioactive. Y-90 decays with a half-life of 64 hours to stable zirconium-90.

Sr-90 Y-90 Zr-90

Since the half-life of Sr-90 is so much greater than the half-life of Y-90, the Y-90 will be produced until it eventually reaches secular equilibrium with Sr-90 (they will have equal activities).

Secular Equilibrium

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If the half-life of the daughter is only slightly greater than the parent, the daughter activity will grow to an activity greater than the parent activity.

After this time, the daughter activity will begin to decay at about the same rate as the parent. This is called transient equilibrium.

Transient Equilibrium

Parent Activity (AP)

Daughter Activity (AD)

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An example of transient equilibrium is a technicium-99m (Tc-99m) generator used at a hospital. The parent radionuclide in the generator is molybdenum-99 (Mo-99), which decays to Tc-99m with a half-life of 66 hours. The Tc-99m then decays with a half-life of 6 hours.

Mo-99 Tc-99m Tc-99

Since the half-life of Mo-99 is only ten times greater than the half life of Tc-99m, the Tc-99m eventually reaches transient equilibrium with Mo-99 in the generator.

Transient Equilibrium

(Cut-away model of a Tc-99m generator)

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SAMPLE PROBLEM 4


1. True or False: A radionuclide with a very short half-life will have a lower

specific activity than the same quantity of a radionuclide with a very long half-life.

2. What is the stable progeny at the end of the serial decay of U-238?

3. If a radioactive progeny has a much shorter half-life of than its parent radionuclide, what type of equilibrium could eventually occur?

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INTERACTIONS

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Ionizing Radiation

Ionizing radiation has sufficient energy to remove orbital electrons from atoms or molecules with which it interacts.

The specific interaction that occurs depends on the type of radiation.

- beta particles- alpha particles

- photons- neutrons

Radiation

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Charged ParticleInteractions

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1. Ionization:

An electron is ejected from an atom by the passage of a charged particle

Charged Particle Interactions

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2. Excitation:

An electron is raised to a higher orbit by the passage of a charged particle, leaving the atom in an excited state.

Both ionization and excitation events usually result in the emission of characteristic X-rays since orbital electrons transition between energy shells.


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3. Bremsstrahlung or “Braking Radiation”

• When a charged particle is deflected from its path by a nucleus, an X-ray is emitted

• Maximum energy of X-ray is equal to the kinetic energy of the electron

X-ray

e

+

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• Shielding energetic beta-emitting isotopes requires consideration of bremsstrahlung production.

• Bremsstrahlung production depends on the atomic number (Z) of the shielding material. The fraction of beta energy that is converted to photons follows the relationship:

f = 3.5 x 10-4 Z Emax

• Use low-Z materials (e.g., plastic) to shield high-energy beta-emitting isotopes andminimize the production of bremsstrahlungx-rays.

Bremsstrahlung

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Penetrating Distances

Lucite

• Alpha particles are easily shielded by the dead layer of skin on your body.

• Beta particles are typically shielded using plastic or low-Z material because they can penetrate tissue (~0.5 cm per MeV).

• Gamma rays and X-rays are more penetrating and require high density or very thick shielding (e.g., depleted uranium, lead, concrete, or water).

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Range of a Charged Particle

• Range is the average distance a charged particle travels in a medium before coming to rest.

• The path of a heavy charged particle is almost a straight line, but the path of electrons (betas) is not straight.

b

Range

a

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Charged Particle Energy Transfer

• Specific ionization – average number of ion pairs created per unit distance a charged particle travels

Alpha particles in air: 20,000 – 60,000 ion pairs/cmBeta particles in air: 100 ion pairs/cm

• Linear Energy Transfer (LET) – rate of energy transfer per unit distance along a charged particle’s path (MeV/cm)

5.3 MeV alpha : 47 mm in tissue474 MeV/cm1 Mev beta: 4300 mm in tissue 1.87 MeV/cm

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Specific Ionization and LET

• Alpha particles have high specific ionization and high LET due to their mass and double positive charge

• Beta particles have low specific ionization and low LET due to their small mass and single negative charge

a particle

++++++++++++++++++++++++++

- - - - - - - - - - - - - - - - - - - - - - - -

b particle -

++ +

+

-

- -

+

-

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Photon Interactions

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Photons vs. Charged Particles

Since photons have no charge, they interact with matter differently than charged particles

For photons, we discuss the probability of interaction per unit distance travelled

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Photons interactions that are important to health physics:

• Photoelectric Effect

• Compton Scattering

• Pair Production

Photon Interactions

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Photoelectric Effect

1. Incoming photon interacts with an atom as a whole.

2. Photon disappears after giving up all its energy, and an electron (usually from the K-shell) is ejected from the atom.

