Operational
Health
Physics
Training (Moe)
3 - PROPERTIES
SECTION
There
are
four
main
OF ALPHA.
types
of
present.
sions.
These
Other
will
be dealt
A.
Alpha
with
the
energy
and
Rutherford
and
collecting
Q
When
a
these
Most
2)
The
3)
Some are
4)
A few are
The
first
these
hazard
in
the
following
from
high
energy
which
discus-
reactions
the
from
Q particle
in
a
a
a helium
tube
light
a dis-
each
is
glass
the
same range
scattered
near
scattered
nucleus
with
spectrum
emitter.
by
electrodes.
obtained
showed
the
the
of
mass
3.1)
have
range
particle
atoms
of
the
the
that
have
about
path
of
of
the
naturally
4 to
is
high
naturally
the
par-
the
same discrete
the
alphas
occurs
particle.
that
radioactive
of
the
speed,
speed
they
radioactive
of
have
nuclei
9 MeV.
lost
mainly
substance.
with
all
occurring
and relatively
from
source.
almost
scattering
traversed
collision
to
one-twentieth
from
Q
gas.
shows
the
particles
an
direct
that
from
order
Alpha
in
(1)
Figure
path.
closer
end of
large
their
above
ejected
their
the
distances
the
a given
end of
imply
near
of
of
(see
tracks.
radionuclide
are
of
the
at
given
in
straight
mentioned
a
energies
processes:
with
life
photographs
along
often
energy
emitted
of CYparticles:
energies.
of
occurred,
properties
speeds
have
tube
travel
other
with
the
radon
have
by
kinetic
that
from
property
particles
(:He)
half
cloud-chamber
alphas
Alpha
excitation
two
the
alphas
most
The
relative
of
lines.
1)
Because
usually
the
as one
as appropriate.
nucleus
showed
properties
infrequently,
large
characteristic
of
The
light.
a
helium
emitted
atoms
a helium
in
Examination
energy.
of
primarily
sections
is
particles
characteristic
ticles
The properties
be treated
result
later
Royds
discharge
revealed
will
y and x rays
Particles
The a particle
crete
physics.
determination
that
in
(we include
in health
properties
radiations
GAMMA. X RAYS AND NEUTRONS
radiation
which
must be dealt
with
type)
radiations
are important
in the
they
BETA.
an orbital
by ionization
Ionization
electron,
and
occurs
by
and
(2)
Operational
Health
Physics
Training (Moe)
3-2
Figure
interaction
of
electrons
of
the
energy
atom
(see
loss
of
an
Illustration
of alpha tracks as seen in a cloud chamber.
(From F.Rasetti, Elements of Nuclear Physics. New York:
Prentice-Hall,
Inc., 1947; Fig. 53, P.. 303)
3.1
a
the
the
by
loss
place.
so
into
When
production
a
1.
The
pair
in
.
in
W value
a
.
an ion
pair
in
the
does
a given
occurs
remove
not
average
it
the
from
the
expended
by
result
energy
when
from
substance
available
to
Q
frequently
reactions
is
usually
that
occur
unless
as Be,B),
to
E
particles,
except
can
media,
become
to
orbital
medium.
very
(such
the
Excitation
pair
the
and
at
with
the
higher
a,
but
CYemitter
is
no reactions
> 20 MeV,
but
can take
then
neutron
feasible.
Loss
defined
substance.
I
not
accelerated
nuclei
is
given
most
element
with
.,
I
nuclear
are
Enerzv
enough
are
particles
Specific
is
processes
occur
particle
3.2).
of
light
by reactions
ion
the
Figure
potential
short
of
Consequently,
not
a
case
an
example,
is
incorporated
a.
do
For
range
this
ionization
generally
their
In
(see
electron
creating
energy
energies.l
the
the
in
the
Other
ion
3.3).
energy
fields
medium
to
Figure
than
these
absorbing
transferred
particle
greater
electrostatic
as the
This
mean
value
energy
is
needed
different
to
for
create
a! parti-
an
Operational
Health
Physics
Training (Moe)
3-3
i
Figure
3.2
Figure
Electrostatic
3.3
interaction.
Excitation.
--.-
-~_ _.._.. ~-.---~_-------.
--__
Operational
Health
Physics
Training (Moe)
3-4
cles
in
various
pure
helium,
energy.
Q
is
from
relatively
W value
22 in
xenon
to
in
a given
constant
for
Q
double
positive
high
number
Because
of
the
forms
a
rather
particle
The
In
specific
air,
relative
particles
in
air
46 eV/ion
pair
gas for
is
(ip)
in
different
35.08
eV/ip
a
(5.6x
an
a
idea
of
If
the
energy
may
loss
along
produce
energy
>
loss
charge
of
the
lo6
path
and
ion
of
ip/m.
the
large
pairs
the
So
by measuring
its
Q is
that,
per
unit
very
high.
one
ionization
mass,
may
an
path
get
produced
a
along
path.
against
the
gradually
distance
the
energy
substance
ionization
of
increases
Finally,
a
ranging
J/ip).
length.
the
but
The
lo-l8
gases,
ionization
is
will
as
lost.
pick
produced
penetration
the
An
Figure
3.4
01
an
a
loses
a peak
whose
up two electrons
DISTANCE
in
particle
reaches
by
value
energy
and become
Q
particle
substance,
energy
the
(see
and drops
is
is
to
ionization
Figure
zero
entirely
a neutral
plotted
helium
3.4).
as all
lost
atom.
OF PENETRATION
The ionization increases as the velocity of the alpha
Particle decreases
with the depth
of penetration.
(R.E.Lapp/H.L.Andrews,
NUCLEAR RADIATION PHYSICS,
2/e, 1954, p.139. Reprinted
by permission of PrenticeHall, Inc., Englewood
Cliffs, NJ)
the
in
a
Operational
Health
Physics
Training (Moe)
3-5
Stonninz
2.
The
loss
in
unit
path
the
Power
linear
the
stopping
material.
It
length
linear
is
power
S is
seen
from
Figure
as
the
o
increases
stopping
power,
related
to
3.4
that
loses
the
specific
the
energy
energy.
energy
loss
per
One may define
S,
as
3.1
in which
dE gives
dl
along
the
the
path
linear
one
of
the
by the
which
velocity
electron,
v of
linear
Q
fails
for
the
and excitation
The mathematical
particle.
express
stopping
Q particles
ionization
expression
of very
loss
at
the
low
very
for
energy.
end of
the
power
for
heavy
particles
of
charge
ze is
J/m.
3.2
be
is
the
B
the
a
of
a slowly
varies
its
which
results
The
mass
stopping
by the
density
p of
is
number
[Z]
of
with
increased
the
ionization
mass
a function
is
mean
near
of
the
of
the
ionization
in
so that
squared.
linear
of
expressed
velocity,
velocity
the
particle
rest
is
power
the
decreases,
the
and the
stopping
inversely
in
m,
(which
function
velocity
charged
number
linear
varying
given
a
medium,
atomic
The
medium).
and
the
stopping
and the
power
for
of
atomic
the
B is
constant
atoms/cc
particle,
energy,
increase
NB = KoNB
will
stopping
loses
will
the
[I]
as
cannot
N
and
units
power
4xe4z2
mov2
Ka
v,
potential
charged
as ionization
expression
dl
speed
the
linear
dE=
in
of
transferred
a! particle.
The
given
energy
stopping
Therefore,
path
the
stopping
the
SI
the
As the
power
end of
the
path.
divided
S
-=1,dEJ
P
p dl
power,
the
(6
kg
25x1()13
'
S/P,
is
the
linear
stopping
substance:
MeV
cm2>
g
3.3
power
Operational
Health
Physics
Training (Moe)
3-6
In
of
two
is
often
to
m with
(s,P)m
air.
respect
= S/D of
A is
the
3.
Ranpe
use
air
will
lose
their
the
their
be only
particles
the
up
substance,
mass
in
air
at
the
power.
For
and other
power
ratio
Q
media
(S/p),
of
a
= (B/A)m
(B/A) air
3.4
weight.
in
specific
short
about
15°C
stopping
is
then:
ionization
distances.
a few centimeters.
Most
the
of
same
For
the
of
Q
instance,
alphas
distance.
from
The
and 760 mm Hg can be estimated
particles,
the
range
a given
range
with
in
source
R
the
of
a
aid
of
relationships:
R,(in
m) = 5.6~10~~
E (for
= 3.18x10
A
in
as thee reference
large
energy
energy
in
is
importance
stopping
relative
atomic
of
the
of
relative
the medium
of air
effective
Because
they
taken
to air
a quantity
or
The
S/p
where
work,
powers
air
compared
medium
physics
stopping
particles,
are
health
air
convenient
E<4 MeV)
-3 E3/*
Rule
of
(for
4<E<7
Thumb
for
4<E<8
MeV
3.5
MeV).
roughly
estimating
Q range
is
R air
The
approximately
-
(Ea _ .025)
80
range
by the
of
m for
a
Bragg-Kleeman
%l= P;>s,pJ-m
in
media
other
3.6
than
air
can
be
relationship:
3.7
found
Operational
Health
Physics
Training (Moe)
3-7
where
(S/p),
respect
to
is
air.
the
relative
Bragg
mass
showed
that
stopping
for
power
a number
of
of
the
medium
with
substances:
3.8
From
this
relationship,
then,
for
the
from
range
any
in
substance
0 * 32%
R a'
pm
<
=
3.82
and
nl*+
is
almost
atomic
Since
the
to
R air
and
the
range
(p = 1.09x104
good
with
from
of
mass
mass
at
is
the
range
238u
of
the
(238)
The
760
mm
of
quantityKfor
a
3.11
,
element
i of
power
+ f
+ $l6
weight
tissue,
in
in
atomic
air,
Ai.
(S/p),
(S/P)~
= 1,
for
such
of
3.12
a great
alphas
particles
16
alphas
and
Ptissue.
a
=
+&I
3
and
expression2:
in
difference
solids
(E
kg/m3 > .
f
15°C
+ 15%.
power
stopping
there
gas,
the
stopping
=R tissue
Pair
a
kg/m3
n3*+...
fraction
the
Because
solid
1.226
n2*+
the
equal
3.10
+ n2A2 + n A
3 3 +..........
&-=
is
=
can be found
nlAl
ni
pa
is'usually
This
relationship
Hg.
compound
or a mixture
where
3.4,
3.9
Et,(inm)-
where
equation
BA
= BaAm
(S/P),
we find
since
= - 90 = 11.52.
7.81
in
will
=
4.198
density
be very
MeV)
between
small.
in
a
Find
UO:!
Operational
Health
Physics
Training (Moe)
3-8
Ra = 3.18x10-3E3/2
= 3.18x10-3(4.198)3/2
= 2.74x10-*
fact
makes
on
the
source
MeV
to
tissue
the
human
get
damage
the
a
will
be
be
a
these
surface,
in
In
has
pm)
particle
7.5
to
them,
essential
since
and not
of
spread
out
over
energy
to
be
more
effective
very
of
a!
dense
a
origin
the
more
are
means
organs
deposition
in
real
specific
this
This
all
the
high
In
of
no living
body.
and
tissue.
small
then,
the
important.
organ
particles
approximately
to
point
of
needs
very
the
layer
With
becomes
near
by
be affected.
range
living
emitted
"dead"
a emitters
external
than
will
short
localized
in
most
dense
to humans
the
tissue
in
energy
penetrate
For
is
ranges
a hazard
the
by
can be done
of
an cc particle
body,
surrounded
short
of highest
living
source
found
a
little
the
addition,
reasons,
just
when
particular
been
will
layer.
lodged
that
particle
dead
the
less
o
the
highly
is
tissue.
the
skin
Q
damage
source
absorbed
of
the
great
m(9.27
have
much
The
inside
of
will
Thus,
particle
So,
be damaged
source
particles
body.
through
ionization
a!
substances
on
will
= 9.27x10q6
radiations.1
Once
Q
a
radioactive
skin
-2
that
the
external
natural
cm).
Hazard
The
other
(2.74
1.09x104
Relative
substances
air
.32(11.52)2.74x10
Ruo*=
4.
m in
case,
the
that
the
the
the
alphas.
body
energy
if
will
a larger
along
producing
concern
the
be
volume
path
damage.
as
an
of
3 For
an internal
hazard.
B.
Beta
the
either
bY
Particles
Beta
particles
nucleus
of
positive
a
radionuclide.
were
the
found
unstable
electrons
The
to be high-speed
atom.
(positrons)
concept
Further
investigation
or negative
of
p
electrons
emission
electrons
has
emitted
has
shown
from
that
may be emitted
been
extended
to
Operational
Health
Physics
Training (Moe)
3-9
either
emission
of
positrons
is
same;
they
particles
a
the
alphas,
betas
continuous
energy
spectrum
energies
may
spectrum
atom.
Most
about
4 MeV.
of
up
to
be
found
known
The
He
spectrum.
a
proton
not
in
with
3.5).
discrete
The atom
maximum
with
maximum
of
a source
about
l/3
Emax
Fermi
was
that
when
and an anti-neutrino
in
able
a
to
p-
was also
the
was emitted,
Typical
(MeV)
beta spectrum.
of
for
Figure
max
p
that
energy
up to
in
case
of
the
positrons
of
shape
a neutron
In
the
of
Em,
the
E
ENERGY
electrons
theory
predict
emitted.
show
characteristic
case
the
developed
these
but
value
particles
0.4
3.5
emits
emit
is
of
energies
and is
theory
Figure
mass
charges.
