DR. MOHAMMED MOSTAFA EMAM

INAYA MEDICAL COLLEGE

(IMC)RAD 243- LECTURE 28OCT2015

Units and Measurement of Radiation

Radioactive Decay Law

• This law is given by:

Nt = No . exp (-λt)

whereNo = initial number of radioactive nuclei

Nt = number of radioactive nuclei at time tλ = decay constant (s-1)

• It tells us that the number of radioactive nucleiwill decrease in an exponential fashion withtime with the rate of decrease being controlledby the Decay Constant.

• The decay constant depends on nothing but the nuclear properties.

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Half-Life

• Half Life is an indicator that expresses

the length of time it takes for the radioactivity

of a radioisotope to decrease by a factor of two.

• Some of the radioisotopes have a relatively

short half life.

• These tend to be the ones used for medical

diagnostic purposes because they do not

remain radioactive for very long following

administration to a patient and hence result

in a relatively low radiation dose.

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Logistic Problems with Radioisotope

Handling

• Short half lives (e.g. 99mTc):

Transportation over long distances

• Long half lives (e.g. 226Ra):

Safe storage for a long period of time

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Relationship between Decay Constant

and Half Life

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1

6930

t

.

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Units of Radioactivity

• SI (metric) unit (Becquerel, Bq):

The Becquerel is defined as the quantity of

radioactive substance that gives rise to a

decay rate of 1 decay per second.

• Traditional unit (curie, Ci):

1 Ci = 37 GBq

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Weight of a Given

Radioactivity• Let

• A = activity (in Bq)

• λ = decay constant (s-1)

• L = Avogadro’s number (6.23×1023)

• M = molecular (atomic) weight

• The weight corresponding to the given

radioactivity is calculated from:

L

AMW

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Typical Radiation System

• The quantities which can be measured in a

radiation system are usually associated with

• the source

• the radiation beam

• the absorber

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The Radiation Source

• When the radiation source:

• is radioactive the quantity that is

typically measured.

• is the radioactivity of the source

measured in Becquerel's or in curies.

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The Radiation Beam

• The characteristic of a radiation beam

that is typically measured is called the

Radiation Exposure.

• This quantity expresses how much

ionization the beam causes in the air

through which it travels.

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The Radiation Beam

• The SI unit of radiation exposure is the

coulomb per kilogram (C∙kg-1).

• It is defined as the quantity of X- or γ-

rays such that the associated

electrons emitted per kilogram of air at

standard temperature and pressure

(STP) produce ions carrying 1 C of

electric charge.

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The Radiation Beam

• The traditional unit of radiation exposure is

the roentgen, and is given the symbol R. It is

defined as the quantity of X- or γ-rays such

that the associated electrons emitted per

kilogram of air at STP produce ions carrying

2.58 x 10-4 C of electric charge.

• Often it is not simply the exposure that is of

interest but the exposure rate, i.e., exposure

per unit time. The units which tend to be

used in this case are the C∙kg-1s-1and the

R∙h-112

The Absorber

• Energy is deposited in the absorber

when radiation interacts with it.

• It is usually quite a small amount of

energy but energy nonetheless.

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The Absorber

• The quantity that is measured is called

the Absorbed Dose and it is of

relevance to all types of radiation be

they X- or γ-rays, α- or β-particles.

• The SI unit of absorbed dose is called

the gray (Gy). The gray is defined as the

absorption of 1 J of radiation energy per

kilogram of material (J∙kg-1).

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The Absorber

• The traditional unit of absorbed dose is

called the rad, which supposedly stands

for Radiation Absorbed Dose.

• It is defined as the absorption of 10-2 J

of radiation energy per kilogram of

material.

• 1 Gy = 100 rad

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Equivalent Dose

• Often the effectiveness with which different

types of radiation produce a particular chemical

or biological effect varies with a Quality factor

that is characteristic of the type of radiation.

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Equivalent Dose

• The dose-equivalent (DE) in sievert (Sv) is the

product of the dose in Gy and that quality factor.