The photoelectric effect is the predominant interaction mechanism for low energy photons.

e-

KL

M

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Compton scattering is dominant for intermediate photon energies.

1. Photon (g) interacts with outer orbital electron.

2. Photon is scattered after transferring energy to the electron, which is ejected from the atom.

3. The scattered photon (g’) leaves at a different angle with less energy.

Compton Scattering

q

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Pair Production

Must occur in the close vicinity of a nucleus. The incoming photon is absorbed and an electron-positron pair appears.

Requires minimum incoming photon energy of 1.022 MeV (0.511 MeV for the electron + 0.511 MeV for the positron)

Positron ultimately combines with a stationary electron. They annihilate to produce two photons, each having 0.511 MeV energy and travelling in opposite directions

e-

e+

0.511 MeV

0.511 MeV

e+ e-

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Linear Attenuation Coefficient

The linear attenuation coefficient (m) is the total probability that a photon will interact as it travels through a material (units of cm-1).

It is the sum of the probabilities of the different photon interactions occurring:

= PE + CS + PP

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Photon Interactions with Matter

PROBABILITY (m)

Note: Curves will shift slightly depending on the material

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Neutron Interactions

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• Symbol - n• No charge• Rest energy (mass) 939.507 MeV

Primary neutron interactions with matter:

• Scattering (Elastic and Inelastic)• Absorption (Neutron Capture)

Properties of Neutrons

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Neutrons are usually classified by the amount of kinetic energy they possess:

• Thermal (0.0025 eV)• Slow (1 - 100 eV)• Epithermal (100 eV – 100 keV)• Fast (100 keV – 1 MeV)• Ultrafast (>1 MeV)

Properties of Neutrons

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Elastic scattering - neutron interactions with particles of roughly the same mass (somewhat like billiard ball collisions)

• Important for hydrogen-rich materials (e.g., water, wax, concrete). The hydrogen nucleus is approximately the same mass as a neutron, so scattering with hydrogen nuclei can result in the neutron losing much (or all) of its kinetic energy.

• Accounts for about 80% of fast neutron dose to tissue

Elastic Scattering of Neutrons

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Elastic Scattering of Neutrons

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Inelastic scattering – neutron interactions with particles of much greater mass, like iron nuclei

• During this process, kinetic energy and momentum are not conserved. Rather, some of the kinetic energy is transferred to the target nucleus which excites the nucleus.

• The energy that was transferred to the target nucleus is typically released as a gamma ray.

Inelastic Scattering of Neutrons

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Inelastic Scattering of Neutrons

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• Nuclear reactions in which an atomic nucleus interacts with one or more thermal neutrons and they merge to form a heavier nucleus.

• The heavier nucleus that is formed is usually created in an excited state. It may shed its excess energy as particles or gamma rays.

• For certain nuclei (e.g., U-235), absorption of a neutron may cause the nucleus to split into fragments or fission.

Neutron Absorption Reactions

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The probability that neutrons will be absorbed by a nucleus of a given element is called the cross section.

Unit is the barn, where 1 barn = 10-24 cm2

One barn is roughly equivalent to the cross-sectional area of a uranium-238 nucleus.

IMPORTANT NOTE: Absorption cross sections are very dependent on neutron energy (typically, cross sections increase as neutron energy decreases).


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(n, particle)

CoCon 605910

(n, gamma)

LiMoUUn 1399523692

23592

10 *

(n, fission)

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Fission occurs when a neutron interacts with a fissile nucleus, causing the nucleus to split into radioactive fission fragments.

Fission Reaction

Neutrons are produced which can create more fissions.

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Neutron Activation

Activation is the process by which a stable nucleus absorbs a neutron and become radioactive.

Cobalt-60 (Co-60) is the activation product that contributes the most dose to workers at commercial nuclear reactors.

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1. What are three interactions through which charged particles lose their kinetic energy?

2. What is the threshold energy for pair-production to occur?

3. What is the term for the total probability that a photon will interact with the atoms or molecules within a given media?