This
value.
rest
tables
(E)
and
opposite
emitted
Figure
The
nuclide
sources
assumed
but
maximum
Enrico
His
electrons.
equal
(see
energy
1934,
decay.
are
some
w>
In
positron
fi
average
electrons
(B+>.
to
have
Unlike
all
and
/3of
and
the
p
converted
3.5,
the
sum
Operational
Health
Physics
Training (Moe)
3-10
of
the
Emax.
energy
In
positron
of
the
and
case
the
by
do
latter
occur
process
MeV (see
in
and lead
occurs
to
the
sum of
of
orbital
ways
for
equals
energy
of
pass
leading
mechanism.
predominantly
the
as they
electrons,
emission
(Ey)
the
Em,.
number
frequent
to
the
equa:L
a
with
most
anti-neutrino
But
to
through
ionization
interactions
of x rays
with
the
(bremsstrahlung).
the
more
energetic
of
lo-15
MeV,
The
electrons,
E> 1
3B.3).
When
are
the
the
emission,
is
energy
is
and
03
positron
collisions
excitation,
nucleus
B
neutrino
lose
Loss
and
of
emitted
Electrons
matter.
the
an electron
produced
released.
which
Since
energy
reaches
of
can
this
an energy
interact
energy
betas,
with
is
these
well
the
nucleus,
above
the
take
place
reactions
high
energy
and
highest
photons
neutrons
known
mainly
are
emission
in
electron
accelerators.
An
this
important
process,
results
in
In
the
the
a
given
until
processes
leading
electron
as
mately
the
1.
those
lo-l8
J/ip).
those
for
MeV.
104-lo5
an
as
Q. But
a)
at
for
ions
its
per
meter
(e+)
a large
are
the
smaller
(l/2
path
of
energy.
The
same for
the
mass
(approxi-
that
intervals.
of
number
kinetic
charge
frequent
electrons
ionization
square
Ionization
less
its
substance
lower
anti-matter
make
of
of
In
MeV each).
will
because
annihilation.
and
0.511
all
is
of
an a),
Consequently,
as do alphas.
Loss
values
in
values
Roughly,
the
of
the
and
3E.4)
(e-)
electron
in
as many
W value
matter
loses
place
Energy
alphas.
the
of
specific
the
in
for
speed
air
for
air
is
electrons
energy
of
the
eV/ip
are
loss
electron
electrons
33.85
range
for
much
(5.42x
lower
electrons
for
from
than
varies
energies
up to
approximately
ip/m.
At
increases
of
produce
The
inversely
the
take
Soecific
the
for
(see
(2 7 rays
ionization
that
The
energy
eventually
to
do not
positrons
of
substance,
interactions
electrons
of
it
l/7300
for
combination
release
collisions
10
reaction
(see
low
energy,
Figure
3.6).
the
It
specific
reaches
energy
a minimum
loss
decreases
value
above
as energy
1 MeV.
Then,
Operational
Health
Physics
Training (Moe)
3-11
BREMSSTRAHLUNG
4’
/
I
I
A
50
1
ENERGY
Figure
the
The general shape of the stopping power
vs. energy curve for beta particles.
3.6
total
energy
relativistic
for
spectrum.
given
source
spectrum.
specific
energy
2.
for
the
Stonping
is
excitation
dE=
dl
N
is
of
expected
betas
energy
because
energy
value
obtained
should
due
to
of
the
than
loss
for
for
be higher
equal
most
energies
to
the
the
the
maximum
betas
maximum
electrons
spectrum
than
of
emitted
value
increases
should
the
the
by a
of
the
as the
be higher
electrons.
stopping
power
for
electrons
due to
ionization
and
by:
2Te4NZ
mov2
the
increases
Power
linear
given
for
specific
the
energy
production.
loss
lower
monoenergetic
The
where
have
the
as
electrons
is
will
decreases,
that
energy
This
Since
increases
and bremsstrahlung
monoenergetic
beta
than
loss
effects
The
value
(MeV)
B’
atoms/cc
= K,NZB’
of
the
3.13
,
medium
of
atomic
number
Z. The
electron
Operational
Health
Physics
Training (Moe)
3-12
stopping
number,
the
mean
rate
of
are
greatly
B',
ionization
energy
traveled
1.2-4
times
loss
is
the
3.
of
between
rays
electron
the
production
this
process
both
of
is
Z
path
to
may
radiate
mass
amount
except
shifts
the
electron
expression
electron.
and
gives
Since
the
electrons
substance,
straight-through
the
ionization
substance
nuclei
the
actual
path
(about
and excitation
may be given
as a result
of
the
of
absorbing
As the
energy
increasingly
x ray
production
from
up in
the
interactions
are
The
inefficient
increases
more
by
substance.
of bremsstrahlung
becomes
of
in
some energy
1 MeV.
particle
close
is
either
above
important.
1 MeV,
However,
commercial
Figure
energy
of
3.7).
any amount
the
the
atomic
charged
unless
For
electrons
be
the
beam
forward
on the
During
tubes
used
or decelerated
in
its
per
atom
is
roughly
the
absorbing
of
Because
the
particle
energy
thin
targets,
direction.
angles
increases
4-6
of
in
the
to
to very
high
cause
its
electron
energy
proportional
matter
to
and m is
dependence,
for
all
the
particles
GeV range.
maximum
an incident
an
charge
kinetic
a l/m2
the
If
the
the
total
negligible
is
off.
will
acceleration,
up to
number
given
This
zero
completely
energy
electron.
from
almost
right
be
a substance,
this
is
at
may
traversing
particle.
in
will
while
a force
bremsstrahlung
is
accelerated
radiation
to an atom
(see
the
matter,
electromagnetic
electrons,
to
the
the
lost
below
bent
As
of
This
a given
than
production
rays
of bremsstrahlung
electrons.
of
through
the
exert
bremsstrahlung
path
and
will
of
substance.
energy
in
a charged
The
total
Ek.
Z
(Z/m) 2s where
the
that
nucleus
be
speed
- Bremsstrahlung
source
field,
the
the
and medicine.
passes
on
x
the
dentistry
electron
path).
to
energies
electric
line
electrons
When
an
greater
through
leading
for
much
produced
high-speed
the
passing
to
passing
of
actual
Production
in
interactions
in
the
often
addition
x
function
of
in
Radiation
electron
form
along
straight
In
a
potential
scattered
path
an
is
intensity
beam
values,
of
of
the
low-energy
the
maximum
Operational
Health
Physics
Training (Moe)
3-13
Figure
For
in
the
cone
very
forward
of
high
energy,
direction.
half-angle
Bremsstrahlung.
3.7
The
8, given
the
angular
bremsstrahlung
is
distribution
is
very
mostly
highly
peaked
confined
to
by7
m c2
fl=-
- 2
E0
in
which
E is
the
For
of
its
total
an
initial
(rad)
energy
electron
energy
3.14
,
of
the
beam
which
is
electron
incident
converted
(MeV).
on a thick
to
x rays
target,
is
given
the
fraction
approximately
bY2
F-
where
energy
energy
Z
is
in
7X10-4
the
MeV
as x rays
ZEk,
atomic
of
when
the
the
3.15
number
beam.
beam
of
Thus,
is
the
absorbing
a 1 MeV beam
absorbed
in
lead
substance
will
lose
(Z=82).
and Ek is
about
6% of
the
its
a
Operational
Health
Physics
Training (Moe)
3-14
the
In
converted
to x rays
F-
where
1
Em,
MeV
p
will
in
zero
which
in
of
maximum
lose
about
The
to
Em,.
for
energy
stopping
around
50
collision
energy
of
shields.
in
bremsstrahlung
cases,
the
calculations,
Figure
3.6,
as
will
thin
loss
shown by the
In
p
energy
contain
maximum
case,
that
will
of
of
energy
the
x rays
the
normally
one uses
the
a
when
x rays
energy
This
if
this
bremsstrahlung
one may assume
linear
this
energy,
rad.
/3 for
result
attenuation
For medium
bremsstrahlung
the
loss
radiation
loss
energy
and excitation)
-
loss
on the
Z materials,
become
the
comparable
dominates.
One may
(bremsstrahlung)
to
by9
EZ
700
energy
3.17
of
the
electron
(MeV)
and Z is
the
atomic
medium.
is
of
the
ratio
a 1 GeV e-
J1000)(29)
700
production
line.
of bremsstrahlung
co1
What
indicates
effect
of radiative
(ionization
kinetic
loss
the
dotted
and the
ratio
(3
dl
km
dl
-
energy
result
energy
for
absorbing
S
-=rad
Sco1
The
its
distribution
design
Above
the
EXAMPLE
collision
of
the
the
E is
the
of
,f3 spectrum.
l/3
is
S
-=rad
Sco1
number
3%
the
of
to
to
MeV.
estimate
which
energy
correspond
power
roughly
in
fraction
E max.
3
loss
linear
the
most
Returning
total
source,
829
In
factor
coefficient
j3
3.16
spectral
shielding
safety
a
a
ZE,,,
the
emitted
purposes
of
approximately
lead.
up
are
is
3.33~10-~
is
absorbed
from
case
of
in
the
copper
radiative
energy
loss
to
the
energy
by
(Z=29)?
= 41 . 4 .
that
at
the
this
--.
electron
energy!
loses
>97%
of
its
Operational
Health
Physics
Training (Moe)
3-15
4.
Range
The stopping power for
Z of the absorber increases.
This
electrons
decreases as the atomic
occurs because substances of high
number
Z have
fewer
electrons
per gram and these are more tightly
bound. Consequently,
But as Z increases,
the
the range
tends
to increase
as Z increases.
increases.
The effect
of multiple
multiple
scattering
of the electrons
scattering
is to increase the actual path of the electron
in a substance.
This
tends
to decrease the range which is the linear
distance through the
act to balance each other, so that the density
medium. These two effects
gives
one a good idea of its relative
ability
to stop
of a substance
It
is common to express
the range of electrons
in terms of
electrons.
density-thickness,
measured
in
kg/m2,
i.e.,
t(m)p(kg/m3)
= Range
is then nearly independent
of the type of absorbing
(kg/m2> . The range
substance.
have expressed
the relationship
between
Katz and Penfold"
in mathematical
form.
the range
and the energy
(MeV) of the electron
this becomes
Expressed in SI units,
E1s265-0'0g541n
R(kg/m2)=4.12
E(0,01<E<2.5
MeV)
3.18
or
In E = 6.63
- 3.2376
(5.6O93-lnR)1/2,
3.18a
and
R(kg/m2)
= 5.30E - 1.06
3.18b
(E>2.5 MeV).
the range of electrons
in any
These expressions
can be used to find
as a continuous
/3 spectrum is
in terms of kg/m2. As far
substance
turns
out that
the maximum range of the ,3 is equal to
concerned,
it
electron,
'whose energy is the same as the
of a monoenergetic
the range
of the /3 spectrum. Thus, one can use the same relationmaximum energy
ship
to find
the range
What
is
substance?
of betas in matter.
the
range
of a
1.5
MeV j? in
kg/m2
of
any
Operational
Health
Physics
Training (Moe)
3-16
R = 4 12 Cl 5)1.265-0.09541n1.5
4 12
=
In
5+265-0.0386
(1
R = In
4112
From
to
a
practical
be
much
than
the
about
0.2
/3 in
than
maximum
Rule
of
any medium
is:
E
1
j? radiation
5.
is
but
greatly
in
air,
the
a given
of
the
j3
of
particles
a ,9 source
turns
out
energies
much
less
have
range
of
a j3 source
is
taken
as
line.
tells
straight
us
/3
ratio
is
about
estimate
the
maximum
that
beta
gives
of
from
ionization
t of
the
ionization
versus
is
(MeV).
approximation
for
lower
is
good
energies.
For
m/MeV.
to
absorption
a
traverse
before
is
passage
the
is
plot
through
one gets
fractional
is
for
constant,
equation
found
slope
of
ionization
denoted
describing
a
decay.
The
the
the
yields
radioactive
in
that
to
paper
process.
of
passing
an absorber
decrease
This
The
It
on semilog
an exponential
substance.
absorbers
and after
measured.
thickness
constant
coefficient.
source
substance
after
similar
the
3.5
range
produced
absorber
the
the
The
by p,
,6 absorp-
is
I = IoemPt,
range
Absorption
particles
of
This
energy
overestimates
thickness
line
to
3.19
The
unit
thickness
per
called
the
attenuation
tion
range
can be used
B-particle
ionization
straight
the
the
average
which
range
Exponential
through
It
of
The
maximum
MeV
thicknesses.
initial
Most
Thumb
the
various
plot
this.
average
5E (k)
m2
Suppose
a
the
R."
which
above
mg/cm2).
energy.
R-
in
'
ln1.5
-I- . 1.226
= 1.91295
standpoint,
less
A
of
(677
5+X!6.