• The dose-equivalent (DE) in rem is the product of

the dose in rad and that quality factor.

• Recently, the newly defined radiation weightingfactors, WR have been adopted to represent the

Quality factor.

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Radiation Weighting Factors

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Inverse Square Law• The radiation produced in a radioactive source is emitted in all

directions.

• We can consider that spheres of equal radiation intensity exist around the source with the same number of photons/particles spreading out as we move away from the source.

• Consider an area on the surface of one of these spheres and assume that there are a certain number of photons/particles passing though it.

• If we now consider a sphere at a greater distance from the source the same number of photons/particles will now be spread out over a bigger area.

• Following this line of thought it is easy to appreciate that the radiation intensity will decrease with the square of the distance from the source.

• This effect is known as the Inverse Square Law.

• As a result if we double the distance from a source, we reduce the intensity by a factor of two squared, that is 4. If we treble the distance the intensity is reduced by a factor of 9, that is three squared, and so on.

• This is a very useful piece of information if you are working with a source of radiation and are interested in minimizing the dose of radiation you will receive.

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Interaction of Radiation with

Matter

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Physical Characteristics of the

Major Types of Radiation

One of the main effects to be noticed irrespective of the typeof radiation is that ions are produced when radiationinteracts with matter.It is for this reason that it is called ionizing radiation.

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Alpha Particles• α-particles have a double positive charge and therefore they

will exert considerable electrostatic attraction on the outerorbital electrons of atoms near which they pass.

• The result is that some electrons will be attracted away fromtheir parent atoms and that ions will be produced.

• α-particles are quite massive relative to the other types ofradiation and also to the electrons of atoms of the materialthrough which they are passing. As a result they travel instraight lines through matter except for rare direct collisionswith nuclei of atoms along their path.

• The energy with which α-particles are emitted is alwaysdistinct. For example 221Ra emits an α-particle with an energyof 6.71 MeV. Every α-particle emitted from this radionuclidehas this energy.

• α-particles are very damaging biologically, and this is onereason why they are not used for in-vivo diagnostic studies.

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Beta Particles• β-particles have a negative electric charge (positrons

are not considered here since these particles do notlast for very long in matter before they are annihilated).

• Because of their negative charge they are attracted bynuclei and repelled by electron clouds as they passthrough matter. The result is ionization.

• The path of β-particles in matter is often described asbeing not straight-forward, since they tend to reboundfrom atom to atom.

• The energy of β-particles is never found to be distinctin contrast to the alpha-particles above. The energies ofthe β-particles from a radioactive source forms aspectrum up to a maximum energy.

• β-particles are quite damaging biologically and this isone reason why they are not used for in-vivo diagnosticstudies.

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Spectrum of Beta Radiation

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Gamma Rays• The energies of γ-rays emitted from a radioactive

source are always distinct. For example:• 99mTc (Technetium 99m) emits γ-rays which have an

energy of 140 keV.

• 51Cr (Chromium-51) emits γ-rays which have an energy of 320 keV.

• γ-rays have many modes of interaction with matter.

• Those which are very important to nuclear medicine imaging are • the Photoelectric Effect

• the Compton Effect

• The effects described here are also of relevance to the interaction of X-rays with matter since as we have noted before X-rays and γ-rays are essentially the same entities.

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Photoelectric Effect• When a γ-ray collides with an orbital electron of an

atom of the material through which it is passing it can transfer all its energy to the electron and thus cease to exist.

• On the basis of the Principle of Conservation of Energy we can deduce that the electron will leave the atom with a kinetic energy given by:

kinetic energy = energy of the γ-ray - orbital binding energy

• The resulting electron is called a photoelectron.

• The following phenomena are of importance:• An ion results when the photoelectron leaves the atom.

• The γ-ray energy is totally absorbed in the process.

• X-ray emission can occur when the vacancy left by thephotoelectron is filled by an electron from an outer shellof the atom (electron capture).