4. Write 23 barns numerically, including the appropriate SI units.

SAMPLE PROBLEM 5


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QUANTITIES AND UNITS

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Quantities and Units

Radiation causes biological damage by depositing its energy in living tissue. In order to fully understand the mechanisms that govern this process, you should understand the following quantities and their units:

• Exposure• Kerma• Absorbed Dose• Equivalent Dose• Effective Dose

• Committed Equivalent Dose

• Committed Effective Dose

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Exposure

• Exposure is the amount of ionization produced in air from photons (X-rays and gamma rays)

• When photons interact with air molecules, they ionize the molecules creating charge carriers

• Thus, the unit used to measure exposure is the coulomb/kg (C/kg), which is charge per unit mass.

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• Exposure applies only to photons

• Exposure applies only to measurements in air

• Exposure is defined only for photon energies up to 3 MeV

Exposure

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• Kerma (Kinetic Energy Released per unit Mass)

• Kerma is the sum of the initial kinetic energies of all the charged particles liberated by photons and neutrons that interact within in a mass of material.

• The unit of kerma is the J kg-1

• The special name for the unit of kerma is gray (Gy)

Kerma

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The exposure, X, in units of C kg-1, is related to kerma in air (Ka)as follows:

X =

Where:

• g is the fraction of secondary electron energy that is radiated as bremsstrahlung

• W is the average energy spent by an electron to produce an ion pair in a given medium

• e is the charge of an electron

W

Ka (1 – g) e

Kerma vs. Exposure

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Absorbed Dose

• The energy imparted by radiation or secondary ions created by radiation in a given mass of any material

• The unit for absorbed dose is Joules per Kg (J kg-1)

• We give this unit a special name, the gray (Gy)1 Gy = 1 J kg-1

• Absorbed dose applies to all ionizing radiations at all energies in all media, including human tissue

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Absorbed Dose vs. Kerma

Energy imparted is the energy incident minus the energy leaving the mass (basically the energy that is absorbed locally by the medium)

• Kerma represents the transference of energy from photons (or neutrons) to directly ionizing particles. The subsequent transference of energy from these directly ionizing particles to the medium (e.g. air or tissue) is represented by the absorbed dose.

• In a region of electronic equilibrium, the kerma and absorbed dose are equal.

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Absorbed Dose

• Absorbed dose is a general quantity that encompasses all radiation types (i.e., alpha, beta, gamma, etc.). It does not take into account the different qualities of the different types of radiations.

• To account for the biological effectiveness of each type of radiation, you must use a radiation weighting factor (WR).

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Radiation Weighting Factors

Radiation Type and Energy Range wR

Photons 1

Electrons and muons 1

Protons and charged pions 2

Alpha particles, fission fragments, heavy ions

20

Radiation Weighting Factors are used in radiation protection to adjust for differing biological effects.

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Radiation Weighting Factors

Radiation Type and Energy Range

wR

Neutrons A continuous function of neutron energy

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• WR is selected for the type and energy of the radiation incident on the body, and is used to calculate a biological meaningful quantity called Equivalent Dose.

• The equivalent dose in a tissue T is given by:

HT =

where DT,R is the absorbed dose averaged over the tissue or organ T, due to radiation R.

Equivalent Dose

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Equivalent Dose

• Equivalent dose is a weighted absorbed dose, and is the dose to a given organ or tissue.

• The unit of equivalent dose is the joule per kilogram, with the special name of sievert (Sv).

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Effective Dose

The effective dose is the sum of the weighted equivalent doses in all the tissues and organs of the body.

Effective dose is the dose quantity reported to workers and to regulators. It is given by:

E =

where HT is the equivalent dose in tissue or organ T and wT is the weighting factor for tissue T.

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Tissue Weighting Factors

• Account for fact that the probability of stochastic effects (cancer or hereditary genetic effects) depends on the organ or tissue irradiated

• Represent the relative contribution of irradiation of each organ or tissue to the total bodily detriment.

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Tissue Weighting Factors

Tissue or Organ WT

Bone-marrow (red) 0.12

Colon 0.12

Lung 0.12

Stomach 0.12

Breast 0.12

Remainder Tissues *

0.12

Tissue or Organ WT

Bladder 0.04

Oesophagus 0.04

Liver 0.04

Thyroid 0.04

Tissue or Organ WT

Gonads 0.08

Tissue or Organ WT

Bone surface 0.01

Brain 0.01

Salivary glands 0.01

Skin 0.01

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Intakes of Radioactive Material

• When radioactive material (RAM) is inhaled or ingested, the result is an intake into the body.

• Intakes of RAM are usually expressed in units of Bq or multiples thereof.

• Once radioactive material enters the body, an uptake can occur, which is the absorption of the RAM into a specific organ or tissue.