(1
'
= ln4.12
+ 0.49710
kg/m2
4 12
=
(l.5)1-226
= 1.41585
R = 6.77
= 4 12c1 . ,)1.265-0.0954(0.40547)
3.21
is
Operational
Health
Physics
Training (Moe)
3-17
where
I,
is
through
a
the
initial
thickness
coefficient
t
(in
attenuation
intensity,
of
absorber
the
of
weight
of
substance
the
is
(in
absorber.
Thus,
intensity
and
have
P/P
kg/m3,
in
the
4,
Experiments
m-l).
coefficient
density
I
can
/J is
shown
the
mass
is
the
the
of
mass
the
atomic
attenuation
by 12
coefficient
.!A - 1.7 Em&l4
m2/kg
P
substances,
where Em,
for
most
tion
coefficient
3.22
is
in MeV.
In
terms
of
the
mass
1 = Ioe-(P/P)X,
where
x
valid
the
P
independent
express
passing
attenuation
that
where
(m2/k>,
is almost
one
after
is
3.23
expressed
provided
the
attenua-
as
distance
kg/m2,
i.e.,
of penetration
is
tp.
This
well
within
relationship
the
range
/3-
or
is
of
the
B*
6.
Relative
Hazard
Depending
source
t9
at
constitute
may
particles
hence
from
sources
/3-
source
are
of
to
easily
usually
only
/3
low-Z-number
require
thicker
hazard.
are
mm
able
in
or
living
they
ranges
very
particle
near
less
absorbers.
absorbers
This
hazard
For
to
than
factor
of metal
may result
such
of
the
their
dead
Since
greater
layer
most
this,
of
vital
range,
skin
and
organs
are
by /3 particles
which
is
reduces
Since
positron
an
most
or plastic,
the
the
case
for
external
/?
j3 particles
hazard
will
source.
stopped
of
a
be unaffected
problem.
amount
the
is
amount
will
skin-exposure
by a small
Because
tissue.
emitters.
a
energy,
to penetrate
more,
tissue
external
The
radiation).
an external
positron
absorbed
An
energy
50
primarily
exist
particle
energy
having
and
the
keV
their
depth
most
70
of
deposit
a
upon
in
x ray
positron
reduce
from
an
production
emitters,
the
external
x rays
produced
absorber
when a high(bremsstrahlung
can be minimized
the
hazard.
annihilation
by using
y rays
Operational
Health
Physics
Training (Moe)
3-18
As an internal
as Q particles.
The
damage
will
tissue
volume
the
not
energy
path
the
deposited
by the
means
outside
that
will
organ
the
less
even
dense
of
concern
that
larger
concern.
in
energy
energy
as an internal
of
Some of
interact
available
is less effective
in producing
3 Nevertheless,
damage may still
are
means
be involved.
may not
the
as significant
A much
a small
some of
Also,
tissue.
not
a particles.
/3 source
or bremsstrahlung
which
are
of @ particles
as for
7 rays
p emitters
the
will
not
deposition
damage
along
than
the
that
be significant,
radiation
be
so
source.
Wave Properties
C.
Up to
attention
this
energy.
These
water.
definite
velocity.
is
propagated.
being
water.
However,
disturbance
through
One sees
waves
with
a wave motion
advance
From
the
movement
In
this
case,
the
with
surface
through
the
particles.
We turn
as a disturbance
in
a definite
moving
of
a form
the
to
which
one can infer
the
any extent.
medium
but
In
the
medium
a
and
a smooth
motion
wave disturbs
moves
entire
across
of
of water,
velocity
our
body
has
that
a
energy
surface
this
of
of
the
example,
itself
does
the
not
greatly.
If
down,
one fastens
a rope
a wave motion
distance
between
will
two adjacent
(Figure
3.8).
The
symbol
The
frequency
of
a wave,
u,
unit
time.
v is
to
The velocity,
v(in
m/s)
the
number
a rigid
be set
ment
where
dealing
matter
show the
only
moves
been
A wave may be defined
The wave moves
transmits
move
we have
point,
now to waves.
medium.
in
range
be lost
Q particles.
that
tissue
be as localized
of p particles
for
p particles
may actually
mass,
absorbed
greater
about
Annihilation
tissue
hazard,
up in
body
the
particles
X is
is
the
v,
of
rope.
in
often
the
used
numb-er
the
and moves
wave
same phase
to
represent
which
given
end up and
is
the
or displacewavelength.
pass
a point
by
3.24
= VX,
of waves/s
free
The wavelength
of waves
is
the
and X is
the
m/wave.
Operational
Health
Physics
Training (Moe)
3-19
WAVELENGTH
X
I
Figure
The
3.8
velocity
wave
of
moving
in
called
refraction.
the
denote
A
media
travels
of
of
and
and
medium.
the
That
different
from
wave
is
the
is,
the
same
velocities.
The
one medium
to
another
is
a property
of
the
period
the
wave
denote
the
combination
electromagnetic
is
some interest
interference.
Reflection
is
that
Electromagnetic
an
wave
the
exhibit
property,
properties
Electromagnetic
When
will
related
of waves.
dissimilar
to
media
frequency
reflection
scattering
denotes
a
of
7,
is
the
source
time
for
work
are
s/wave).
wave
diffraction,
D.
when
The
(7 = l/v
a property
different
velocity
Other
used
wave is
disturbance.
1 wave
two
the
through
change
of
Electromagnetic
wave. (R.E.Lapp / H.L.Andrews,
NUCLEAR RADIATION PHYSICS, 2/e, 1954, p-139.
Reprinted
by permission
of Prentice-Hall,
Inc.,
Englewood
Cliffs, NJ)
usually
deflected
in health
The
term
of waves
referred
to
of waves
diffraction
occurs
to
form
at
the
is
used
interface
as backscatter.
some degree.
to
physics
to
of
Reflection
Interference
is
a term
a new wave motion.
Waves
waves
are
wave
of main
moves
concern
through
to
matter,
the
health
there
physicist.
is
set
up an
Operational
Health
Physics
Training (Moe)
3-20
electric
field
E
direction
of
motion
to
a
rise
magnetic
to
(see
are
mitted
perpendicular
light,
ultraviolet
differ
only
In
x
magnetic
and
wavelength.
field
changes
is
also
"feeds"
means
rays
are
interest
it
the
the
and
rise
it
gives
other.
Electro-
disturbance
is
trans-
Microwaves,
electromagnetic
is
the
gives
changing
of propagation.
7
Our
E field
each
This
direction
rays
electric
field
way,
waves.
the
the
As the
this
transverse
to
in
the
field.
both
3.8).
Since
electric
waves
to
Figure
field.
an
magnetic
perpendicular
the
heat,
waves
properties
of
which
x and 7
rays.
The
speed
The letter
of
c is
X
and
used
wavelengths
equals
lo-lo
10m8 to
lo-l3
emitted
X
that
be
called
photons.
the
rays
a vacuum
wavelengths.
angstrom
have
the
classical
is
(It
unit,
A";
wavelengths
in
concept
a continuous
3~10~
is
energy
common
the
These
small
Y
constant,
known
energy
as
E of
of
h.
were
quantum
of
the
the
intensity
energy.
which
energy
which
is
intensity
an
isotropic
from
of
which
given
energy,
radiation.
Planck
Planck
Constant
radiation
of
frequency
h the
and has
Y is
derive
of
integral
E,
directly
is
two terms
of
gives
By
definition,
the
is
transported
by
x
point
and
to
7
are
constant,
a value
of
6.626
x
by
3.25
a wave
perpendicular
come to
up in
action
given
the
concept.
have
These
called
the
to
as being
classical
energy
(quanta)
the
energy
E = hv = he/X.
mits
to
unit
range
an attempt
abandoned
packets
frequency
the
radiant
In
as quanta
to
now
manner.
was radiated
that
The
The
m/s.
one angstrom
in
pictured
Max Planck
He stated
is
Js.
of
7
by a fundamental
it
short
an emitter.
proportional
1O-34
and
in
speed.
very
theoretically,
assumed
but
this
terms
absorbed
He
related
have
1900,
law
by
denote
wave
m.
and
units
electromagnetic
in
m).
to
radiation
to
rays
7
denote
up
an
the
rays
source
time
rate
intensity
the
be
radiation,
at which
is
wave per
direction
may
of
the
unit
of
given
the
the
average
area
motion
in
units
intensity
the
wave
time
across
of
of
at
the
rate
at
a surface
wave.
MeV/m2
a point
trans-
The
s. For
varies
Operational
Health
Physics
Training (Moe)
3-21
inversely
Given
a
from
the
as
the
point
square
source
source
is
IAal/r2
of
of
given
the
distance
of
the
radiation,
that
point
intensity
from
at point
the
source.
A distant
rA
by
3.26a
A
or
3.26b
=A = k/r:
At point
the
B,
intensity
is
similarly
given
by
3.26~
From
these
two equations
we get
3.26d
or
This
law
expression
is
subject
1)
2)
A
useful
distance
source
generally
to
mathematical
of
attenuation
must
be negligible.
The
dimensions
of
must
be small
compared
Rule
of
receptor,
be ~5%.
form
for
the
inverse-square
law.
The
two conditions:
The
between
or
the
is
Thumb,
is
in
greater
a
point
the
the
radiation
source
with
applying
than
source
in
and
the
the
the
detector
distance
condition
3x the
may
intervening
larger
be
at
between
2 above,
the
point
them.
states
dimension
assumed.
space
that
of
The
either
error
if
the
the
will
Operational
Health
Physics
Training (Moe)
3-22
The
the
inverse
source
and
intensity
at
given
in
the
This
If
point
all
this
I (in
MeV/m2s)
energy
S
is
assumed
to be at
intensity
= S/Surface
area
of
137cs
at
a distance
of
1 m from
to
the
intensity
at
3 m.
W
(1.59x105
m2s
equation
IAr2
1
E.
A
=
B
MeV
cm2s
= IBr2
nature.
radiation
were
6)
the
radius
surface
A is
then
2~10~~
MeV/s.
Use the
inverse
Find
the
square
law
'
B
1.59x109~1)
unknown
3)
4)
5)
point
of
3.27
Roentgen
2)
source.
)
2
= l.77xlo8
discovered
From his
x
rays
experiments
MeV )
cm 2 s
(1.77~10~
";V
ms
(3)2
X and y Radiation
1)
by the
47r(1)2(m2)
= 1 5gx1o9
from
rA
3.28
emits
source.
distance
point
= S/4?rr2.
the
A is
emitted
through
the
at
a sphere
about
of
intensity
the
of
pass
rate)
value
and the
about
will
the
(MeV/s)
center
between
10 MeV
s
2x10
47rr2
fluence
Sphere
intensity
&SC
source
source
power
the
time
of
A
B. The
directions
unit
(energy
EXAMPLE:
compute
all
the
in
per
at
by the
be
relationship
one knows
value
emitted
emitted
point
the
emitted
Let
general
If
is
energy
The
the
interest.
she can find
source.
source
sphere.
expresses
of
the
energy
the
law
point
he or
and
source.
of
A,
of
A
r(m),
the
terms
between
the
square
in
1895,
the
so
following
termed
because
properties
of
of
determined:
Most substances
are transparent
to x rays.
Many substances
glow when exposed
to x rays.
X rays produce
ionization
in gases.
X rays are produced
when energetic
electrons
strike
solids.
Photographic
plates
are affected
by x rays.
X rays are not deflected
by electric
or magnetic
fields.
this
their
new
Operational
Health
Physics
Training (Moe)
3-23
The
same properties
were found
for
7 rays by other
workers
later.
Further
work showed that
x and 7 rays were electromagnetic
waves.
The only distinction
made at the present time is one of origin:
emitted from the nucleus of the atom; x rays
gamma rays refer to radiation
refer
to radiation
which is produced outside of the nucleus of the atom.
When a beam of energetic
electrons
is stopped
in any dense
substance,
x rays
(bremsstrahlung)
are produced. The spectrum of x rays
has a continuous
distribution
from zero up to the energy
E of the
Some lines
of much greater intensity
than the bremsstrahlung
electrons.
(see Figure 3.9). These are called characteristic
x rays. The
also appear
are a property
of the target substance.
wavelengths
of these lines
Characteristic
x rays
M) undergo transitions.
appear when electrons
CHARACTERISTIC
X-RAYS
from the inner
shells
y
CONTINUOUS
RADIATION
(BREM SSTRAHLUNG)
X min.
Figure
3.9
WAVELENGTH
X
Typical x-ray spectrum. (R.E.Lapp / H.L.Andrews,
NUCLEAR RADIATION PHYSICS, 2/e, 1954, P.102.
Reprinted
by permission
of Prentice-Hall,
Inc.,
Englewood
Cliffs, NJ)
(K, L,
.~ _.-------.
._-~-
Operational
Health
Physics
Training (Moe)
3-24
The
remove
all
characteristic
electrons
from
characteristic
of
the
the
atom
undergo
visible
range.
the
range
rays
and
the
optical
energy,
with
the
than
the
lines
a
low
As
its
energy
tungsten
given
inner
from
(Z=74)
If
the
to
A'.
8000
lines.
