radioactivity and radiation

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Radiation Physics and Dosimetry

Ibrahim Idris Suliman, PhD

Institute of Radiation Safety,

Sudan Atomic Energy Commission



2

Carry enough energy which if deposited in matter can

produce ions

Types of RadiationTypes of Radiation

Radiations

Electromagnetic Particles

Non-ionizing indirectly ionizing charged uncharged

• Radar

• Radio

• IR (heat)

• Visible• ultraviolet

• !particles

• " !particles• "#!particles• fast ions

• neutrons• $!rays• %!rays



RADIOACTIVITY ANDRADIOACTIVITY ANDRADIATION SOURCESRADIATION SOURCES

Chapter I



E&EC'R*+,E'IC R*-I*'I,E&EC'R*+,E'IC R*-I*'I,

&ight is electromagnetic radiation

a form of energy

.as both electric and magnetic components

Characterised by

wavelength (/)

fre0uency (1)



2*VE C.*R*C'ERI3'IC32*VE C.*R*C'ERI3'IC3

2avelength (/)4 'he distance between twoconsecutive pea5s in the wave




6re0uency (1)4 'he number of waves (or cycles) per unit time




'he product of wavelength (/) and fre0uency (1)is constant



P*R'IC&EP*R'IC&EC.*R*C'ERI3'IC3C.*R*C'ERI3'IC3

Particle!li5e properties

Photons or 0uanta

7 8 h1 8 hc9/

where h is Planc5:s constant

6or a typical diagnostic $!ray

/ 8 ;<=>!== m photon energy is ?; 5eV



E&EC'R*+,E'IC 3PEC'R@E&EC'R*+,E'IC 3PEC'R@




* triangular prism dispersing light




Name (m) ν (Hz) Interesting Facts

Radio9'V =>!= A =>!B => A =>B &ow D ν are reflected

from earth:s atmosphere

icrowaves =>!F A =>!= =>== A => Cellular phonesG Radar

Infrared =>!H A =>!F =>=B A => D.eat radiation

Visible B<=>!H A H<=>!H HJ<=>=B A BF<=>=B K =9B> of total spectrum

@ltraviolet =>!L A HM=>!H =>=? A =>=B DNurning rays of sun

$!rays =>!== A =>!L =>= A =>=? tissue damageG ionisation

+amma rays O=>!== =>= tissue damageG ionisation



+E,ER*& PRPER'IE3+E,ER*& PRPER'IE3

Intensity (I) of a beam of radiation

rate of flow of energy per unit area (*) perpendicular to

the beam

Reduction in intensity by

the inverse square la

attenuation by interaction with matter



I,VER3E 3Q@*RE &*2I,VER3E 3Q@*RE &*2

'he intensity of a beam of radiation decreases as the inverse of the

s0uare of the distance (r) from that source

where E is the rate of energy emission of the source

*pplies to all radiations under defined conditions

for a point source

in the absence of attenuation

;B r E I π

=



I,VER3E 3Q@*RE &*2I,VER3E 3Q@*RE &*2



15

Nuclear PropertiesNuclear Properties

• The nuclear charge is +e times the number (Z ) of protons.

• Hyrogen!s isotopes"

# Deuterium" Hea$y hyrogen. Has a neutron as %ell as a

proton in its nucleus.

# Tritium" Has t%o neutrons an one proton.

• The nuclei of the euterium an tritium atoms are calle

deuterons an tritons.

• &toms %ith the same Z ' but ifferent mass number A' are

calle isotopes.



16

Nuclear tructure

a) Proton positi$e charge

mass *.,- */2, 0g 1 * u

b) Neutron

isco$ere by Cha%ic0 (stuent of utherfor)

hypothesi3e to account for mass of atom

isco$ere %ith scattering eperiments

3ero charge

mass *.,4 */2,

0g 1 * u mass of neutron 1 mass of proton + mass of electron

neutron can e5ect electron to form proton' but it!s not a

proton an an electron



17

Nuclear PropertiesNuclear Properties

• The symbol of an atomic nucleus is .%here Z 6 atomic number (number of protons)

N 6 neutron number (number of neutrons)

A 6 mass number (Z + N )

X 6 chemical element symbol

• 7ach nuclear species %ith a gi$en Z an A is calle a

nuclide.

