01 Radiation Units

8/9/2019 01 Radiation Units

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Radioactive decay is the process by which unstable

atoms transform themselves into new chemical

elements

Introduction


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1 Bq = 1 disintegration per second

Activity

The amount of a radionuclide present

SI unit is the becquerel (Bq)


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Multiples & Prefixes (Activity)

Multiple Prefix Abbreviation1 ------- Bq

1 x 106 Mega (M) MBq

1 x 109 Giga (G) GBq

1 x 1012 Tera (T) TBq

1 x 1015 Peta (P) PBq


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UnitsCurie (Ci) = 3.7 x 1010 dps

Becquerel (Bq) = 1 dps (SI)

1 Ci = 3.7 x 1010 Bq


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The Decay Constant is denoted by

NOTE: Units on are

Typically or sec-1 or “per second”

Decay Constant

1

time

1sec


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A = N

where “A = activity” has units of

disintegrations per second(dps or Bq)

Activity


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The half-life is the time required for an amount of any

radionuclide to decay to one-half of its initial value.

The relationship between half-life and decay constantis:

Half-Life and Decay Constant

T½ =0.693


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Half-Life


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Radioactive Decay

The amount of activity decayed away after“n” half -lives is given by

A

Ao

1 -

represents the fraction of the initial

activity that still exists at time t

A

Ao


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Half-Life

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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Exercise 1

A criticality accident occurs in a Uranium processing facility.

1019 fissions occur over a 17 hour period. Given that the fissionyield for 131I is 0.03 and its half-life is 8 days, calculate the 131I

activity at the end of the accident. Neglect 131I decay during the

accident.

Activity = N = x

x ( 1019 x 0.03) = 3 x 1011 Bq 131I

0.693

8 days

1

86,400 sec day-1

3 x 1011 Bq

3.7 x 1010 Bq/Ci= 8.1 Ci 131I


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Radioactive Decay Equation

N(t) = No e-

t

= -

N(t)dNdt

Expressing the equation in terms of activity:

N(t) = No e- t

A(t) = Ao e- t

where A(t) = activity at any time t

and Ao = the initial activity at time t = 0

or

Integrated


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Mean Life and Half-Life

However, when t = T½, the activity decreases to ½ of the

original value:

A = Ao e- t

or

A

Ao = e- t

A

Ao =

½Ao

Ao = ½

½ = e - T½

Take the natural logarithm of both sides

ln (½) = -T½ ln (½) = ln (e ) - T½


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1=

ln (½)

-T½ Regrouping terms yields

But ln (½) = - ln (2) so:

1=

- ln (2)

-T½

ln (2)

T½ =

but ln(2) = 0.693

1=

ln (2)

T½

Mean Life

= 1.44 T½ = Tm 1 =

0.693T½

where Tm , mean life,,

Mean Life and Half-Life


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A radionuclide has a half life of 10 days. What is the

mean life?

Exercise 2

Mean Life = 1.44 T1/2

= 1.44 x 10 days

= 14.4 days


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M = molecular weight of sample

Av= Avogadro's number(= 6.02 x 1023 nuclei/mole)

= r =ioisotope decay constant ( = ln 2 /half-life)

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The specific activity of a radioactive source is defined as the

activity per unit mass of the radioisotope sample.

Activity can be calculated from


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Calculate the specific activity of pure tritium (3H) with a half-

life of 12.26 years.

Substitute T1/2 =12.26 years and M=3 grams/mole to get the

specific activity in disintegrations/(gram – year).

Exercise 3


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ENERGY

• It defined as the kinetic energy gained by an electron

which its acceleration through a potential differenceof 1 volt.

•

The unit for energy is the electron volt or eV

• The electron volt is a convenient unit because the

energy gained from an electric field can be easily

obtained by multiplying the potential difference by

the number of electronic charges carried by the

particle.

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• For example, an alpha particle that carries an

electronic charge of +2 will gain an energy of 2 ke Vwhen accelerated by a potential difference of 1000

volts.

• SI unit of energy

1eV=1.602 x 10-19 J

1fJ(=10-15 J) = 6.241 x 103 eV

femtojoule (fJ)

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• The energy of an X-or gamma-ray photon is related to

the radiation frequency by

where h = Planck's constant

(6.626 x 10-34

J · s, or 4.135 x 10-15

eV · s)v = frequency

The wavelength λ . is related to the photon energy by

where λ is in meters and E is in e V.23


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What is the lowest wavelength limit of the X-rays emitted by a

tube operating at a potential of 195 kV?