X rays
of
optical
electron
to
have
electrons
in
is
the
only
be found
in
orbits
may be in
by a substance
The
will
removed,
outer
radiation
off
shorter
which
electron
characteristic
given
is
by any method
a K-shell
spectrum
spectrum
will
have
difference
between
the
of
amount
wavelengths,
x
energy
i.e.,
higher
spectrum.
beam
as heat.
For
the
ratio
target,
by equation
If
the
4000
the
excited
shells.
transitions,
lost
be
may appear.
energy
is
may
The visible
in
associated
the
lines
lines
a
lines
strikes
example,
of
a target,
for
radiative
a large
portion
a 300 keV e- beam
loss
to
of
striking
collision
loss
is
and there
is
3.17:
S
The
total
E loss
so that
S,,d
+ Scol
Sco1 - 97% of
Part
a
is
of
probability
The wavelength
the
total
the
energy
is
that
all
the
of
this
= (3.2~10~~
photon
Scol
E loss.
lost
in
kinetic
will
+ l)Scol=1.032
x ray
energy
be given
production
(-
3%),
may be converted
by equation
to
a photon.
3.25
E = hv = hc/Xmin,
where
given
E represents
the
energy
of
the
electron.
The
electron
energy
is
by
E = Ve,
where
V is
Thus,
we obtain
x min(in
the
accelerating
3.29
voltage
and e is
-34
)(3x108)
m) = -hc = ( 6.626~10
Ve
V (1.6~10-~')
the
charge
= 1.24x10
V
on the
-6
electron.
3.30
also
Operational
Health
Physics
Training (Moe)
3-25
or
x
Here,
for
min
(in
Xmin
is
a
the
given
x
in
3.9,
line,
by
and
is
the
voltage
remains
the
predicting
developed
of
Kramers.
about
shape
'*13
represented
of
highest-energy
V
can be obtained.
ray
Figure
roughly
wavelength
accelerating
higher-energy
curve
3.31
A;) = 1.24x104/V.
the
(volts).
If
Moreover,
the
same.
V
response
is
shown
the
window,
produced
increased,
of
the
relation,
curve
in
ray
is
shape
A simple
the
This
x
for
Figure
a
response
useful
thick
targets,
3.10a,
as the
for
was
solid
by
I = A(Emax-E).
Because
of
end
the
function
the
the
rays.
the
by equation
3.32.
for
the
of
same
decay
which
emitted
when
state
energy
may
be
emissions
< 4 MeV.
emitted
from
in
The
an x ray
spectrum
both
number
x rays
produced
portion
(as
shown
as a function
of
x ray
tube.
of
the
in
the
that
and Figure
pre3.10a,
higher-energy
occur
at
Figure
x
roughly
3.10b,
wavelength,
production
a
Depending
from
these
will
in
is
as variations
3.30
lower
intensity
may differ
equation
of
emitted
by
by
Q
the
nucleus
after
portion.
the
1.5
which
is
X.
equipment
can be found
4.
decay
which
the
by filters,
as well
a small
concerning
are
rays
dotted
current
from
contains
plotted
4 of Reference
Gamma
atoms,
As seen
details
and/or
filtration,
of
intensity
distribution
Chapter
the
shape
rays
the
and beam
and
continuous
Further
in
x
highest
the
like
voltage
voltage,
The
x min
high
more
media
spectrum
in
looks
absorbing
pulsating
dicted
absorption
spectrum
of
upon
the
of
p
emission
of
emitting
from
radioactive
any
from
the
nucleus
emission,
give
also
give
an atom
has
either
nucleus
sources
of
in
range
off
off
7
an excess
an
a
an
a radioactive
or
7
rays.
Many
rays.
Gamma
energy
above
its
fact,
these
p.
excited
from
atom.
10 keV
In
state.
rays
Typical
- 7 MeV,
but
Most
atoms
are
lowest
rays
7 ray
mostly
Operational
Health
Physics
Training (Moe)
3-26
b)
]
x min. ‘A
Emax
a> Intensity versus energy
for Kramers’ rule.
Figure
1.
Interactions
The
occurs
mainly
large
of
by
number
x
and
of
small
number
of
ionization
the
of
ionizing
directly
along
called
indirectly
ionization
occurs
released
by photon
Each
when
which
to
in
an
or
in
radiations,
radiation
their
the
respective
ionizing
after
interactions
lose
radiation
produces
produced
interacts
as
reason
paths.
photon
p
a rather
In
is
with
ions
in
the
case
almost
matter,
all
only
turn
produce
B,
they
are
a
most
substance.
Q
cited
This
has
and
above,
Photons,
radiation.
the
and
a substance.
These
such
for
Q
particles
is
7 ray
formed.
the
by
through
which
are
occurs
these
passing
x
ions
matter
of
ionization
primary
Particle
directly
energy
ions
the
rays,
that
is,
wavelength,h.
Matter
of
primary
versus
X ray intensity.
ionization.
7
secondary,
3.10
With
transfer
b) Intensity
interacted.
their
energy
.
x
follows
and
since
That
is,
by producing
called
produce
ions
rays,
are
7
most
the
ion
of
electrons
pairs.
the
Operational
Health
Physics
Training (Moe)
3-27
Three main ways in which x and 7 rays from radionuclides
interact
with
matter
are by means of:
the photoelectric
effect,
the
Compton effect,
and pair production.
All three processes yield electrons
which
then ionize
or excite
other atoms of the substance. Other photon
reactions
require
more energy
to be feasible.
When the photon energy
10 MeV, photon-nuclear
reactions
can release photoneutrons.
exceeds about
exceptions,
are
7
reactions
in 2H and gBe, which
Notable
are
possible
process
for
much lower
energies.14.
For very high energy photons,
of photon-induced
fission
(photofission)
can also occur.
2.
Photoelectric
the
Effect
In the Planck
concept,
each x or 7 ray is a photon with
energy
E=hv. The photon
retains
all of this energy until
it interacts.
The photon
may interact
with
an electron
in an orbit of an atom of the
substance.
In the photoelectric
effect
(see Figure
3.11), all of the
Figure
3.11 The photoelectric
effect. (R.E.Lapp / H.L.Andrews,
NUCLEAR RADIATION PHYSICS, 2/e, 1954, P.113.
Reprinted
by permission
of Prentice-Hall,
Inc.,
Englewood
Cliffs, NJ)
Operational
Health
Physics
Training (Moe)
3-28
photon
energy
used
in
is
given
removing
4.
The
rest
of
the
electron.
The
energy
up in
the
of
this
electron
process.
from
the
the
photon
energy
is
This
electron
will
then
relationship
between
the
Part
atom:
the
this
carried
photon
is
off
cause
photon
of
the
work
as the
Ek is
the
The
is
electron
is
i.e.,
4
photons
less
for
the
will
interact
increases,
atomic
in
copper
to
Z4-5/E3-4.
When
be
K
a
are
sometimes
all
of
called
an
outer
electron
one
have
characteristic
electrons
atom
x
alternative
the
outer
to
emits
and
return
7
mode
to
in
Auger
a heavy
its
original
process
which
rays
of
is
decay,
values
of
of
the
in materials
in
an inner
lead
atom.
As E
Also,
the
a high
(Z=82)
than
proportional
orbit,
the
When such
x rays
E, the
with
approximately
photoelectron
electron
energies
occurs
Another
which
the
energy
rays
small
photon
be greater
released.
electrons.
the
must
the
is
vacancy
a transition
removed
may appear.
from
These
the
x rays
radiation.
minus
the
ray
called
Auger (oh-zhay)
effect
tries
If
the
kinetic
Many
electric
of
is
of
energy
extent
from
outer
x
are
a greater
characteristic
when
shell,
from
electrons
the
occur
removed
energy
shells
are
to
to
the
fluorescent
Sometimes
from
is
of
outer
effect
may be emitted.
then
the
For
electrons
occurs
one
photon
all.
likely
electron
by
the
in
inner
more
when the
at
electrons
effect
the
photon
shell,
occur
the
electron.
important
The photoelectric
filled
occurs,
However,
is
(Z=29).
the
1 MeV.
to
of
to
is
with
Z; the
given
effect
process
effect
number
will
than
more
photoelectric
3.33
energy
photoelectric
low,
than
kinetic
energy
and excitation.
E = hv = Ek + 4,
where
is
function
kinetic
ionization
and the
energy
vacancy
shells
(see
Figure
3.12).
These
emitted
which
are
equal
to
energy
of
energy
the
by an electron
released
binding
in
filled
is
form
of
the
the
of
an ejected
electron.
the
Such
electrons.
may result
electrons
These
atom.
ground
may
called
that
is
take
the
place
photoas the
state.
occur
internal
is,
processes
when
the
for
a radioactive
conversion.
excited
nucleus
substance
This
is
may emit
an
a 7
Operational
Health
Physics
Training (Moe)
X-RAY
Figure-3.12
Auger electron effect. An L shell e- fills a K shell vacancy,
and an Auger e- is simultaneously
emitted from the M shell.
ray or it
may eject
an electron
from one of the inner shells.
In other
interacts
with
the electron
words,
the nucleus
to get rid of excess
If
the nucleus
emits
the y ray,
the energy of the photon is
energy.
an electron
is ejected,
its kinetic
energy will be
given
by E=hv. If
binding
energy
of the electron
in
Ek=hv-4
,
where
4
is
the
This process most often occurs with K-, L-, and M-shell
the given
shell.
electrons
and in the higher-Z
emitters.
the internal
conversion
coefficient
ai as
One may define
.th
shell to the number of
the ratio
of the number of electrons
from the 1
Then, oK is number of K electrons/number
of
unconverted
7
rays.
unconverted
y rays.
CY=XCY-
i
Thus,
1
the total
coefficient
Q is given
by
3.34
Operational
Health
Physics
Training (Moe)
3-30
In
the
decay
presented
in
scheme
a number
sometimes
In
addition,
Kc4
.
L+M
can result
7
counter
per
dis.
a
K
has
Consider
=2.
eK
=-=7
7
conversion
conversion
error
the
coefficient
conversion
may
be
of ways:
of K-shell
eof unconverted
aK = zz:
Internal
literature,
if
one does
a
measured
a source
The number
of
3.35
coefficients
important
is
K
7
not
in
the
take
this
are
given
measurement
of
process
efficiency
of
1~10~
of
Bq,
in
disintegrations
0.1
which
will
into
as a ratio,
activity.
Serious
account.
cts/dis
aK=1.6
i.e.
Suppose
assuming
a
1
7
and
be given
by:
aL+aM
K+L+M+7=N.
aK
-=-=
aL+aM
Remembering,
then,
K
by substituting
1.6
7 + 0.8
3.4
N
which
be
10
3x106
is
yield
3~10~.
photons
scheme,
which
.294-0.3
only
is
the
fraction
of
disintegrations
3.4
actually
will
7 + 7 = N
7 = N
Y=L=
of
2; L + M= t = and K = 1.6
7
L+M
This
are
will
counted.
would
30% of
a
the
7.
So
result
However,
be
interpreted
actual
source
that,
in
for
3~10~
without
x
paying
lo8
since
cts/s,
as
strength.
1
attention
-3x106
0.1
=
the
Bq,
only
to
3x107
the
y/s
1 out
decay
dis/s,
Operational
Health
Physics
Training (Moe)
3-31
3.
Comuton Effect
In the case
impinges
upon
of
the
Compton effect
(see Figure
3.13)
a 7 ray
an electron
and gives
up only part
of its
W,)
a photon of lesser energy (hv) is scattered
energy.
The result
is that
at an angle
0 with
the initial
direction
of the photon. The electron
the initial
direction
of the 7
is
scattered
at an angle
4 with
This
process
occurs
in such a manner that both energy and momentum
ray.
The electron
has a kinetic
energy equal to the difference
are conserved.
between
the incident
and scattered
photon. The electron
will
in energy
lose this energy by ionization
of the atoms in the substance.
The change in wavelength
of the photon in a Compton process is
given by
01 - X0) = AX = 0.0242
hVO
):::>A+
(1-cos
fl)
3.36
8
-m-m-+
0
Figure
3.13
The Compton effect.
(R.E.Lapp 1 H.L.Andrews,
NUCLEAR RADIATION PHYSICS, 2/e, 1954, p.117.
Reprinted by permission of Prentice-Hall,
Inc.,
Englewood
Cliffs, NJ)
Operational
Health
Physics
Training (Moe)
3-32
(in
Angstroms),
initial
and
the
in
energy
of
the
this
is
E2
E e =-=-=A
m c2
of
of
the
process
The
is
shield
later
reason,
effect.
is
is
can acquire
backscattered
given
of
E7(1
- cos 0)
Compton
effect
is
5
MeV
7
in
most
light
but
energy,
process
upon
in
a Compton
(B = 180").
In
by
gamma
rays
is
since
the
of
gamma
rays,
correction
a
point
must
for
elements.
The
as
in MeV.
of
then
The
energy
El
which
into
are
the
of
often
be
proportional
This
beam.
interest
be made
to
of
leads
than
take
electrons
in
the
to
Z/A.