• Z characteri3es a chemical element.

• The epenence of the chemical properties on N isnegligible.

• Nuclies %ith the same neutron number are calle isotones

an the same $alue of A are calle isobars.



Size of nuclei

Some Properties of Nuclei

• How close an α particle can approach

to a nucleus of charge Ze?

d

Zeek

r

qqk mv ee

))(;(

;

= ;=; ==

silver forfm;>

nucleusgoldforfmF;m=>;FB =B

;

;

=×≈= −

mv

Zek d e

Rutherford’s estimate1 fm = 1!1" m

#ppro$imatel% most nuclei are spherical and

ha&e an a&erage radius r 'F9=

> Ar r =

#ll nuclei ha&e nearl% the same densit%( Nuclear sta)ilit%• *he force that )ind nucleon together +strong force, is stronger than

the -oulom) force . this gi&es sta)ilit% to nuclei(• /ight nuclei are most sta)le if N=Z0 while hea&% nuclei are more sta)le

if NZ(



19

Nuclear tabilityNuclear tability

• The bining energy of a nucleus

against issociation into anyother possible combination ofnucleons. 7. nuclei R an S.

• Proton (or neutron) separationenergy "

# The energy re8uire to remo$eone proton (or neutron) from anuclie.

• &ll stable an unstable nucleithat are longli$e enough tobe obser$e.



2inding energ%

2inding 3nerg%

• *he total mass of a nucleus is alwa%s less than the sum of the masses

of its nucleons( *herefore the total energ% of the )ound s%stem +the nucleus, is less than the com)ined energ% of the separated nucleons(

*his difference is called )inding energ%(• 2inding energ% of deuteron . a )ound s%stem of a neutron and a proton

+also the nucleus of deuterium,

eV;;;Bu)eV)9(=JF=)(u>>;FLL>(

u>>>;FLLu>=B=>;;)u>>L??J=u>>HL;J=()(

==

=−+=−+=∆

b

d n p

E

mmmm

• 2inding energ% per nucleon pea4s at

a)out #=5( *his means the elements

around this pea4 are more sta)le( *he a&erage )inding energ% per nucleon

is 6 7e8(



21

B. E .+ mc2 = m1c

2 + m2c2 + ...= m

ic

2∑

9ass efect

From special relativity, adding energy increases mass:

B. E .= mi − m∑{ }c

2

B. E .= ∆mc2

∆m = mass defect = constituents - composite



RadioactivityRadioactivity The activity A of a radioactive material with N radioactive atoms isdefined as the spontaneous nucleus disintegration per unit time:

For a mixture of n radioactive materials valid:

The unit of radioactivity is Becquerel, Bq Bq ! "# $ disintegration per second% &urie ! '()*++ Bq

(=I=)dN

Adt

= − − − − − − − − − − −

(=I;)n

i

i

A A= − − − − − − − − − −∑

λ λ



Radioactive decayRadioactive decay The activity A of radioactive material is proportional to the numer of

radioactive atoms N for the specific nuclide:

-here . /"#0 is the decay constant( And it is for the specific radionuclide( 1f we apply in the equation $(% this yields:

after solving this differential equation we otain:

N$+% and N$t% are the numer of atoms of the radionuclide respectively attime + and after time t(

(=F) A N λ = − − − − − − − − −

(=IB)dN

N dt

λ = − − − − − − − − −

( ) (>) (=IJ)t N t N e λ −= − − − − −



Radioactive decayRadioactive deca y

Because the activity of the radionuclide is proportional to the numer ofradioactive nuclide eq( $('%, it is also valid for the activity that:

A$+% and A$t% are the activity of the radionuclide respectively at time + andafter elapse of time t(

The half life of the radioactive material T 23is time required for the nuclidesto decay to half of its initial activity(

4ou can wor5out also that:

( ) (>) (=?)t A t A e λ −= − − − − − −

=9 ;

ln ;(=IH)T

λ

= − − − − − − − −

=9 ;( ) (=9 ;) (=L)

t

T A t = − − − − − −



9eca% constant and half!life +cont’d,

• 3$ponential deca% and half!life

t e N N

λ −= >e$ponential deca%

! *he half!life *1:; of a radio acti&e su)stance

is the time it ta4es for half of a gi&en num)er

of radioacti&e nuclei to deca%(

;9=

> ;=

T t n N N

n

=

=

;9=

>>

;

T e N

N λ −=

λ λ ?F>;ln

;9= ==T

• <nits of acti&it% R +curie and )ecuerel,

decays9s=>FHCi= =>×≡ unit)(3I decay9s=N0= =



3$ample ' #cti&it% of radium

• *he half!life of the radioacti&e nucleus is 1(5$1> %r( f a sample

contains >($115

such nuclei0 determine the followings' +a, the initial acti&it% in curies

s=>J>s9yr)=>yr)(F=J?=>?=(=>HF

;9= ×=××=T !===

;9= s=>BI=9?CFI> −×== T λ

+), the num)er of radium nuclei remaining after @(6$1> %r

Ci==Ci=>==decays9s=>;B !JJ

>> µ λ =×=×== N R

Ra;;?

LL

lives!half >IFlife!yr9half =>?I=

yr =>LIBF

F

=×

×=n

nuclei=>LIF;)nuclei)(=9=>>IF();9=( =JFI>=?

>

×=×=→= N N N n

+c, the acti&it% at this later time

Ci=Bdecays9s=>FJ B µ λ =×== N R



Radio #cti&ities

3$ample' Radon gas

• Radon is a radioacti&e gas that can )e trapped in the )asements

of homes0 and its presence in high concentrations is a 4nown health hazard( radon has a half!life of >(6> da%s( # gas sample contains

@($16 radon atoms initiall%(

+a, How man% atoms will remain after 1@( da%s ha&e passed if no more

radon lea4s in?

Rn;;;

L?

!=

;9= day=L=I>9?CFI> == T λ atoms=>=HIFatoms)=>>>IB( Hdays)>=B)(day=L=>(L

>

!=

×=×== −− ee N N t λ

+), Ahat is the acti&it% of the radon sample after 1@( da%s?

!=!?B!= s=>;I>Cs)=>day9LI?B=)(day=L=I>( ×=×=λ

N0??Fdecays9sF?? === N R λ +c, How much time must pass )efore BBC of the sample has deca%ed?

t N e N e N N t t λ λ λ −=+== −− )ln()ln()ln()ln()ln( >>>

days;JJs=>;>;

s=>>;

))>=>9(ln()9ln()ln()ln( ?

=!?

>>>> =×=×

==−

=−

N N N N N N t

λ λ



"pecific activity, A"pecific activity, Ass

1n one gram of a material which constitute out of a one sort of atoms$nuclide%, there will e NA26 atoms( where NA Avogadro7s numer /mol#0 and6 is molar mass /g mol#0( The specific activity As /activity per unit mass0 isgiven y:

This type of material is called free carrier 1n some cases the radioactive material constitute out of sorts of atoms( The

numer of atoms of a certain element in gram material, existing out suchmolecules is n(NA26molecuul where n is the numer of nuclide of the atom thatappear in the chemical onding ($e(g( 3 atoms hydrogen in water molecule:

839% and 6molecuul 6olar mass $for water 6 ! (+;%(with the atomic fractionfatom it possile to calculate the numer of the radioactive atoms( <quation$(=% will ecome:

=( ) (=C) A s

N A Bqg

M

λ −= − − − − − −

(=I=>) A s atom

N A nf

M λ = − − − − − −



Radioacti&e sources

-hart of the Nuclides

sotopes Z = constant ? s o ) a r s # =

c o n s t a n t

l

h d



Alpha decayAlpha decay

> The type of decay ta5e place in radioactive nuclidewith high mass numer where 6mother ? 6daughter @ 6

$6!mass%( The mother radionuclide decay todaughter 4 as follows:

B B ;

; ; (=I=C) A A

Z Z X Y He Qα

− +

−→ + + − − −

The energy freed from the reaction C is sharedetween the : particles and the daughter nuclide alsonamed recoil nucleus( the conservation of energy andmomentum requires that'

B(=I;>)reoi!

reoi!

m E E Q

M m A

α

α α

α

= • ≈ • − − − −+

-here A is the mass numer of the mother nuclide

9 P



9eca% Processes

#lpha deca% +cont’d,

• 3$ample ' 9eca%ing radium

He Rn Ra B

;

;;;

L?

