Transcript Radiation Physics

Radiation Physics
Ya-yun Hsiao
Outline
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Radiodecay
Interactions of radiations with matter
Example

A 6.2 mg sample of 90Sr (half-life 29.12
year) is in secular equilibrium with its
daughter 90Y (half-life 64.0h). (a) how
many Bq of 90Sr are present? (b) how
many Bq of 90Y are present? (c) what is
the mass of 90Y present? (d) what will the
activity of 90Y be after 100 years?
Secular equilibrium: λSrNSr=λYNY
T1/ 2 Sr
Y
29.12  365  24h
Nsr 
NY 
NY 
NY  3985.8 NY
Sr
T1/ 2Y
64h
NSr +NY =NTOTAL=
NY=
6.2  10 3 g
atoms
 6.022  10 23
 4.148  1019 atoms
g
mol
90
mol
4.148  1019 atoms
 1.04  1016 atoms
3986.8
NSr=1.04x1016 atoms /3985.8=4.147x 1019 atoms
A(t)= λN(t)

(a)
ASr 
ln 2
 4.147  1019 atoms  3.13  1010 s 1  3.13  1010 Bq
29.12  365  24  3600s
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(b)

(c)

(d)
AY 
ln 2
 1.04  1016 atoms  3.13  1010 s 1  3.13  1010 Bq
64  3600s
mY=
N (t )
1.04  1016 atoms
M 
 90 g  1.55  10 6 g
23
Na
6.022  10 atoms
AY  ASr (t )  ASr e t  3.13  1010 Bq  e

ln 2
100 y
29.12 y
 2.897  10 9 Bq
Example
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Consider the following beta decay chain
with half-lives indicated,
210Pb (22y) 210Bi (5d) 210Po
A sample contain 30 MBq of 210Pb and
15M Bq of 210Bi at t=0 (a) calculate the
activity of 210Bi at time =10d (b) If the
sample were originally pure 210Pb, how
old would it have been at t=0?
Interactions of photons
with matter
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Photoelectric Effect
Compton Effect
Pair production
Photoelectric effect
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Most of this energy goes
to an atomic electron
(with a small amount to
the nucleus) resulting in a
free electron and an
ionized atom.
The photoelectric effect
may only occur if the
incident photon has an
energy higher than the
binding energy of the
atomic electron.
Top insert to illustrate the interaction of a photon with an atom to eject
an electron from the K shell to produce a photoelectron. When the hole
in the K shell is filled, characteristic radiation is emitted. Main graph –
Photoelectric attenuation coefficients for water and lead plotted on a
log-log scale.
Compton Effect
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An interaction
between a photon
and an atomic
electron
An inelastic process
Some of the kinetic
energy of the
photon is required
to overcome the
binding energy of
the atomic electron.
Compton Effect
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And the recoil electron energy is given by

α (1  Cos θ  
T = hν – hν' =
h ν 


1

α
(1

Cos
θ


High energy incident photons suffer a large
energy change, but low energy incident photons
do not. This is important in radiotherapy since
when the incident energy of the photon is large
most of the available energy goes into kinetic
energy of the recoil electron, which goes on to
deposit energy in tissue, and very little energy
goes to the scattered photon
Pair Production
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Pair production is an interaction between a
photon and a nuleus in which the photon
is transformed into an electron-positron
pair. In the center of mass syst~m, the
energy threshold for this e-p pair creation
is 2moC2 = 1.022 MeV.
Pair Production
Mass Attenuation Coefficient
μ σ τ k
  
ρ ρ ρ ρ
Mass Energy Transfer Coefficient
Mass Energy Transfer Coefficient
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Photons do not deposit energy in a
material. It is the fast electrons that they
produce following interaction that deposit
energy. Over many interactions there will
be an average energy transfer, , to the
electron.
The mass energy transfer coefficient is
tr/ρ
Etr
μ tr 
hν
.μ
Mass Energy Absorption Coefficient
Letting g represent the average fraction of the
initial kinetic energy transferred to electrons that
is subsequently emitted as bremsstrahlung
Mass Energy Absorption Coefficient