The
presents
out
to
in
removed
or
and a thick
of
a beam,
a greater
may
amount
expect.
account
pre-
a problem
radiation
one would
into
the
truly
scattered
This
photoelectric
physicists,
not
beam
first
decreases
Z.
are
a wide
at
of
to health
effect.
between
effect
the
number
photons
In
as
intermediate
Compton
energies
Compton
the
interest
scattered
7 ray
quickly
upon
of
radiation.
back
important
will
the
a beam
reaching
photon
3.38
depends
substances
the
the
not
in
scattered
a
depend
7
predominant
some
radiation
not
by
scattering
from
be
given
Compton
design
shield,
photon
energy
is
interaction
absorbed
an electron
electron
initial
Compton
For
dominant
which
1 + 1.96
increasing
substance.
does
see that
E7+0.256
photon
=
and
effect.
radiation
one can
the
2
The
with
this,
of
E2
E
keV
wavelengths
3.37
El
200
the
E7+0.511
E
is
7
scattered
the
the
From
scattered
the
Es
cosl9)
where
the
energy
when
energy
are
photon.
maximum
the
Xl
respectively.
of
incident
attained
case,
and
photons,
wavelength
The
process
X0
scattered
change
the
where
this
For
of
this
buildup
Operational
Health
Physics
Training (Moe)
3-33
4.
its
Pair
Production
The
process
energy
and forms
production.
This
near
the
of
E
nucleus
conserved.
The
2moc2,
where
=
the
Since
must
have
rest
MeV
is
portion
positron
Eventually
m,
this
the
nucleus
kinetic
positron
is
for
the
it
is
does
energy
order
through
interacts
in
for
mass
is
pair
of
to
occur.
conserve
ionization
of
momentum
is
electron
production
the
MeV,
given
photon
beyond
1.022
pair
Both
atoms
in
an electron
in
the
the
and
substance.
substance
MeV
3.14
and a
electron
ELECTRON
Figure
by
the
electron-positron
of
can
or positron.
photon
momentum.
called
as occurring
production
an
up all
is
way that
pair
energy
with
this
0.511
the
gives
3.14)
to
to
to
Figure
equivalent
occur,
energy
in
only
energy
and a positron,
(see
needed
rest
MeV for
kinetic
sufficient
pictured
an electron
process
as
the
lose
of
of
an electron
energy
is
21.022
imparted
to
an atom,
mass
When
process
minimum
an energy
a photon
two particles,
pair
be
in which
Pair production
and annihilation.
(R.E.Lapp 1 H.L.Andreys,
NUCLEAR RADIATION
PHYSICS, 2/e, 1954, 1x120. Reprinted
by permission of Prentice-Hall,
Inc., Englewood
Cliffs, NJ)
in
a
Operational
Health
Physics
Training (Moe)
3-34
process
called
changed
into
annihilation.
two
directions.
photons
These
photoelectric
or
is
interact
Compton
effects.
this
process
The
energy.
pair
21.022
MeV,
production
is
That
so
is,
large
E<
10
MeV.
increase
of
result
7
of
tion
at
illustrates
process
(shown
reaction
occurring
probability
marked)
the
and
the
in
matter
so
we
may
employ
protect
that
people
and
electrons
In
pair
likely.
The
effect,
and
matter
for
decrease
with
7
have
in
the
or cascade.
effects
with
energy.
minimum
Figure
The
absorp-
3.15,
of
the
which
specific
probability
one
materials,
which
contain
shielding
materials
is
for
of
a
which
absorbing
a
the
large
procedures
lose
the
energy
occur
of
in
radiation.
of
when
the
of
rays.
The
they
ionize
electrons
a given
For
absorption
and protective
‘these
range
number
the
three
the
will
substance
this
will
reason,
electrons,
are
be
high
the
Z
best
photons.
of
a
substance,
with
from
then
interactions
how well
Absorption
equipment
which
a dense
more
Photon
to
with
total
concerned
Suppose
may take
are
occurrence
are
The
Thus,
Compton
graphically
of
absorber.
iron.
determine
substance.
shown
of high
a shower
will
we
matter.
a
is
nucleus
Compton
substance
7
gammas
given
interactions
physics,
absorbing
5.
the
health
produce
short.
This
energy
increases
each
the
reactions
effect,
and
that
individually
processes
very
the
photon
the
Z.
creates
main
opposite
unless
the
cascade
with
production
is
relative
in
but
is
through
for
Z2 of
In
to
barriers
the
Pair
energy.
the
occurs
photoelectric
effects
7
high,
particles
nearly
all
only
of high
is very
the
in
at
to
photoelectric
for
energy.
some
radiation
processes:
the
these
proportional
substances
of
substance
important
interactions
account
the
occur
multiplication
three
Both
not
mass
emitted
in
is
production
photon-electron
production,
MeV each,
does
energy
more
the
further
for
a pair
The
0.511
also
photon
that
accompanying
pair
is
the
process,
production
predominates
When
place.
pair
process
this
of
may
Since
energy
In
x and 7 Rays
narrow
beam
interactions
of
monoenergetic
may
occur
photons
in
any
is
of
the
sent
through
three
ways
Operational
Health
Physics
Training (Moe)
3-35
0.1
Figure
3.15
already
mentioned.
scattering
and
effect
and
scattering
scattered
through
process
will
will
this
coefficient,
attenuation
is
As
slope
narrow
described
I = IoeBPX,
the
beam
of
by an equation
the
by Compton
photoelectric
beam,
a Compton
an absorption,
of
absorber.
case
paper
for
that
the
give
is,
a
relative
a straight
a constant
semilog
photons,
x and 7
fractional
The value
linear
equation
passes
decay,
substance.
on the
to
as it
of
will
total
monoenergetic
similar
is
the
the
line
beam
radioactive
of
called
the
A plot
there
thickness
straight
beam
a narrow
of
process:
and
in
beam.
the
the
unit
of
in
on semilog
an exponential
p
occurring
intensity
of
is
by
the
assume
the
relative
thickness
the
a
from
the
per
we
interactions
from
equivalent
absorber
denoted
For
the
x
intensity
is
be
3.16).
constant,
absorption
thicknesses
is
removed
Since
measure
Figure
absorption
ray
decrease
in
be
be removed
us
versus
(see
will
absorption,
production.
various
intensity
line
Energy
pair
Let
10
Relative probability
of photon
iron (Fe) versus energy E.
by
photon
1.0
E
of
attenuation
plot.
x
and
3.21,
3.39
y ray
Operational
Health
Physics
Training (Moe)
3-36
ABSORBER
Figure
where
I,
passing
3.16
the
through
a
The
is
the
intensity
sum of
the
thickness,
(in
m),
I is
and
p
the
is
intensity
after
total
linear
the
m-l).
linear
photon
zero
x
(in
total
of
at
thickness
coefficient
probability
X
Absorption
of X and Y rays.
(R.E.Lapp / H.L.Andrews,
NUCLEAR RADIATION PHYSICS, 2/e, 1954,p.109. Reprinted
by Permission of Prentice-Hall,Inc.,Englewood
Cliffs,NJ)
is
attenuation
THICKNESS
attenuation
interaction
probability
coefficient
per
for
each
unit
of
~1 represents
path
the
length.
three
The quantity
processes,
that
7
effect,
is
production.
and
the
c7 is
the
material
a
One
must
consult
the
value
of
substance.
Such
. ,
for
the
p
substance
constant
~1 for
data
a
is
(see
only
attenuation
coefficient
Compton
coefficient
absorbing
is
attenuation
linear
that
The
p
is,
3.40
p=7+u+$T,
where
the
for
effect,
a
a
can be found
the
z
of
given
of
the
photoelectric
is
that
for
energy
of
the
3.15).
literature
or
for
pair
the
a given
of x and y radiation.
or curves
x
p
Thus,
energy
tables
energy
in
and
function
Figure
coefficient
given
for
y
in
rays
(References
order
in
to
find
a certain
15-17).
y
Operational
Health
Physics
Training (Moe)
3-37
In
attenuation
these
curves
or
coefficient
converted
to ms/kg
The
attenuation
tables,
given
by dividing
mass
in
the
attenuation
coefficient
one will
units
value
in
of
cm2/g
coefficient
divided
by the
more
density
often
find
cm2/g.
the
These
may
p is
in
kg/m3.
be
by 10.
pm
is
simply
the
p of
the
absorber:
p,(in m2/W = P/P,
where
mass
linear
3.41a
Thus,
-1
P -~,dm).
What
lead?
The
3.41b
.
is
the
linear
density
of
attenuation
lead
is
coefficient
for
1.134x104
In
compound
the
case
can be found
m-l(.522
of
from
a compound
the
gamma
and
pm=0.0046
kg:
m3
m2/kg:
/I = /.~,p = (0.0046)(l.134x104)=52.2
a l-MeV
in
cm-').
substance,
the
coefficient
for
the
equation
3.42
where
(P/P>2
the
is
compound.
element
of
ith
element
the
the
fraction
weight
The weight
as
fraction
(Weight
mass
The
appears
it
of
of
in
the
ith
an element
Fraction)i
attenuation
symbol
the
coefficient
pi
mixture.
element
in
= kiAi/A,
represents
It
is
and the
a compound
is
given
density
found
of
the
the
density
by the
of
the
ith
of
the
product
compound.
from:
3.43
of
Operational
Health
Physics
Training (Moe)
3-38
where
ki
is
molecular
weight
For
in
the
of
the
example,
The
HzO.
0.00635
number
m2/kg,
atoms
of
atomic
mass
Ai,
and A is
the
compound.
find
mass
ith
of
the
attenuation
attenuation
coefficient
coefficients
respectively.
for
for
l-MeV
gamma
H and 0 are
0.0126
rays
and
Then,
2
= ‘;‘.
PO + (;)HPH
kA
= 0.00635°
kA
HH
pH,O
AH2O
'-
pH20 + 0.0126
AH2O
(103>
= 0.00635~(103)+0.0126~
A graph
of
p/p
6.
for
Half
A
half
value
the
intensity
selected
Value
of
concept
is
layer
is
from
found
x1/2
This
value.
allied
is
the
It
x1/10
is
beam
a
similar
is
quick
thickness
of
radiation
the
half
Appendix
of
to
life
shielding
in
estimates
a substance
one-half
of
which
its
initial
radioactivity.
related
10
the
reduces
value.
The half
value
3.44
which
to
is
equation
the
thickness
E.
Laver
in
the
in
cm-l)
= 0.693/p.
with
In
= /I
to
the
Value
usefulness
This
m-1(.0704
can be found
- Tenth
of
(HVL).
This
Closely
Laver
quantity
layer
materials
= 7.04
the
In 10
= =x1/2
concept
reduces
of
the
HVL is
initial
the
tenth
intensity
value
to
layer
one-tenth
HVL by:
=
3-32
x1/2
3.45
or TVL.
its
Operational
Health
Physics
Training (Moe)
3-39
Given
factor
the half
value
(AF) for a shield
layer,
one
of thickness
can
quickly
estimate
the attenuation
x, from
AF = 2n
in
for
for
which n = x1x1/2 is the number of HVLs. For example, the HVL in lead
a 1 MeV 7 ray is 0.0133 m (1.33 cm), find the attenuation
factor
a lead thickness
of 0.15 m:
.15 m = 11.28
n = .0133m
Similarly,
‘$1.28
2487
AF
=
=
if
the TVL is known, then the attenuation
.
factor
AF = 10n,
is
3.47
in which n = x/xl,lo.
The concepts
HVL and TVL are useful
scattered
radiation
may be ignored.
If the shield
the photon
beam is narrow, significant
scattered
the point
of interest.
For these cases, the total
p may be used to obtain
an estimate
of the
and/or
wide photon
beams (Figure 3.17),
shields
the number of photons at the point over
increase
the HVL or TVL.
7.
for conditions
in which
is not too thick and/or
radiation
may not reach
attenuation
coefficient
HVL or TVL. For thick
scattered
radiation
may
that estimated by use of
Mean Free Path
The
mean
photon,
of initial
path (mfp) is equal
x = l/p.
free
path
energy
E,
to the reciprocal
X is the average
distance
which a
travels
before interacting.
The mean free
of the attenuation
coefficient:
Operational
Health
Physics
Training (Moe)
3-40
If
the
thickness
intensity
of
beam
of
7
the
rays,
length.
But
energy,
E.
note
When
attenuation
an absorber
7
beam
one
relaxation
length.
reduces
the
a
used
term
the
path
that
the
mfp
is
photon
make
The
reduced
by the
penetration
beam
changes.
value
which
those
X = l(m).
P
in
with
fluence
signify
which
factor
e.
In
through
l8
the
by a factor
of
the
can
the
the
photon
the
path
and
is
travel-
the
photons)
relaxation
length
spectrum
of
is
changes
the
reaches
in
the
which
in
scattered
attenuation
is
fluence
gives
length
the
absorber
interacted
energy
of
radiation
free
length
a narrow
and so will
of
not
the
relaxation
initial
mean
plus
to predict
For
e. The uncollided
relaxation
used
the
thickness
(uncollided
as the
then
the
changes
relaxation
shield,
e.
when scattered
have
situations,
the
be
which
beam
Eventually,
then
to
many
of
between
photons
total
So,
path,
called
energy
medium.
Whereas,
the
its
refers
free
of
sometimes
a property
a distinction
mfp
uncollided
thickness
that
one mean
by a factor
is
interacts,
in
to
be reduced
free
may
distance
will
equal
mean
a
to
is
the
coefficient
important,
ing
of
photon
a constant
the
rest
of
the
absorber.