;;?

LL

+→

-alculate the amount of energ% li)erated in the deca%'

u;;?I>;>=HFuBI>>;?>;u>=HJH=I;;; =+=+ α mmd

uI>I>>J;;Cu>;>=HFI;;?u>;JB>;I;;?)( =−=+−=∆ α mm M m d p

eVBLH=eV9u)u)(CF=BCB >>J;;C>( == E



DD## decaydeca y D# decay 9ccurs at radionuclide with excess numer of neutron( The access

neutron diminish at the nucleus of the atom and neutron is converted toproton, where electron and anti#neutrino originate and emitted as radiationparticles(

1n most general forms, the mother nuclide decay to a daughter 4 in an

isoar process i(e( the mass numer A is not changed in the decay(

The transferred decay energy CD which emitted in the nuclear

transformation is shared etween the D# particle and the anti#neutrino( Thea average D energy is 2' of the maximum energy(

R

(=I==)n p vβ −

→ + + − − − − − −

R >

= = (=I=;) A A

Z Z X Y v Qβ β −+ −

→ + + + − − −

R

GmaM

=(=I=F)

F E E β β ≈ − − − − − −



DD@@ decaydecay

> 9ccurs in radionuclide with excess numer of protons, the proton in thenucleus is converted in to neutron( This is also in the form of wea5interaction(

(=I=B) p n vβ +→ + + − − − −

The neutron stayEs in the nucleus, where the positive particle eta

plus, D@

, and the neutrino v oth leave the atom with certain 5ineticenergy(

;+ particle is electron with positive charge also called positron( Thepositron gives itEs 5inetic energy in further interaction with ordinaryelectron( The positive and negative electrons are then converted totwo photons each with energy ; 5e $represents the rest massenergy of electron% and are emitted in opposite directions( Thisprocess is called annihilation and is a characteristics of the ;+ radiation



DD@@ decaydecay

> This decay process has threshold energy of +33 5e $two times rest massof electron%(

> 1n general, the mother nuclide decays to daughter nuclide 4 in D@ decay and isoar process

>

= = (==J) A A

Z Z X Y v Q β β +

−→ + + + − − − −



electron captureelectron capture

> 1f the decay energy of radionuclide with excess protons is less than +335e, then D@ decay is not possile( 1n that case, other form of wea5interaction will ta5e place:

(=I=?) p e n v−+ → + − − − − −

•3lectron capture is one form of radioacti&e deca%( # parent nucleus ma%

capture one of its or)ital electrons and emit a neutrino( *his is a process which•competes with positron emission and has the same effect on the atomic

num)er( 7ost commonl%0 it is a D!shell electron which is captured(

,!!!!!1(1E+



Alpha decayAlpha decay

> The type of decay ta5e place in radioactive nuclide with high mass numerwhere 6mother ? 6daughter @ 6 $6!mass%( The mother radionuclide decay todaughter 4 as follows:

B B ;

; ; (=I=C) A A

Z Z X Y He Qα

− +

−→ + + − − −

The energy freed from the reaction C is shared etween the :

particles and the daughter nuclide also named recoil nucleus( theconservation of energy and momentum requires that'

B (=I;>)reoi!

reoi!

m E E Q M m A

α

α α

α

= • ≈ • − − − −+

-here A is the mass numer of the mother nuclide



1somer decay1somer decay

• &fter alpha an beta ecay the nucleus of the formenuclie remain in an ecite state. The ecite nucleusreturns to the groun state $ia number of stepsemitting high energetic photons. These monoenergeticphotons emitte from the nucleus of the raionuclieare calle gamma rays. & nucleus that remains in such

an ecite state is 0no%n as a nuclear isomer becauseit iffers in energy an beha$ior from other nuclei %iththe same atomic number an mass number.