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Intakes of Radioactive Material

• ICRP 60 defines the annual limit on intake (ALI) for each radionuclide

• The ALI is based on an average effective dose limit of 20 mSv per year

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Committed Equivalent Dose

• Following an intake into the body of a radioactive material, there is a period during which the material gives rise to equivalent doses in the organs or tissues of the body at varying rates

• The time integral of the equivalent-dose rate is called the committed equivalent dose, HT(τ), where τ is the integration time in years following the intake.

• For radiation workers, τ is 50 years, which assumes a 50 year working life.

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Committed Effective Dose

The committed effective dose E(50) for workers is defined as:

E(50) =

where HT (50) is the committed equivalent dose and wT is the specific weighting factor for the tissues and organs affected.

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Traditional Units and SI Units

Quantity SI Unit Other Units

Conversion Factor

Activity becquerel (Bq) curie (Ci)3.7 x 1010

Bq/Ci

Absorbed dose

gray (Gy)

rad100

rad/Gy

Equivalentdose

sievert (Sv) rem100

rem/Sv

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1. Exposure is a quantity that only applies to what type of radiation?

2. List the following in order of increasing radiation weighting factors: a) 5 MeV

protons, b) electrons, c) 90 keV neutrons, d) alpha particles.

3. What is the SI unit for Equivalent Dose?

SAMPLE PROBLEM 6


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TIME, DISTANCE AND SHIELDING

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Time, Distance and Shielding

Although exposure to ionizing radiation carries a risk, it is impossible to completely avoid exposure. Radiation has always been present in the environment and in our bodies. We can, however, avoid undue exposure through the following protection principles:

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100 mSv/hr @ 3 ft25 mSv/hr @ 6 ft

Effect of Distance on Dose Rate

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Inverse Square Law

Intensity of a radiation field decreases as distance is increased due to changes in geometry.

Applies to the force of Gravity, Light, Heat, Electric Fields, Sound and Radiation.

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Inverse Square Law Equation

The general formula of the equation is:

I1(d1)2 = I2(d2)2

Where: I is the Intensity (or dose rate) and

d is the distance from the source

Hence, I2 = I1(d1/d2)2

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SAMPLE PROBLEM 7

The dose rate from a 3.7E6 MBq point source of Co-60 at 2 meters is 0.32 Sv/hr.

Find the exposure rate at 4 meters.


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Specific Gamma-Ray Constant

• The gamma constant, , allows the calculation of dose rate:

• for a point source,• of a gamma-emitting radionuclide,• for a given activity,• at a specified distance from the source.

• G is typically given in mSv/hr at one meter from a 1 Mbq source

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The units of the gamma constant are commonly given as:

at 1 m = mSv

hr · MBq

mSv · m2

hr · MBq

Specific Gamma-Ray Constant

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109Pd 1.3E-7 131I 7.6E-5 54Mn 1.4E-4

133Xe 2.8E-5 65Ni 8.0E-5 192Ir 1.6E-4

99Mo 3E-5 65Zn 8.9E-5 59Fe 1.8E-4

125I 7.4E-5 137Cs 1.0E-4 60Co 3.7E-4

Sample Gamma Constants

mSv · m2

hr · MBq =

For the same activity and the same distance:

Co-60 ≈ 2 x Ir-192, 4 x Cs-137, 5 x I-131Ir-192 ≈ 2 x I-131

Cs-137 ≈ 1.5 x I-131

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There are two point source equations in which the inverse square law is used:

Drate = A

d2

D = A t

d2

Calculating Dose / Dose Rate

Here: A = activity of the point sourced = distance from the point sourcet = time

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What is the dose received by an individual that spends one minute at 3 m from an unshielded 3.7E6 MBq point source of pure 192Ir?

(Given = 1.6E-4 mSv m2 hr-1 MBq-1)

SAMPLE PROBLEM 8


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I = I0e(-x)

Where:

• I0 is the unshielded intensity (or dose rate)

• I is the shielded intensity (or dose rate)• m is the linear attenuation coefficient for the

shielding material in units of cm-1

• x is the thickness of the shielding material in cm

Shielding Equation

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Shielding Calculations

• To perform shielding calculations, the linear attenuation coefficient, , for the shielding material must be determined

• In most tables, you will find the mass attenuation coefficient which is / and has dimensions of cm2/g

• To go from cm2/g to cm-1

(/)() =

Example: What is the linear attenuation coefficient for1 MeV photons in water (see next slide)

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Attenuation Coefficients vs. Energy

From this graph, we find that the mass attenuation coefficient for 1 Mev photons in water is about 0.07 cm2/g.