'en/p
8.
up
narrow
the
to
beam
of
beam,
it
coefficient
narrow
p
beam
be
this
less
the
thus
in
the
that
coefficient,
beam
is
this
valid.
concepts
case,
from
This
then
a wide
within
the
On the
other
this
annihilation,
than
the
to be lost
treats
into
One
tion
is
path.
elsewhere
all
In
assumed
well
scattered
positron
rays.
is
one
a path
from
7
point,
have
if
a
7
the
beam.
coefficient
been
is
based
upon
scattered
The use
of
a
out
the
of
total
is
often
called
the
(see
Figure
3.17),
then
coefficient.
If
along
this
beam
beam,
rays
Added
fluorescence
beam.
given
For
by using
approach
Pen/P,
given by
to
this
to
this
in
the
rays
from
other
these
problem
place
be scattered
parts
of
the
the
true
away
beam may
produced
and bremsstrahlung
case,
equation
will
may be photons
radiation,
complex
/I in
radiation
some of
hand,
path.
of
by
formed
attenuation
will
mass
absorp-
be
3.39.
is
to
of
use
j.b.
the
The
energy
attenuation
of
Operational
Health
Physics
Training (Moe)
l-l
DETECTOR
3.17
Figure
Wide beam
of gamma
rays in an absorber.
penx’
I=Ioein
which
kg/m2,
Pen/P 2
photon
Pen/P
to
interacts
As
tector,
the
energy
photons
sorbed
tor.
photons
been
wide
made
beam
use
will
arrive
at pen/p.
will
lead
p/p
leads
using
,uen/p
based
an overestimation
of
an
underestimation,
detector.
In
the
fluence
since
health
as
energy
physics
loss.
to
a de-
The lower
likely
on
the
carried
a substance
some energy
of
coefficient,
the
be more
So,
units
absorbed
for
through
in
in
The
will
to
the
result
interactions
event.
to
passes
x'
being
Corrections
of photons
survive
next
reach
to
energy
path.
processes
which
the
energy
To
have
of
beam
and
m2/kg
quantity.
dimensionless
the
attenuating
in
of
probability
along
a
units
in
a
the
away by photons
photon
is
achieve
gives
3.49
p
to be abthe
at
initial
the
some
work,
detecdegraded
peniP
Operational
Health
Physics
Training (Moe)
3-42
is
preferred
graph
since
of
Appendix
it
will
for
perJp
introduce
some
a safety
selected
factor
in
absorbers
calculations.
can
be
ratio
of
A
found
in
E.
9.
Buildup
Factor
The
gamma
buildup
fluence
to
factor
that
which
b
is
defined
would'be
as the
calculated
by use
of
the
the
actual
narrow
beam
coefficient:
true
b=
fluence
calculated
or
In
fluence
I = I,be-px.
this
case
buildup
factor
buildup
buildup
of
10.
great
large
and
absorbed
cause
to
a
otherwise
the
damage
through
external
it.
to
the
factor
the
the
Section
value
of
corrects
the
for
detector.
literature.17*lg
in
the
Tables
The use
of
of
the
8.
to
the
x
tissue
of
adjacent
may lead
to
7
will
rays
hazard
often
extend
and more
7
These
areas.
To
reduce
required.
Also,
are
scattered
Any cracks
penetrate
to
the
tissues
more
vital
the
at
hazard,
scattered
radiation
or beams
throughout
hazards.
may be significant
while
radiosensitive
tissues
external
Direct-source
streaming
do
as
radiation.
is
in
and
the
one direction,
The deeper
field.
means
hazard.
in
exist
shield
significant
(shielding)
no hazard
to
air
source
matter
ensure
Because
I if
reaching
are
in
the
contribute
adequate
in
sources
of photons
from
hazard
fluence
buildup
be discussed
ray
absorbing
may
The
true
radiation
will
7
distances
photons
the
Hazard
range
extensive
calculate
available
concept
X
3.51
scattered
Relative
3.50
I,e-ILX
known.
are
factor
The
can
is
factors
I
_I
one
underestimation
an
=..
may be
photons
or breaks
may
in
an
of radiation.
such
body
will
than
a high
degree,
as photons
pass
be exposed
skin,
resulting
in
Operational
Health
Physics
Training (Moe)
3-43
in damage that
affects
the well-being
of the body to a greater
extent.
This makes x and 7 rays of greater
concern as external
hazards than
either a! or /3 particles.
From the standpoint
of internal
hazards,
x and 7 rays are
The longer tissue range of
not as significant
as a or i3 particles.
photons
means less energy
loss in a small tissue volume than for either
a! or
p
particles.
Since
photon
energy
loss
occurs
only
at
interaction
sites, energy loss is not continuous
along the photon path. In
a small
tissue mass, few interactions
occur, since the path is small. For
those
that
do occur, the density of energy deposition
is similar
to that
Photons that do not interact
in the organ carry away
for
beta particles.
and therefore
not effective
in producing
energy
that
is not deposited
damage.
F.
Neutrons
we have discussed the properties
of the three
In previous
sections,
types of natural
radiation.
These occur as the result
of the natural
decay
of a nucleus.
In this section,
we will discuss the neutron.
The neutron is
found mainly as the result of nuclear reactions.
The work of Bothe and Becker showed that
a very
penetrating
with
alphas from
radiation
was emitted
when beryllium
was bombarded
consisted
of gamma rays. Curie
polonium.
They assumed that the radiation
radiation
ejected protons from a sheet of
and Joliot
showed that
this
of conservation
of energy and
paraffin.
Chadwick
applied
the concepts
momentum
to
show that
the gamma ray assumption would not hold. He assumed
consisted
of particles
of zero charge and mass about
that
the radiation
Thus, neutrons are emitted
equal
to the proton, which he named neutrons.
when beryllium
absorbs an a according to the reaction:
'Be + $Ie-+lzC+liC
4
This
the
+ 2.
work by Chadwick in 1932 indicated
that the neutron came from
This view
helped
to form the present concept of a nucleus
nucleus.
Operational
Health
Physics
Training (Moe)
3-44
composed
emitted
Also,
of
protons
from
almost
neutrons
and
any
are
neutrons.
element
Later
work
revealed
when bombarded
produced
by cosmic
ray
with
that
neutrons
high-energy
bombardment
of
are
particles.
the
earth's
at-
mosphere.
Studies
slightly
of
the
larger
zero,
since
than
it
has
emission
bY
B
minutes.
1.
charge.
Free
neutrons
0.782
MeV)
with
=
the
be
discovery
produced
target
(a,4
high-energy
or
(r,n>
reactions.
particles
as
are
also
Some of
making
the
an
been
the
intimate
used.
B,
commonly
used
neutrons
which
strength
is
are
a
that
Z of
it
is
a neutron
unstable;
half
they
life
Be,
T%
is
decay
=
10.5
since
have
most
they
shown
of
radioactive
The use
neutrons
that
by either
the
neutrons
Neutrons
the
undergo
also
transuranic
when
result
elements
spontaneous
fission.
from
can be
Neutrons
reactions.
these
reactions
-
These
of
a
past.
sources
and
Recently,
it
gives
a
spectrum
the
of
expressed
241Am
used
often
are
common
238Pu
materials.
yield.
These
energies,
up to
terms
of
about
the
by
powder
239Pu
and
prepared
divided
as target
highest
in
are
and finely
2lOP0,
and F are
are:
sources
emitter
226Ra,
often
have
produce
Some of
since
Na,
ways.
targets.
of
Li,
of
studies
may yield
properties
the
neutron,
variety
suitable
mixture
in
the
a reactor.
substance.
used
number
Accelerators
fusion
(a,4
target
emitters
in
during
a.
confirmed
atomic
substances
sources
emitted
a
strike
process
neutron
of
in
certain
used
The
no net
and
fission
mass.
neutron
in
sources
the
the
of Neutrons
Since
can
of
a proton
(Emax
Sources
neutrons
properties
sources
of
a
have
Be is most
sources
10 MeV.
activity
emit
Source
of
the
Q
emitter.
Because
sources
must
neutron
source
be sealed
but
of
in
have
the
metal
a high
high
toxicity
of
Ra-Be
containers.
gamma-ray
_--
Ra,
PO,
sources
background.
Pu,
and Be,
provide
Pu-Be
these
a strong
sources
have
Operational
Health
Physics
Training (Moe)
3-45
low
-y activity,
have
a
short.
but
low
-y
Radium
radon
is
adequate
contain
from
be checked
for
in
the
exposed
to
7
greater
than
beryllium
2.23
4
and
MeV,
deuterium
The
amount
of
the
literature
below
neutrons
over
anisotropic.
the
some
(138
also
days)
production;
source.
the
Each
a magnitude
(a
not
is
since
container
is
This
source
of
will
emit
are
thus
low neutron
binding
should
are
given
neutrons
gamma rays
substances
re-
lo-30%.
sources
,n>
emit
a
and
with
always
half
life
about
is
when
with
energy
limited
mainly
to
energies
(1.67
and
these
sources.
in
the
7 emitters
closely
sources
which
proportional
emit
nearly
A
are
to
the
monoenergetic
1 MeV.
of
9,
17,
-
impinging
for
new
Reactors
-
The
a spectrum
of
energy,
fission
MeV
(p,n>,
given
in
can produce
up to
neutrons.
and
monoenergetic
produce
substances
in
by high-
(r,n>,
machines
process
extending
yield
producing
target
of
10
27 MeV. 14
up to
are
caused
target
these
Since
many
energies
reactions
(a,W,
useful
range.
accelerators
sources
a suitable
(a,n>,
are
particles,
(7,n)
Nuclear
on
are:
energy
some
20).
sources
wide
high
of
sources
These
sources
deuteron
all
is
these
used
charged
at
for
1,
Accelerator
d.
neutrons
often
in
do
characteristics
reactions
high-energy
Proton
that
nuclei
have
emitter.
particles
of
neutrons
sure
Some
-
short
Accelerator
charged
.'
be
20).
target
rate
(References
C.
(d,n)
radon
17 and
sources
the
7
generally
Types
of
can have
background
is
The
speed
9,
which
7
emission
neutrons,
the
danger
sources
respectively).
drawback
used.
1,
The
PO-Be
life
is
of
reactions
The
further
effect
characteristics
MeV.
Ra-Be.
half
must
symmetry
This
Most
210Po
neutrons
spherical
(r,n>
rays.
than
buildup.
(References
b.
added
of
anisotropy.
literature
the
pressure
of
The
the
one
emission
a loss
yield
but
gas,
the
The
sults
have
radioactive
lower
a
activity,
sources
a
to
give
very
can be used.
monoenergetic
reactors
approximately
produces
17 MeV.
Operational
Health
Physics
Training (Moe)
3-46
A
reactor
provides
2.5-3-O
n
a significant
are
emitted
source
per
of neutrons
thermal
fission
since,
in
on the
presently
average,
known
nuclear
fuels.
e.
these
Spontaneous
fission
sources
are
to
are
desirable
sources
like
spectrum.
9,
13,
and
Fusion
research
indicated
effects
often
advantageous
range
in
+ ti
(2.45
MeV)
3
+ F@
+ 5
(14.1
MeV)
In
these
the
which
and
a.
are
most
in
- When light
+ FzHe
are
from
reactors.
they
notable
spectra
have
of
These
a fission-
these
discussed
types
of
in References
released.
elements
Two
are
fused
to
of
interest
reactions
form
a
in
reactions,
nearly
monoenergetic
neutrons
of
the
be produced.
Enerpv
types
certain
they
in
since
sources
f"
Neutron
following
neutrons
will
on
the
by fission
the
these
neutron
are'
strongly
to
present
of
The
sources
are
The
Protection
produced
neutrons
energies
2.
at
-
20.
nucleus,
fusion
is
that
calibration
characteristics
f.
heavier
as
252Cf
The
sources.
similar
sources
of
interactions
energy
of
predominate
to
they
the
Thermal
thermal
neutron.
depending
treat
neutron
predominate.
Measurements
energy
which
As
on the
in
energy
interactions
The
(NCRP)14
neutrons
National
has
undergo
the
case
of
the
in
terms
of
neutrons.
Council
classified
depend
of
on
neutrons
quite
y rays,
It
the
is
energy
Radiation
according
scheme:
neutrons
equilibrium
with
When neutrons
matter,
they
are
have
slowed
speeds
down so that
comparable
Operational
Health
Physics
Training (Moe)
to
molecules
gas
velocity
is
from
at
about
equation
room
2.2~10~
One may use
0.5
called
us
10
but
of
energy
greater
nation,
it
of
the
of
for
important
to
20
to
the
With
most
of
neutrons
is
then,
the
eV.
energy
range.
energy
region
Neutrons
in
remove
relativistic
10 MeV.
of
neutrons
is
this
interval
are
in
energy
from
range
Again,
this
is
an arbitrary
use.
-
This
the
reactions
in
range
includes
NCRP does
this
not
neutrons
use
this
of
desig-
range.
interactions
experimental
and the
of
the
a neutron
is
the
neutron
reaction
For
occurs.
matter
field
can enter
of
occurs
the
in
a
There
while
passing
depends
upon
the
neutron.
which
one must
supply
nuclear
As the
forms
of physics.
any element
neutrons
still
into
energy
then,
neutron,
the
which
energy
This
nuclei.
in
a neutron
effect
energy
with
work
which
processes.