• <amma raiation is a highenergy electromagneticraiation that originates in the nucleus. It is emitte in

the form of photons' iscrete or bunle of energy thatha$e both %a$e an particle nature.



1nternal conversion1nternal conversion

> This is an alternative to gamma#ray emission, which is the usual method for an excited nucleus to return to the ground state(

> 1n internal conversion, the excited nucleus transfers its energydirectly to one of the most tightly ound orital electron causing itto e eGected from the atom( The conversion electron is eGectedfrom the atom with 5inetic energy equal to the gamma energyminus the inding energy of the orital electron( After theeGection of the internal conversion electron the vacancy is filled yanother shell electron and the atom eGects one or several x#rays orAuger electrons(



"pontaneous fission"pontaneous fission

> -ith high H numer can the instale nucleus spontaneously rea5 up intotwo parts( By this type of decay neutrons come free( Further gammaradiation and eta particles are emitted( The reaction equation is writtenas follows:

=

; >( ) (=I;=)

A A p q

Z Z r r "# X Y Y p q n Q

−

−→ + + − + − −The splitting fragment ha$e ecess neutrons an there for theyare ; raiators



&haracteristic x#rays and Auger electron&haracteristic x#rays and Auger electron

> 1n the decay process of electron capture and internal conversion a

vacancy will e created in the nearest electron shell $the 5#shell%( Thevacancy will e filled y another electron from outer shell emittingcharacteristic x#rays, also called as fluorescence radiation( Theemitted photon is characteristic, ecause the photon energy equals thedifference in the inding energies etween the two shells of thetransition and that is characteristic for the concerned atom(

> The decay scheme of x#ray spectra is given special notation etweenwhich shills the transition will ta5e place( "o called 5 x#rays whichcomes free y transition from I to J shell( Because I#shell has threesu#shells, this can e further specified: 5 x#rays which comes as aresult of transition from I111 su#shell to 5#shell( 53 x#rays which comesas a result of transition from I11 su#shell to 5#shell( The transitionfrom I1 to 5#shell is foridden for quantum mechanical reasons( JD x#rays comes as a result of transition from 6#or N#shell to 5#shell



&haracteristic x#rays and Auger electron&haracteristic x#ra ys and Auger electron> As an alternative to emitting x#ray, the radionuclide can emit so

called Auger electron(



Karent#daughter relationKarent#daughter relation

> The disintegration of radionuclide always lead to stale nuclide( 9ut oforiginal nuclide Np, also called parent radionuclide, a daughter nuclide Nd is formed, which is also radioactive( The activity of the parentradionuclide as a function of time spent can e written y the decay law

eq( $(L%( For the daughter radionuclide this not the case( The numer ofnuclide for the daughter radionuclide can e calculated via twoprocesses: via decay process of the parent and via the decay process ofthe daughter disappear atoms of the radioactive daughter $removal%(

> For Np and Nd one can find the following differential equations:

P = <>p >



p

p p

d p p d d

dN

N dt

dN N N

dt

λ

λ λ

= −

= −,!!!!!!!!!!!!!!!!!!!!!1(;;+

9ut of these formulas we can find the numer of daughter

radionuclide Nd at a time t, also the amount of activity as Ad attime(

Karent#daughter relation

( ) (>)( ) (>) p d d t t t d

d p d

d p

A t A e e A eλ λ λ λ

λ λ

− − −

= − +

−

,!!!!!!1(;@+

( ) (>)( ) (>) p d d t p t t

d p d

d p

N t N e e N eλ λ λ

λ

λ λ

− − −

= − +

−

,!!!!!!1(;>+



Karent#daughter relation

$% .p M +, secular equilirium

$3% .p .d $not .p M+, e(g( T p!+T d%

transient equilirium

The time at which maximum daughteractivity is availale: tmax

( ) (>)(= )d t

d p A t A e λ −

≈ −

!arent "ctivity

Time

#aughter "ctivity

#aughter "ctivity

!arent "ctivity

Time

pd d

p p d d p

T A

A T T

λ

λ λ = =

− −

transient equilirium

secular equilirium

maM

=BB ln lnln

p d p d p

p d d d p

T T T t

T T T

λ λ

λ λ

−= =

− −



Parentaughter relationParentaughter relation

> $'% .p?.d $ no equilirium%#aughter "ctivity

!arent "ctivity

Time

9tained y minimiOing

with respect to t(

( ) p d t t e e

λ λ − −−

Nuclear Reactions



Nuclear Reactions

Nuclear reactions

• *he structure of nuclei can )e changed )% )om)arding them with

energetic particles( Such changes are called nuclear reactions(• First person who o)ser&ed a nuclear reaction in the following process