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• From the previous graph, the mass attenuation coefficient, /, for 1 MeV photons for water is 0.07 cm2/g

• To get the linear attenuation coefficient, we multiply by the density of the absorber material

• The density of water is 1 g/cm3

• (/)() = (0.07 cm2/g)(1 g/cm3) = 0.07 cm-1

Calculating m

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What is the dose rate after shielding a source that emits only 1 MeV photons if the unshielded dose rate is 100 mSv/h and the source is shielded by 1 cm of lead?

Given: The density of lead is 11.35 g/cm3.

SAMPLE PROBLEM 9


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The shielding equation does not fully account for photon interactions within shielding material when you have broad beams or very thick shields. To account for scattered photons and other secondary radiations, we use the buildup factor, B.

Shielding & Buildup

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Shielding Equation with Buildup Factor

I = I0 B e(-mx)

• B = [1 + 2 / 1] ≤ 1

• The buildup factor is dependent on the type and amount of shielding material and the energy of the photon.

• Buildup factors have been calculated for many different types of shielding materials, and can be found in tables.

1 = unattenuated dose rate2 = scattered dose rate

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RADIATIONDETECTION

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Radiation detection relies on the fact that radiation will interact with a detection medium. These interactions cause excitation and ionization events that can then be measured and quantified.

Detecting Radiation

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Detecting Radiation

The media that are used in radiation detectors can be solids, liquids, or gases.

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Gas-FilledDetectors

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• The earliest radiation detectors

• Characterized by an operating voltage that is applied to a gas-filled detector volume

• The detector anode collects electrons formed during ionization of the detector gas by incident radiation

• “Geiger Counter” is one popular example

Gas-Filled Detectors

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Basic Design of Gas-Filled Detectors

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There are three main “regions” in which gas-filled detectors operate. The operating region depends on the high voltage placed across the detector:

• Ionization region

• Proportional region

• Geiger-Mueller (GM) region

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• The earliest radiation detectors

• Characterized by an operating voltage that is applied to a gas-filled detector volume

• The detector anode collects electrons formed during ionization of the detector gas by incident radiation

• “Geiger Counter” is one popular example


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Gas-Filled Detector Operating Regions

IONIZATION

REGION

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Ionization Region

• Detectors operating in this region have sufficient voltage across the anode so that all ionization events in the detector gas create ion pairs that do not recombine before they are measured. For these detectors, the detector output is equal to the energy deposited by the interacting radiation.

• These types of detectors can be used to differentiate between alpha, beta or gamma

• If the meter is set to discriminate between the pulses created by an alpha or beta particle, the count rate of either particle can be determined

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Proportional Region

• This region involves higher anode voltage than the ionization region, causing additional ion events to occur as charge carriers accelerate toward the anode.

• The secondary ionizations make the detector’s output pulse is larger than a detector operating in the ionization region, so signal amplification is not required.

• These detectors can still discriminate between different types of radiations.

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• The high voltage is sufficient to cause very high gas multiplication of electrons, with each primary electrons causing an avalanche of additional ionizing events. This creates a very large output pulse.

• Pulse size detected is the same for each event, whether the incident radiation is alpha, beta, or gamma.

• Thus, detectors operating in this region cannot discriminate between various types or energies of incident radiation.

Geiger-Mueller (GM) Region

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• Ionization chambers are typically used for measuring dose rates

• Proportional counters are typically used for quantification of contamination during surveys and counting smears/air samples

• GM detectors are typically used to detect presence of radiation, e.g. beta contamination friskers and low dose rate (< 200 mR/hr) meters


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Ion Chamber Instruments

Model 9

RO-2

451P

Pocket Dosimeter

RSO-50E

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• Ionization chambers are typically used for measuring dose rates

• Proportional counters are typically used for quantification of contamination during surveys and counting smears/air samples

• GM detectors are typically used to detect presence of radiation, e.g. beta contamination friskers and low dose rate (< 200 mR/hr) meters


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Proportional Counter Instruments

“Rem Ball”(BF3 or He-3)

Model 15(He-3)

“Hand and FootMonitor”

Floor Monitor

Tritium Monitor

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GM Instruments

Energy-compensated

“Pancake” probes

“Pocket meter”

“Radiographer”

“Teletector”

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ScintillationDetectors

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Scintillation Detectors

• These detectors use a solid scintillation crystal rather than a fill gas. Ionizing radiation interacts within the scintillation crystal, which changes the kinetic energy of the radiation into visible light photons.

• The photons are fed into a photosensitive cathode that converts a fraction of the light photons into electrons via the photoelectric effect.