(n,2n)
neutrons
Although
particular
lighter
a
Fast
neutron
processes
interaction
MeV,
probable
Matter
substances
To
For
MeV.
describe
binding
nucleus.
energy.
10
The
the
this
10 keV.
neutrons
present
matter.
The
the
thermal
= 0.025
- This
-
descriptive
of
of
to
general
study
number
properties
eV
approximately
Interactions
part
except
0.5
keV to
useful
The
limit
neutrons
than
is
erg)
neutrons
Relativistic
d.
through
of
the
neutrons."
Fast
approximately
designation
upper
use
"resonance
C.
a
21 5(4.02x10-l4
Intermediate
let
arbitrary,
are
energy
case,
= ~(1)(1.66x10-27)(2.2x103)2
eV as the
b.
large
The
this
.i
= 4.02x10-
3.
m/s.
In
1.7,
E = +v2
often
temperature.
with
is
holds
at
about
a neutron
least
this
reactions
are
energy
ranging
neutron
8 MeV,
energy
the
in
much
most
from
increases,
9
Operational
Health
Physics
Training (Moe)
3-48
more
complex
term
used
emitted
processes,
such
describe
a process
to
from
an excited
For
mode
of
interact
neutrons,
interaction.
particles.
For
collisions
with
nuclei.
t@e
conserved
transfer
(Figure
in
neutron
energy
elastic
scattering
this
An
of
is
in
is
of
Spallation
of
light
(n,n)
is
a
the
no
and
one can view
elastic
is
fragments
the
which
not
good
assumption
thermal
up to about
can pass
energy
depend
to
charge,
it
does
not
very
close
to
as
and momentum
isotropic,
on
the
scattering
most
nuclides
intermediate
as
pictured
is
for
region.
Figure
3.18
= I/2
= mv
mv2
KINETIC
Elastic collision.
the
.---
energy
when
the
For hydrogen
COLLISION
and momentum
be
angle.
ENERGY = I/2 mv2 = 1/2(mv,2+m2v22)
MOMENTUM
= mv = mv,+m2v2
Energy
a
will
14 MeV.
AFTER
COLLISION
KINETIC
ENERGY
MOMENTUM
are
predominant
V
BEFORE
a
interactions
may be
scattering
will
the
neutron
collision
in
isotropic
has
a nucleus
reason,
If
collision
is
neutron
collision
scattering
Isotropic
a number
scattering
the
field
3.18).
the
can occur.
which
elastic
electric
charged
billiard-ball
in
Because
the
spallation,
nucleus.
fast
with
as
are conserved.
Operational
Health
Physics
Training (Moe)
3-49
greatest
The
loss
when
the
the
most
will
lose
The
average
recoil
nucleus.
For
reason,
will
(n,n'r)
nucleus
to
the
hardly
with
is
the
high
with
is
lost
about
appears
beam
energy
lose
neutron
have
lost
neutron
As
of
a single
mass
of
the
Z are
energy
for
energy
range
above
to
occur.
This
process
(see
Figure
3.19).
an excited
state
In
and comes
equal
mass.
the
for
same
in
the
off
collision.
very
slowing
MeV,
a loss
inelastic
large,
For
as a putty-ball
the
neutron
raises
in
energy.
The
AFTER
COLLISION
EXCESS ENERGY IS
EMITTED
AS
ELECTROMAGNETIC
RADIATION
BOTH
UNITED
Figure 3.19 Inelastic
collision.
is
the
this
scattering
(b)
MOMENTARILY,
MASSES
ARE
all
hydrogen
hu
BEFORE
~~OLLISION
the'
down neutrons.
f
(a)
of
over
collisions.
process,
with
nucleus).
average,
becomes
is
a neutron
energy
with
is pictured
the
each
kinetic
En,
elastic
0.5
Thus,
(hydrogen
collision
use
collision
a proton
nucleus
in
poor
an elastic
energy
in
any
in
as the
lost
the
begins
collision
energy
a
a
a collision
which
En/2.
substances
In
of
of
in
of
energy
approximately
by
particles
energy
The
n,
energy
colliding
fraction
interacting
neutron
of
type
the
Operational
Health
Physics
Training (Moe)
3-50
excited
nucleus
energy
the
as
often
a
7
ray.
excitation
state
this
important
for
ground
this
process
to
the
nucleus.
is
about
state
may
100
be
at
upper
end
of
nuclear
by emitting
occur,
In
the
the
This
fast
reactions
excess
must
supply
state.
process,
energy
to
the
first
For
light
then,
is
more
(> 1 MeV).
neutron
begin
the
elements,
ground
of higher
the
neutron
heavy
3 or 4. MeV.
the
as
state
above
and neutrons
well
to
keV
nuclei
as
elastic
the
heavier
Near
scattering
to
,For
energy
excitation
elements,
returns
range,
occur
inelastic
as frequently
as
scattering.
The
mediate
process
neutrons.
this
region.
The
When
absorbing
energy
of
level
increases
the
greatly.
energy
than
at
energy
becomes
Thus
an energy
is
an
energy
substance
either
slightly
about
energy
of
absorption
state
absorb
higher
100
energy
equal
to
eV,
more
or lower.
capture
inter-
occurs
the
probability
will
for
also
with
nearly
the
the
dominant
combined
nucleus,
than
still
resonance
energy,
product
less
of
neutron
produces
of
scattering
phenomenon
the
nucleus,
elastic
in
of
the
a nuclear
of
absorption
neutrons
at
When the
neutron
becomes
this
an important
process.
As
approaches
the
the
thermal
neutron
neutrons
is
nucleus.
The
compound
energy,
usually
by
capture
or
an
reaction
can
occur.
emission
of
a
proton.
For
reaction
occurs.
The
capture
such
capture,
as uranium
in
with
emission
In
matter
to
a
in
the
ionization
occurs
nucleus.
If
process
the
neutron
combines
thus
formed
must
of
7
rays.
then
This
get
is
this
the
capture
of
a neutron
slow-neutron
of
thermal
may lead
is
In
an
to
(p
as the
or
the
case
emission
of
(n,7)
capture
in
thermal
absorbing
rid
of
excess
radiative
the
(n,p>
leads
B and Li,
certain
to
the
heavy
the
(n,a)
nuclei
fission.
secondary
nucleus
in
neutrons
produced
totally
the
capture
it
the
called
nuclei,
case,
for
with
light
medium.
due to
dominant
decreased,
some
almost
recoil
The
further
For
which
is
is
reaction.
and plutonium
UP energy
ionization
excited
which
(n,r>
neutron
range.
nucleus
Ionization
tion
the
result
in
nature.
heavier
of
capture
charged
takes
of
neutron
The neutron
nuclei)
which
or nuclear
particles
place,
interac-
(n,p)
the
gives
causes
reactions,
from
resulting
the
Operational
Health
Physics
Training (Moe)
3-51
ionization
will
depend upon the 7 interacting
in the medium. The loss
of energy by neutrons,
as well
as by 7 rays,
is not a continuous
process
as it
is for
alpha
and beta particles.
The neutron,
or the 7
move
through
matter
with
little
interference
until
an
will
ray,
interaction
takes place.
When this occurs, then energy will be lost. So,
neutrons are also called indirectly
ionizing
radiation.
4.
Cross Sections
As a beam of neutrons moves through matter, certain
interactions
occur.
From the preceding
section we know that the nature of the
substance
and the energy of the neutron will make certain
processes more
likely
to occur.
In discussing
neutron
interactions,
the term cross
section,
denoted
by 0, is used to express
the probability
that
a
neutron
will
interact
with
a given substance. For any given process, if
the probability
is high,
the cross section
will
be large. The cross
section
is expressed
by means of a unit called the barn (b), equal to
the
probability
in terms of an
10e2*
m2.
The
barn
expresses
In a sense, then, the atom may be viewed as presenting
an effective
area.
area to a neutron.
If
a neutron passes through this area, the
target
reaction
occurs.
cross
section
(T is
called
the microscooic
cross
The
section
since
it
expresses
the probability
per atom. Each possible
The total microscopic
cross section,
interaction
has its own probability.
cross sections
for
all
processes
at,
is the sum of the separate
which may occur:
ut = Oscatter
+ ocapture
+ Ofission+.""
3.52
One should
not construe
that
the cross section is simply a
area of the nucleus. The effective
target area
measure of the geometrical
is often much greater
than the
which a nucleus
presents
to a neutron
the radii of a proton and a neutron are about
area.
For example,
impact
to just
occur,
1.3x1O-15
m. For an impact
the same: approximately
Operational
Health
Physics
Training (Moe)
3-52
the
particle
Figure
centers
3.20).
10-15
2
>
The
for
that
can
see
Curves
eV
this
for
at
wish
of
length,
dealing
to
express
substance.
called
the
macroscopic
cross
cross
at
section
is
greater
of
of
area
the
neutron
penetration
probability
of
such
section
It
be
is
area.
One
area.
found
a
Et
a reaction
case,
cross
is
through
in
the
in
the
terms
of
probability
section
X
related
a substance,
is
per
one
thick-
unit
desired.
the
to
the
The
total
path
total
microscopic
equation:
m-l
the
in
a geometric
can
materials
~(2.6~
m2.
impact
simply
(see
section
480~10-~~
than
than
apart
cross
or
b,
m
22).
In
by the
48
much
a circle
total
much more
macroscooic
Bt=Nat
N
21,
the
the
is
is
with
In
is
2.6~10~~~
be
the
number
a
17,
then
But
at
than
would
area
in
more
neutrons
that
(References
where
area
effective
from
be
m2.
0.01
the
literature
may
ness
impact
=2.12x1O-2g
hydrogen
clear
cannot
3.53
number
of
atoms
per
cubic
meter
of
the
substance
of
a substance
in
a
thickness
(=pNa/A).
Let
cross
of
cross
will
total
section
in
the
a
m2
and
cross
sum of
atoms.
macroscopic
section
the
at.
contributions
Thus,
No,
c
replaced
probability
given
/I
per
by
section
cross
coefficient
the
is
volume
is
10s2
The
total
from
each
the
total
p.
unit
By
for
path
X
for
initial
this
case,
energy
of
m.
a
Each
reaction
atom.
reaction
neutrons
gammas,
length.
mean
is
But
N
cross
similar
both
Sometimes
the
analogy,
since
the
free
to
quantities
older
symbol
path
X
for
by
3.54
x = l/C,.
In
terms
10m2 m.
express
neutrons
of
cubic
10m4
has
be the
attenuation
is
of
number
The
the
a
substance
the
section
the
picture
area
section
atom
is
us
X
travels
gives
before
the
average
interacting
distance
in
a
a substance.
neutron
of
a
given
Operational
Health
Physics
Training (Moe)
m
2.6~10-‘~
Figure
As
was
meaning
of
several
energies
the
concept
neutron
will
energy
of
passing
the
are
of
neutron
free
will
not
not
radiation,
carefully.
or if
path
be
Assume
a
a
beam.
fluence
narrow
a spectrum
(in
Assume
n/m2
of
the
the
mfp value
interpret
already
be modified.
monoenergetic,
the
one must
We have
must
beam
substance.
rate
area.
seen
energies
when
present,
practical
most
determined
mfp,
neutron
fluence
is
on one
based
that
are
Since
the
from
reaching
given
a
initial
a spectrum.
Absorotion
q5 = kv
path
because
Neutron
the
photon
underestimate
n beam,
through
in
mean
happens
the
with
present,
probably
This
5.
free
Impact
3.20
case
mean
sources
1/q
point.
meter
the
the
t-
of
Let
s).
given
of
k be the
number
that
further,
4 is
neutrons
each
neutron
a certain
of
energy
neutrons
has
E,
per
a speed
by
3.55
v.
is
cubic
Then
Operational
Health
Physics
Training (Moe)
3-54
The
fluence
rate
cross
sectional
picture
of
passing
through
reactions
1 cubic
per
unit
number
of
one
meter
1
m
of
of
time
the
in
the
of
neutrons
square
meter
a substance,
this
meter
passing
per
the
substance
of reactions
m3 s
in
decrease
Ax will
the
area
number
The
gives
the
unit
time.
probability
is
of
through
In
of
given
by Xt.
substance
will
a sphere
terms
of
a
a reaction
in
The number
of
be
JZ,.
fluence
of
3.56
rate
as the
beam moves
through
a thickness
be
A4 = - &Ax.
In
this
case,
the
beam.
3.57a
we assume
This
that
if
may be written
a neutron
is
scattered,
as a differential
equation
it
is
removed
in
which
from
&& - dk and
Ax
dx
3.57b
This
form
is
seen
before.
the
well
When
known
expression
integrated,
this
for
an exponential
relationship,
gives
q5 = r$,e-"tx,
where
4.
is
plotted
be
the
is
the
recent
fluence
paper,
Et,
only
the
monoenergetic
is
if
whether
the
one
beam.
For
n
has
beam.
case
with
can consider
a
narrow
For
a wide
of
get
to
usage
coefficient,
rate
one will
similar
common
As
from
initial
of
times,
attenuation
valid
3.58
on semilog
value
as
the
been
for
neutrons.