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Photoelectric Effect

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Compton Effect (Scattering)

• Here a γ-ray transfers only part of its energy

to a valance electron which is almost free.

• The electron leaves the atom and may act

like a β-particle

• The γ-ray deflects off in a different direction

to that with which it approached the atom.

• This deflected or scattered γ-ray can

undergo further Compton scatterings within

the material.

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Compton Scattering

Fig. 929

Attenuation of Gamma-Rays

• The photoelectric and the Compton effects

give rise to both absorption and scattering

of the radiation beam.

• The overall effect is referred to as

attenuation of γ-rays.

• Remember: γ-rays and X-rays are

essentially the same physical entities.

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Specific Gamma Ray

Constant (G)• It is defined as the exposure rate per unit

activity at a certain distance from a source.

• SI units:

C∙kg-1∙s-1∙Bq-1 (at 1 m)

• Traditional units:

R∙h-1∙mCi-1 (at 1 cm)

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Specific Gamma Ray Constant G(mSv∙h-1∙GBq-1 at 1 m)

γ-Ray ConstantNuclide

0.004241Am

0.012201Tl

0.01657Co

0.01799mTc

0.04199Mo

0.057131I

0.084111In

0.087137Cs

0.36060Co 32

Specific Gamma Ray Constant and Dose

• Given that an object at distance (d) m

away from the source, and that the source

activity is (A) Bq, one can compute the

dose (D) in Sv/h as follows:

2d

AGD

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Attenuation Model

Io = incident intensityIx = transmitted intensityΔI = absorbed intensity = Io - Ix

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Effect of Atomic Number• The magnitude of ∆I is highly dependent on

the atomic number of the absorbing material.

• For example ∆I is quite low in the case of anabsorber made from carbon (Z=6) and verylarge in the case of lead (Z=82).

• Reason:• The atoms of the high atomic number absorber

present larger targets for the radiation to strikeand hence the chances for interactions via thePhotoelectric and Compton Effects is relativelyhigh. The attenuation should therefore berelatively large.

• In the case of the low atomic number absorber, however, the individual atoms are smaller and hence the chances of interactions are reduced.

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Effect of Atomic Number

It is found that:ΔI = k∙Z3 (where k is a constant)

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Effect of Density• A low density absorber will give rise to

less attenuation than a high density

absorber since the chances of an

interaction between the radiation and the

atoms of the absorber are relatively lower.

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Effect of Thickness

• A thick absorber a greater attenuation than

a thin one.

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Effect of Gamma-Ray Energy

• The greater the energy of the γ-rays the less

the attenuation.

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Mathematical Model of

Attenuation• Ix and Io are related by:

• This final expression tells us that the radiationintensity will decrease in an exponential fashionwith the thickness of the absorber with the rate ofdecrease being controlled by the Linear AttenuationCoefficient (μ).

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Linear Attenuation Coefficient• μ is characteristic of individual absorbing materials.

• Some materials like carbon have a small value and are

easily penetrated by γ-rays.

• Other materials such as lead have a relatively large μ and

are relatively good absorbers of radiation.

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Influence of the Linear

Attenuation Coefficient

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Half Value Layer

• An indicator is usually derived from theexponential attenuation equation which helpsus think more clearly about what is going on.

• This indicator is called the Half Value Layer,and it expresses the thickness of absorbingmaterial which is needed to reduce the incidentradiation intensity by a factor of two.

• We can say that when:

• the thickness of absorber is the Half ValueLayer. 43

Relationship between the Linear

Attenuation Coefficient and the

Half Value Layer

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Mass Attenuation Coefficient• the Linear Attenuation Coefficient is useful

when we are considering an absorbingmaterial of the same density but of differentthicknesses.

• A related coefficient can be of value when wewish to include the density, ρ, of the absorberin our analysis.

• This is the Mass Attenuation Coefficientwhich is defined as

• It is usually measured in cm2g-1.

density

tcoefficien nattenuatio linearmass

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