The photoelectrons pass through a photomultiplier tube (PMT) which generates an electrical signal proportional to the scintillator light output.

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Scintillation Detector Design

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Photomultiplier Tubes

• Inside a photomultiplier tube, there are a series of electrodes called dynodes. Each dynode is at a more positive electrical potential than its predecessor.

• Secondary electron emission occurs at the surface of each dynode. Such an arrangement is able to amplify the tiny current emitted by the photocathode, typically by a factor of one million. This creates an easily measured output pulse.

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Photomultiplier Tubes

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• Alpha particles may be detected using a detector with a thin layer of zinc sulfide scintillator (ZnS).

• Photons are typically detected using a scintillator made of sodium iodide (NaI) or organic scintillators.

• Liquid scintillation counting is used for low-energy beta emitters (e.g. Tritium and C-14). Liquid scintillation counters are large non-portable units.

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Alpha Scintillation Detector

(THIN ZINC SULFIDE)

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Alpha Scintillation

Detector


Gamma Scintillation

Detector

Liquid Scintillation

Counter

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Portable Instrument Selection

• Verify your instrument’s calibration is current (calibration is recommended every 6-12 months)

• Perform a visual inspection and battery check

• Source check the instrument to ensure operability

• Be sure the instrument design is appropriate for the type and energy of radiation you will encounter

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Detecting Alpha Radiation

• Alpha particles can be stopped with a sheet of paper. Therefore, the detection medium used cannot be packaged in a thick or dense housing.

• Zinc sulfide scintillation detectors have thin mylar windows and are commonly-used alpha detectors.

• Gas proportional detectors with very thin mylar windows are also used.

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• Beta particles are more penetrating than alphas, but can be stopped with a relatively thin layer of Lucite (plastic) or other low-Z materials

• Gas-filled detectors must have thin windows

• Solid, plastic scintillators (polymerized organic scintillators) are also used to detect beta radiation

Detecting Beta Radiation

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Detecting Gamma Rays

• Gamma rays are very penetrating, so the most efficient gamma detectors are solids, as large as practical.

• Gamma ray detectors include sodium iodide and germanium crystals, as well as plastic scintillators.

• To measure gamma dose rates, portable dose rate meters are frequently gas-filled ionization detectors. To increase the detection efficiency of these detectors, sometimes the gas is pressurized.

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• X-rays are typically lower energy than gamma rays, and some radioisotopes emit low-energy gammas.

• Detectors that are most efficient for lower energy photons have a thinner solid detector and may have side shielding added to reduce background.

Detecting X-Rays and Low-Energy Photons

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NeutronDetectors

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• Neutrons can be detected using boron trifluoride (BF3) gas-filled proportional detectors.

• Other detectors use lithium or helium as the interacting media to detect neutrons (less shipping hazard than BF3).

• Neutron detectors can also be made of fissile material such as uranium and plutonium (the fission products are what are actually detected).

• Fast neutrons can be detected by using a slow neutron detector surrounded by hydrogenous material to slow down the fast neutrons.

Detecting Neutrons

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When a neutron interacts with the boron, an alpha particle is emitted through the reaction 10B(n,α)7Li.

BF3 Neutron Detectors

Often the detector probe is encased in a material with a low atomic number. This helps slow down, or thermalize, the neutrons to increase the interaction probability.

The alpha particles ionize the detector gas and cause a pulse.

The pulse information is then correlated to the neutron flux rate, and consequently to a dose equivalent value.

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3He Neutron Detectors

These detectors rely on the following reaction with thermal neutrons:

1n + 3He 1H + 3T

• In this reaction, the ions that are created deposit kinetic energy in the detector gas through ionization and excitation events.

• The resulting charge that is measured is then correlated to the neutron flux rate, and consequently to a dose equivalent value.

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3He vs. BF3 Detectors

• Boron has a lower neutron cross section (3840 barns) compared with 3He (5400 barns), therefore boron counters are less sensitive than their helium counterparts.

• The energy released per reaction is higher in B-10 than He-3 which enables BF3 counters to discriminate against gamma pulses.

• BF3 is also considered a hazardous material, so some manufacturers have switched to He-3 to avoid additional transportation requirements.

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3He Neutron Detectors

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• Proton recoil detectors can also be used. They typically use methane gas or solid hydrogenous crystals to scatter fast neutrons. The fast neutrons collide with the nuclei of atoms in the detector, transferring kinetic energy that ultimately creates ionization events, which are detected.