was Rutherford( He found that protons were released when alpha

particles were allowed to collide with nitrogen atoms'

2% )alancing atomic num)ers and mass num)ers0 we can conclude that

the 4nown nucleus G is in fact isotope of o$%gen'

H X N He ==

=BH

B; +→+

H $ N He =

=

=H

L

=B

H

B

; +→+

3$ample ;B(6 ' 9isco&er% of neutron )% -hadwic4 +1B>;,

X % Be He A

Z +→+ =;

?

C

B

B

;Reaction used'

>?B;

==;CB

=→+=+=→+=+

Z Z

A A

n% Be He

=

>

=;

?

C

B

B

; +→+

Nuclear Reactions



Nuclear Reactions &alues• -onsider the nuclear reaction' He% N H B

;=;?

=BH

;= +→+

initial total mass mi ' u=?I>=H=H?u=BI>>F>HBu>=B=>;I; =+final total mass mf ' u=?I>>;?>;uBI>;F?>;u>>>>>>I=; =+mass difference ∆m' u>=BJHBI>−=−=∆ i f mmm

*he negati&e mass difference comes from the fact that part of

the initial mass energ% is con&erted into 4inetic energ%( *he

&alue is defined as 'f the &alue is positi&e0 the reaction is said to )e e$othermic reaction(

mQ ∆−≡

• -onsider the nuclear reaction' H $ N He =

=

=H

L

=B

H

B

; +→+

eV=CBI=u>>=;L;I> −=−=−= f i mmQ endothermic reaction

# careful anal%sis of this reaction re&eals that0 e&en if the incoming

alpha particle has 4inetic energ% of 1(1B@ 7e8 is not enough to ha&e

this reaction happen )ecause0 although the energ% is conser&ed0

the momentum is not( *he incoming particle needs at least 4inetic

energ% of +m:7' mass of incoming:target particle,(

*hreshold energ%

)9=(min Q M m &E +=



Radiometric quantitiesRadiometric quantities

> Radiometric quantities has application in radiation protection, radiationdosimetry and are also used to descrie interaction of radiation withmatter(

> 1n a situation where particles are emitted aritrary in all directions anenter a sphere of a cross#sectional area da( The fluence

> P!dN2da #################$(3;%

> for a point source that emits N particle in all directions, and which arehomogenous each with energy <( the amount of particle fluence thereforethe numer of particle pass a unit area perpendicularly at a distance r from

the point source:;

(;I;J)B

N

r π Φ = − − − − − − − − − − −

P has a unit of m#3



Radiometric quantitiesRadiometric quantities> The energy fluence Q in this case is then, for mono#

energetic radiation:

> 1n special case of homogeneous parallel eam, the fluencedefinition is same as a numer of particles N that passEs aunit area in a flat surface with surface area " perpendicularto the eam:

> Fluence rate and the energy fluence rate can e written as:

;(=;?)

B

NE

r π Ψ = − − − − − − − − −

+?m2,

(=I;H) N

" Φ = − − − − −− − − − −− −+m2,

d

dt φ

Φ=

d

dt ψ

Ψ=+m2*, +?m2*,



Radiometric quantitiesRadiometric quantities

> For radioactive source, it is possile to write the numer of the emittedparticles per unit time for a radiation sort i as a product of the emissionproaility yi and the activity A of the source( Ta5ing the time differentialform of the eq( $(3;% yields for the point source the fluence rate for theradiation sort i(

iφ

;Bi

i

' A

r φ

π = ,!!!!!!!!!!!!!!!!!1(;6+



aiation prouctionaiation prouction

radioactivity and radiation

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