Interaction of radiation with matter - 1
Charged Particle Radiation
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Day 2 – Lecture 1
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Objective
• To understand the following interactions
for particles:
 Energy transfer mechanisms
 Range energy relationships
 Bragg curve
 Stopping power
 Shielding
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Energy transfer mechanism
• Energy transfer from radioactive
particles to other materials depends on:
 the type and energy of radiation
 the nature of the absorbing medium
• Radiation may interact with either or
both the atomic nuclei or electrons
• The interaction results in excitation and
ionisation of the absorber atoms
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Particle Interactions
 When a charged particle interacts with an atom of the
absorber, it may:
 traverse in close proximity to the atom (called a
“hard” collision)
 traverse at a distance from the atom (called a “soft”
collision)
 A hard collision will impart more energy to the material
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Stopping Power
 The amount of energy deposited will be the sum of
energy deposited from hard and soft collisions
 The “stopping power,” S, is the sum of energy
deposited for soft and hard collisions
 Most of the energy deposited will be from soft
collisions since it is less likely that a particle will
interact with the nucleus
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Stopping Power
• The stopping power is a function of the
charge of the particle, the energy of the
particle, and the material in which the
charged particle interacts
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Stopping Power
• Stopping power has units of MeV/cm – the
amount of energy deposited per centimeter
of material as a charged particle traverses
the material
• It is the sum of energy deposited for both
hard and soft collisions.
S=
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dE
dx
Tot
=
dEs
dx
+
dEh
dx
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Mass Stopping Power
• Often the stopping power is divided by
the density of the material, 
• This is called the “mass stopping power”
• The dimensions for mass stopping
power are
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MeV – cm2
g
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Stopping Power
Stopping power is used to determine dose
from charged particles by the relationship:
D= 
dE
dx
in units of MeV/g, where
 = the particle fluence, the number of
particles striking an object over a
specified time interval
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Stopping Power
To convert to units of dose ..we do the
following manipulation.
D=
dE
dx
MeV/g =
dE
dx
(1.6 x 10-10) Gy
1ev = 1.6 X 10 -19 J
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Bragg Curve – Alpha
Bragg Curve - plot of
specific energy loss ( ie
rate of ionization ) along
the track of a charged
particle
Alpha Particle
A typical Bragg curve is
depicted in this graphic
for an alpha particle of
several MeV of initial
energy.
Energy loss curve – increase initially and virtually no
energy deposited at the end of the track.
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Bragg Curve –Beta
The energy deposition of the
electron increases more slowly with
penetration depth due to the fact
that its direction is changed so
much more drastically
Beta Path
As the mass of the beta particle is
the same as the orbital electrons
they undergo several collisions …
the torturous path
Energy loss curve – virtually no
energy deposited at the end of
the track.
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Range – Beta particle
• Depends on the energy of the beta particles and the density
of the absorber
 Beta particle energy reduces as density of the absorber increases
• Experimental analysis reveal that ability to absorb beta
particle:
 Depends on the number of absorbing electrons (electrons per cm 2)in
the path of the beta ray – aerial density
 Lesser on the atomic number of the absorber
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Range - Energy relationship
• Attenuation of beta particles
 interposing layers of absorbers between beta
source
The number of beta particles
o reduce quickly at first
o more slowly as absorber thickness increases
o completely stops after certain absorber thickness
 Range of beta particle - the thickness of absorber
material that stops all particles
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Range – Beta particle
• Aerial density is related to the density of
the absorber
td g/cm2 =
ρ (density of the absorber) g/cm3 X tl
(thickness of the absorber) cm
• beta shields are usually made from low Z
materials
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Range – Beta particles
• Calculate density thickness for aluminium
of thickness 1cm .
Note: (Density of Al = 2.7g/cm3)
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Range – Beta particles
• Calculate density thickness for aluminium
of thickness 1cm .
td g/cm2 = ρ g/cm3 X tl cm
td = 2.7g/cm2
• A graph of beta energy VS density thickness is useful for
shielding and identifying beta source
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Range – alpha particles
• Alpha particles least penetrating of the types of radiation
• Alpha particles are mono-energetic. Therefore the
number of alpha particles not reduced until totally
eliminated at particular thickness of the absorber.
• The thickness of absorber that totally stops alpha
particles is the range of the alpha particle in the material.
• The most energetic alpha particle travels few cms in air,
while in tissue only few microns.
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Linear Energy Transfer
LET is the rate of energy absorption by the
medium
LET =
dE
dx
keV per micron
DE = is the average energy imparted by the
radiation of specific energy in traversing a
distance of dx.
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Linear Energy Transfer
• Specific ionisation is the number of ion pairs formed per
unit distance travelled by the radiation particle and very
useful concept in health physics
• Specific ionisation is very high for low energy beta
particles and decreases as the energy increases.
• Specific ionisation is high for alpha particles.
• Travelling through air or tissue alpha particle loses on average 35 eV per
ion pair it creates .
• The high electrical charge and low velocity means tens of thousands of
ion pair per cm of air travelled.
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Shielding
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Absorbed Dose
 Absorbed dose is energy imparted per unit mass of
material:
 The unit of absorbed dose is the Gray (Gy)
(1 Gray = 1 joule/kg)
 To calculate the dose from charged particles, we need to
determine the amount of energy deposited per gram of
material
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Tissue Equivalent
Stopping Power for Electrons
Energy
(MeV)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mass
Stopping
4.2 2.8 2.4 2.2 2.0 2.0 1.9 1.9 1.8 1.8
Power, S/
(MeV-cm2)/g
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Stopping Power Example
Calculate the dose from a 37,000 Bq source of
32P spread over an area of 1 cm2 on the arm
of an individual for 1 hour
D =  dE
dx
(1.6 x 10-10) Gy
32P
has a 0.690 MeV beta particle (average energy). Assume
that 50% of the particles on the skin interact with the skin
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Stopping Power Example
 = (½)(37,000 Bq)(1 dis/s/Bq)(1 hr)(3600 s/hr) =
6.67 x 107 dis
32P
has a 0.690 MeV beta particle (average energy)
For tissue equivalent plastic and a beta particle with
an energy of 0.690 MeV, the stopping power is 1.96
MeV-cm2/g
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Stopping Power Example
dE
D=
dx
MeV-cm2/g
D = 6.67 x 107 X 1.96 X1.6 x 10-10 J/kg
D = 0.021 Gy
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Where to Get More Information
 Cember, H., Johnson, T. E, Introduction to Health
Physics, 4th Edition, McGraw-Hill, New York
(2009)
 International Atomic Energy Agency, Postgraduate
Educational Course in Radiation Protection and the
Safety of Radiation Sources (PGEC), Training
Course Series 18, IAEA, Vienna (2002)
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