Detecting Neutrons

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1. What are the three main high voltage regions that gas-filled detectors operate in?

2. Name a fill gas used in neutron proportional counters?

3. What type of detectors are typically used to identify the presence of beta or gamma contamination?

SAMPLE PROBLEM 10


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SOURCES OFRADIATION

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Radioactivity in Nature

• Primordial – existing since the creation of the Earth. An example is uranium-238.

• Cosmogenic – formed as a result of cosmic ray interactions

• Human produced – exposure to material that is enhanced or formed due to human actions. This includes occupational and medical exposures, exposure to consumer products containing radioactive material, and background radiation from fallout.

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Terrestrial Gamma Radiation from Primordial Radionuclides

• Dose rates from radionuclides (K, U, Th) in the soil vary throughout the world.

• This map shows exposure rates from radionuclides in the soil of the U.S.

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Natural Radioactivity in Soil

Element*Assumed Activity**

Mass of Element* Activity

Uranium 25 Bq/kg 2,200 kg 31 GBq

Thorium 40 Bq/kg 12,000 kg 52 GBq

Potassium-40 400 Bq/kg 2,000 kg 500 GBq

Radium 48 Bq/kg 1.7 g 63 GBq

Radon 10 kBq/m3 11 g 7.4 GBq

* Potassium-40 is a radionuclide** per kg of soil

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Natural TerrestrialDose Rate Map of Switzerland

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Background Radiation - Radon

• Radon is a noble gas (also called “inert”).

• Radon is an alpha emitter. Many of the radon decay products are also alpha emitters.

• Radon and its decay products are the largest contributors to natural

background dose.

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Background Radiation - Radon

• Radon is produced from the radioactive decay of 238U, an isotope of uranium which is naturally present in the environment.

• Radon can diffuse through the soil and foundations of homes. The diffusion is greater when the soil has low moisture content.

• Radon decay products have an electrostatic charge and are attracted to particulates in the air. These can be breathed in and deposited in the lung.

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Radon Transport Into Homes

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Radionuclides Found in Your Body

Nuclide*Total Mass of

Nuclide Found in the Body

Total Activity of Nuclide Found in

the Body

Daily Intake of Nuclides

Uranium 90 g 30 pCi (1.1 Bq) 1.9 g

Thorium 30 g 3 pCi (0.11 Bq) 3 g

40K 17 mg 120 nCi (4.4 kBq) 0.39 mg

Radium 31 pg 30 pCi (1.1 Bq) 2.3 pg

14C 95 g 0.4 Ci (15 kBq) 1.8 g

*Uranium, Thorium and Radium are elements

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Cosmic Radiation

• Made up of high energy particles that are produced outside of the solar system and from solar flares.

• Cosmic radiation contributes to the background radiation on earth. The earth’s atmosphere provides shielding from most of the cosmic radiation.

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Cosmic Radiation

• Cosmic radiation is reduced as it interacts with the atmosphere

• Dose rate increases by a factor of 2 when going from sea level to 10,000 feet altitude

• Cosmic radiation can be a significant concern for astronauts

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Cosmogenic Radiation

• Cosmic radiation interacts with molecules in the upper atmosphere of the earth to produce radioactive materials that are part of our environment.

• Carbon-14, a radioactive isotope with a half-life of 5,730 years, is produced in this manner.

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Cosmogenic Radionuclides

Nuclide Half-life Source Natural Activity14C 5730 yr Cosmic-ray

interactions, 14N(n,p)14C

0.22 Bq/g

3H 12.3 yr Cosmic-rayInteractionswith N and O

1.2 x 10-3 Bq/kg

7Be 53.3 days Cosmic-rayInteractionswith N and O

0.01 Bq/kg

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Fallout

• Nuclear weapons testing during the 1950’s and 1960’s resulted in fission products being dispersed in the environment.

• Most fission products have short half-lives and are no longer present in the environment (e.g., I-131 with an 8-day half-life). However, isotopes with long half-lives such as Cs-137 (half-life of about 30 years) are still present.

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• Citizens of most developed countries receive exposure to radiation each year from various medical and dental procedures

• Medical exposures are on the rise due the increased use of CT scans and PET scans

Medical Exposures

http://en.wikipedia.org/wiki/File:16slicePETCT.jpg

http://en.wikipedia.org/wiki/File:PET-image.jpg

http://en.wikipedia.org/wiki/File:PAN_TEETH.jpg

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The average annual dose from all sources of radiation is ~ 620 mrem.