Since an x-ray must essentially be created by the de-excitation

of a single electron, the maximum energy of an x-ray emitted in

a tube operating at a potential of 195 kV must be 195 keV.

E=hv E=hc/

Exercise 4


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RADIATION UNITS AND DOSEQUANTITIES

IAEA Post Graduate Educational Course Radiation Protection and Safe Use of Radiation Sources


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Exposure : X

•Exposure is a dosimetric quantity for ionizingelectromagnetic radiation, based on the ability

of the radiation to produce ionization in air .

• This quantity is only defined for

electromagnetic radiation producing

interactions in air.

Diagnostic Radiology Part II : RadiationPhysics

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•Exposure is the absolute value of the total chargeof the ions of one sign produced in air when all

the electrons liberated by photons per unit mass

of air are completely stopped in air.

Exposure : X


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X = dQ/dm


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Exposure : X

•The SI unit of exposure is Coulomb per kilogram[Ckg-1]

• The former special unit of exposure was

Roentgen [R]

• 1 R = 2.58 x 10-4 Ckg-1

• 1 Ckg-1 = 3876 R


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Exposure rate: X/t Exposure rate (and later, dose rate) is the exposure

produced per unit of time.

The SI unit of exposure rate is the [C/kg] per second

or (in old units) [R/s].

In radiation protection it is common to indicate these

rate values “per hour” (e.g. R/h).


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Ab b d d D


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Absorbed dose, D

• The absorbed dose D, is the energy absorbed per unit

mass.• This quantity is defined for all ionizing radiation (not

only for electromagnetic radiation, as in the case of

the “exposure”), and for any material.

• D = dE/dm. The SI unit of D is the Gray [Gy].

• 1 Gy = J/kg.

• The former unit was the “rad”. 1 Gy = 100 rad.


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Relation between absorbed dose and exposure

•

It is possible to calculate the absorbed dose in amaterial if the exposure is known

• D [Gy]. = f . X [Ckg-1]

–

f = conversion coefficient depending on medium

• The absorbed energy in 1 gram of air exposed

to 1 [Ckg-1] of X-rays is 0.869 [Gy]

f (air) = 0.869


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Example of conversion coefficient: f

f values (([[GGyy]] / [[CCk k gg--11]]))

Photon

energy

Water Bone Muscle

10 keV 0.91 3.5 0.93

100 keV 0.95 1.5 0.95


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Mean absorbed dose in a tissue or organ

• The mean absorbed dose in a tissue or

organ DT is the energy deposited in the

organ divided by the mass of that organ.


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• The equivalent dose H is the absorbed dosemultiplied by a dimensionless radiation weighting

factor, wR which expresses the biological

effectiveness of a given type of radiation

• To avoid confusion with the absorbed dose, the SI

unit of equivalent dose is called the Sievert (Sv). The

old unit was the “rem”

1 Sv = 100 rem

Equivalent dose: H


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Radiation weighting factor, wR

•

For most of the radiation used in medicine(X-rays, , e-) wR is = 1, so the absorbed

dose and the equivalent dose are

numerically equal

• The exceptions are:

– alpha particles (wR = 20)

– neutrons (wR = 5 - 20).


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Radiation weighting factor, wR


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Ti i h i f


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Tissue weighting factors, wT

ORGAN /

TISSUE

WT ORGAN /

TISSUE

WT

Bone marrow 0.12 Lung 0.12

Bladder 0.05 Oesophagus 0.05

Bone surface 0.01 Skin 0.01

Breast 0.05 Stomach 0.12

Colon 0.12 Thyroid 0.05

Gonads 0.20 Remainder 0.05

Liver 0.05


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Eff i d E


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Effective dose, E

E = T wT.HT

E : effective dose

wT : weighting factor for organ or tissue T

HT : equivalent dose in organ or tissue T


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Non-SI Units

Quantity Old Unit SI Unit Conversion

Activity curie (Ci) becquerel (Bq) 1 Ci=3.7 x 1010Bq

Absorbed

Dose rad gray (Gy) 1 rad = 0.01 Gy

Equivalent

Dose rem sievert (Sv) 1 rem = 0.01 Sv


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In a mixed radiation environment, a person receives 20 mGy of

γ-ray dose and 2 mGy of slow neutron dose.

Calculate the total equivalent dose received by the person.

01 Radiation Units

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