Average Annual Radiation Exposure for U.S. Citizens

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Natural Radiation Exposure Around the World

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SOLUTIONS TO PROBLEMS

IN SLIDES

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1. What positively charges particles are found in the nucleus of an atom?

2. Is binding energy higher or lower for the innermost electron shells?

3. What is the radioactive isotope of hydrogen?

4. Which isotope has more neutrons: carbon-12 or carbon-14?

SAMPLE PROBLEM 1See slide 43

protons

higher

C-14

H-3 or“tritium”

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1. What particulate form of radiation is identical to a helium nucleus?

2. If the neutron-to-proton ratio of a radioactive atom is too high, what means of radioactive decay will result?

3. Given: Strontium-90 decays via beta decay.

True or False: For every decay of Sr-90, we would measure beta particles that were emitted with the same kinetic energy.


alpha

Beta decay

False, there is a spectrum of beta energies

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SAMPLE PROBLEM 3

A vial contains 1E6 atoms of Cs-137. Cs-137 has a half-life of 30 years. After 15 years, how many atoms of Cs-137 remain?

Use the Decay Equation: A = A0 e(-λt)

Since A = lN, we can rewrite the equation as:

N = N0 e(-λt)

and λ = ln(2)/T1/2 = (0.693/30 y) = 0.023 y-1, so:

N = (1E6 atoms)e[-(0.023 1/y)(15 y)]

N = 7.07E5 atoms

See slide 81

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This problem can also be solved for using a simplified equation based on the number of half-lives that have passed:

N = N0(1/2)n

where n = number of elapsed half-lives

15 years is ½ of the 30 year half-life of Cs-137, so

N = (1E6 atoms)(1/2)0.5 = 7.07E5 atoms

SAMPLE PROBLEM 3(continued) See slide 81

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1. True or False: A radionuclide with a very short half-life will have a lower

specific activity than the same quantity of a radionuclide with a very long half-life.

2. What is the stable progeny at the end of the serial decay of U-238?

3. If a radioactive progeny has a much shorter half-life of than its parent radionuclide, what type of equilibrium

4. could eventually occur?


False

Lead-206(Pb-206)

secular

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1. What are three mechanisms through which charged particles lose their kinetic energy?

2. What is the minimum photon energy required for pair-production to occur?

3. What is the term for the total probability that a photon will interact with the atoms or molecules within a given media?

4. Write 23 barns numerically, including the appropriate SI units.

Ionization, excitation,

bremsstrahlung

1.22 MeV

23E-24 cm2

Linear attenuation coefficient

or m

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1. Exposure is a quantity that only applies to what type of radiation?

2. List the following in order of increasing radiation weighting factors: a) 5 MeV

protons, b) electrons, c) 90 keV neutrons, d) alpha particles.

3. What is the SI unit for Equivalent Dose?


photons

b, a, c, d

sievert (Sv)

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SAMPLE PROBLEM 7

The dose rate from a 3.7E6 MBq point source of Co-60 at 2 meters is 0.32 Sv/hr.

Find the exposure rate at 4 meters.

I2 = I1(d1/d2)2

I2 = 0.32 Sv/hr x (2/4)2 = 0.08 Sv/hr

See slide 151

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What is the dose received by an individual that spends one minute at 3 m from an unshielded 3.7E6 MBq point source of pure 192Ir?

SAMPLE PROBLEM 8

= 1.6E-4 mSv m2 hr-1 MBq-1

A = 3.7E6 MBqd = 3 mt = 1 min = 0.017 hr

D = At/d2 = (1.6E-4 mSv m2 hr-1 MBq-1 * 3.7E6 MBq * 0.017 hr) (3 m)2

≈ 11.2 mSv

See slide 156

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First, you need the linear attenuation coefficient, .m

The mass attenuation coefficient for 1 MeV photons in lead is 0.07 cm2/g,

The density of lead is 11.35 g/cm3

= (/)() = (0.07 cm2/g)(11.35 g/cm3) = 0.78 cm-1


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Now use the shielding equation to determine theshielded dose rate:

I = I0e(-x)

I = (100 mSv/h) exp[-(0.78 cm-1)(1 cm)]

I = (100 mSv/h)(0.46)

I = 46 mSv/h

SAMPLE PROBLEM 9(continued) See slide 161

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Ionization, Proportional,

GM

BF3 or He-3

GM

1. What are the three main high voltage regions that gas-filled detectors operatein?

2. Name a fill gas used in neutron proportional counters?

3. What type of detectors are typically used to identify the presence of beta or gamma contamination?

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END OFHEALTH PHYSICSFUNDAMENTALS

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