If
this
a straight
line
case
radioactive
to
for
use
the
whose
symbol
equation
slope
will
decay.
p
for
In
the
y or n.
y
the
beam,
beam,
rays,
scattered
this
type
this
neutrons
condition
some of
the
of
relationship
are
is
being
removed
may be assumed
monoenergetic
for
neutrons
a
Operational
Health
Physics
Training (Moe)
3-55
scattered
out of the beam will be replaced by neutrons scattered
into the
cross
section
Xt may thus lead
to an
beam. The use of the total
Also, since most n
overestimation
of the effectiveness
of an absorber.
even for
narrow
beam conditions,
the
sources
are not monoenergetic,
relationship
will
not hold. That is, a spectrum of neutron energies will
and the attenuation
will not adequately be given by a single value
exist
of q(Pt)
*
6.
Removal
Cross Section
(ck)
-7
Because
of the large amount
a collision
with hydrogen, this process
neutron
the beam. One can then view
removal
cross section
concept.
The
attenuation.
The removal cross
neutron
of large angle scattering
probability
would
tend to remove n.
The mass macroscopic
/-I
_ R = 0.0206
P
Generally,
the total
cross
the
is given
by**
3.59
kg
removal
cross
0.0206(55.847)-1/3(26)-'294
section
= 0.0021
P
Note that
section
A-1/3Z-*2g4,2.
the removal cross section is about
attenuation
coefficient
for E between
EXAMPLE: Compute
A=55.847).
5,
removal
of energy lost by a fast neutron in
in effect
removes the neutron from
attenuation
in terms of a removal
/1R is then used to estimate
section can be viewed as giving
the
(both elastic
and inelastic),
which
cm2 divided
-F
by 10 equals
&.
kg
2/3 of the average
6-8 MeV.
for
the element
2(*021
kg
F
iron
value
of
(Z=26,
Operational
Health
Physics
Training (Moe)
3-56
The
of
hydrogen
backed
in
up
The
HI .
energy
the
concept
is
be
heavy
nucleus,
large
for
part
hardly
energy.
these
the
suffer
the
the
other
be at
least
range
2-12
In
60 kg/m2
MeV.
that
they
with
neutron
of
In
in
an elastic
but
presence
substances
collisions
collision
cases
upon
to
energy.
energy,
an elastic
In
their
they
any
in
inelastic
of
If
based
there
neutrons
suffer
is
be applied
(provided
by hydrogen.
lose
section
can also
fast
which
However,
of
It
a large
they
angle.
transfer
valid
lose
captured
cross
absorbers
neutrons
will
removal
absorber.
hydrogen
range,
then
of
by
substance
a
concept
that
a heavy
case,
they
collision
may
with
may be scattered
hydrogen
will
over
causes
also
a
a large
be effectively
removed.
Without
the
absorber,
the
range
treated,
occur.
Again,
inelastic
the
presence
removal
elastic
concept
or
hardly
occurs,
neutrons
drops
probable
and
In
case,
the
substance
Since
these
neutrons
this
through.
of
the
below
removal
cross
not
is
lost
in
will
inelastic
still
have
is
the
not
will
lead
In
with
an elastic
much
to
been
the
removed
to
poor
neutron
heavy
As the
nuclei
energy
results
of
the
become
less
to be captured.
neutrons,
from
will
When an
will
energy
up
energy
collision.
lost.
too
or backing
the
scattering
transparent
have
absorber
apply.
be
1 MeV,
will
section
in
scattering
energy
about
neutrons
does
inelastic
any energy
collision
the
of hydrogen
which
the
for
beam,
the
stream
the
use
calculated
attenuation.
Keeping
3.57
the
where
4.
CpR/~>
of
discussion
in mind,
we may rewrite
equation
to.obtain
4 = doe-(p'R)
now
above
is
is
be
the
the
expressed
removal
the
x
fluence
removal
in
cross
rate
cross
kg/m2.
section.
One
in
the
hydrogenous
section,
and
further
restriction
The
region
of
the
material,
thickness
applies
validity
x
to
is
the
limited
must
use
to
Operational
Health
Physics
Training (Moe)
3-57
(pR/p)
x
<
cm2/g)
Section
versus
5.'
the
8.E.l
for
The
one
knows
The
removal
additive,
A
plot
atomic
cross
cross
can
section
section
of
found
used
sections
cross
be
approaches
cross
removal
removal
mass
shielding
removal
the
of
for
for
for
section
in
Reference
(in
14.
See
neutrons.
a compound
each
substances
values
of
can be calculated
the
mixed
constituent
together
if
elements.
is
assumed
to be
so that
PR (compound)
where
ith
= g (WP>iPi
i=l
is
the
value
and
pi
is
('JVP>i
element,
appears
in
3.61
the
compound
obtained
the
(see
from
density
equation
of
equations
the
3.42
3.59
ith
and 3.43
for
element
for
the
as
it
evaluation
of
Pi) *
Neutron
7.
One
of
sorption
by
compound
nucleus
a
Many
tive.
radioactive.
thermal
exposed
term
activation
The
thermal
that
energy
also
fluence
the
atoms
the
The
neutron
substance
is
then
in
this
activation
to
will
activation
that
the
by neutrons
of
a
radioac-
Absorption
most
artificial
absorbs
product
uact'
if it
be activated
ab-
when other
a reactor.
section,
cross
substance
becomes
When a nucleus
imply
is
produces
produced
reason,
reactors.
used
attenuated
process
are
fluence
For
in
is
this
substances
neutrons.
a certain
a neutron
substances,
unstable.
produced
However,
Assume
atom,
per
radioactive
thermal
been
neutron.
many
to
have
probability
neutron
is
by which
radioactive
for
the
thermal
For
which
mainly
radionuclides
the
processes
nucleus.
are
neutron,
the
artificially
substances
occurs
Activation
energy
a
becomes
expresses
absorbs
greater
a
than
occurs.
a
sample
rate
total
is
containing
C#J. If
probability
then
N
oact
is
is
atoms
the
No,,..
is
exposed
probability
The
rate
to
of
of
a thermal
activation
formation
of
Operational
Health
Physics
Training (Moe)
3-58
formation
rate
During
of
the
the
atoms
be given
will
N1
is
rate
atoms
rate
of
the
are
being
formed,
radioactive
atoms
some
N1 will
t.
tl
growth
present
is
then
- decay
rate.
and
X
is
the
is
AN?
3.63
number
is
time
of
equation
of
radioactive
At
stopped
A, = AN1 = ~$a~~.N(l
at
atoms
rate
The activity
irradiation
activity
rate
= formation
the
time
the
radioactive
The net
growth
gives
irradiation
of
= &,,$J -
dt
N'
3.62b
differential
d
The
radioactive
The decay
number
of
corresponding
t that
that
= XNl,
constant.
rate
here
time
decay.
the
transformation
The
3.62a
by
decay
where
= &,ctN.
is
(in
dis/s)
expressed
atoms
present
of
sample
the
after
at
the
time
by
- emAt).
after
an
3.64
a sample
is
removed,
is
given
by:
A = AtemAt
= 40 ,,,N(l
The
until
activity
the
further
that
the
saturation
activity
irradiation
time
this
irradiated
term
At
formation
increase
value
- emXt)emXtl
3.65
of
the
rate
in
is
activity
activity
sample
equal
will
will
A,.
The
in
to
the
sample
attains.
fraction
the
occur.
neutron
decay
For
is
doactN,
term
(1
-
For
of
the
saturation
given
will
increase
At this
sample,
which
emXt)
any
field
rate.
a given
reach
t=Otolfort=co.
gives
the
the
is
varies
irradiation
activity
point,
maximum
called
from
no
the
0
for
time
t,
A, which
the
Operational
Health
Physics
Training (Moe)
3-59
The
neutron
field.
the relationship
constant.
This
number of target
equation
is
valid
if
all
target
atoms are in the same
In effect,
this means that the samples must be thin. Also,
the number of target atoms remains about
assumes that
decrease in the
means that there should be no significant
atoms during the irradiation.
thick
samples,
the neutron
field
For
of a neutron absorber.
This loss is called
prescence
In addition,
the fluence
will
be reduced
due to
atoms. This
is referred
perturbing
effects
need to
is reduced
by the
the flux depression.
rate at the inner central portion
of the sample
of neutrons by the outer layers of
absorption
to as the self-shielding
effect.
Both of these
be accounted for in thermal neutron absorption.
these perturbation
effects
become
As the energy of the neutron increases,
less severe and the corrections
are reduced in magnitude.
Let us work an example, to illustrate
the use of equation 3.65.
A 1O-3 kg tungsten
sample is exposed for
three
days at an average
thermal-neutron
fluence
rate
of 1015 n/m2s in a reactor.
The cross
section
life of W-187 is 24h. What is the
Oact is 40 b and the half
activity
of the sample 12 h after irradiation?
Also, determine A,, the
saturation
activity.
A =
daactN(l
N = (m/A)N,
- emAt).
= (lO-3/O.l86)6.O22xlO23;
t = 3d, tl
aact = 40 b = 40~10~~~ m2.
X = 0.693/l
day = 0.693 d-l
4 = 1015 n/m2s.
Therefore:
A-
1015(40x10-28
- 8.01~10'
and
)lO-36
Bq (0.216
o22x1o23(l
0.186
Ci)
_ e-0.693(3)>e-0.693(0.5)
=0.5d
----.--_.---.-
- -.-.---~
Operational
Health
Physics
Training (Moe)
3-60
As = &~actN
= 1015(40x10-28)10-3
(6.022~10~~)
0.186
= 1.295
8.
neutron
Hazard
Neutron
sources
may
reduce
rather
still
the
produced
adjacent
areas.
throughout
the
In
the
energy.
elastic
scattering
thermal
neutrons
a
range
small
in
for
a
dose
could
energy
of
mass,
tissue
are
more
hazards.
the
more
hydrogen
more
a
reverse
a proton,
proton
than
is
than
true.
the
a
7
the
in
is
of
For
in
extend
are
their
to the
energy
organ
in
and
reactions:
of
has
a
exposed
related
tissue,
14N(n,p)14
a small
in
Intermediate
mass
a photon
ray.
concern
absorption
the
Since
damage
for
done
large
important
Scattered
scattering
tissue.
in
can
interactions
80-95%
in
mainly
For
large.
tissues
about
neutron
concern.
tissue
damage
the
material
inelastic
to cause
of
the
create
radiosensitive,
energy
than
and
body,
up
with
often
can also
capture
Since
matter,
Absorbing
is
material
give
their
the
source.
amount
The amount
processes
C
process.
a much
will
large
the
greater
be greater
organ,
the
7
be greater
neutron
the
rays,
deposition
tissue
hazardous
interactions
transfer
from
This
neutrons
energy,
deeper,
neutrons
is
electrons.
producing
The
14N(n,p)14C.14
recoil
7
the
from
through
Fast
Since
and
far
hazards.
and other
gamma radiation
travel
field.
process
'H(n,-r)
air
radiative
enough
lose
through
shielding
neutron
and
'H(n,-rj2H
in
as external
required
addition,
body.
external
the
the
neutrons
neutron
For
in
may result
As
to
but
Ci).
significant
freely
hazard,
shield
are
be hazardous
neutrons
the
Bq (0.35
Relative
moves
field
x 10"
of
protons
means
are
4-20
than
neutron
7
recoil
energy
and recoil
nuclei
neutrons
should
that
damage
produce
rays.
than
7
times
more
rays,
to
tissue
is
be
Depending
effective.
although
particles,
both
more
will
vary.
dense
than
more
effective
upon
the
On this
are
protons,
basis,
significant
The
that
neutron
neutrons
external
in
Operational
Health
Physics
Training (Moe)
3-61
Neutron
The
hazard.
properties
high
lack
of
fixed
in
sources
of
natural
neutron
the
body
spontaneous
are
not
normally
sources
that
sources
quite
remote.
fission
considered
emit
make
the
chance
This
view
could
rates
become
as an internal
neutrons
of
and
a neutron
change
if
more
readily
AND
MEASUREMENT,
the
physical
source
being
substances
with
available
in
larger
quantities.
REFERENCES
1.
Knoll,
Sons,
G.F.,
New York,
RADIATION
NY (1979).
DETECTION
2.
THE
Evans,
R.D.,
York,
NY (1955).
3.
NCRP Report
No.
cations,
Bethesda,
4.
Hendee,
Publishers,
5.
Rays
and
Teleisotope
y Rays,
in
RADIATION
Johns,
H.E.,
X
DOSIMETRY,
Vol.
III,
2nd ed, edited
by F. H. Attix
and E. Tochilin,
Academic
Press,
New York,
New York (1969).
6.
NCRP Report
No. 51,
100
MeV
PARTICLE
Bethesda,
MD (1977).
7.
Segre,
E.,
Editor,
and Sons, New York,
8.
Rees,
Press,
9.
Chilton,
Prentice-Hall,
ATOMIC
NUCLEUS,
McGraw-Hill
Book
39, BASIC RADIATION
MD (1971).
PROTECTION
CRITERIA,
W.R.,
MEDICAL
Inc.
(1979).
RADIATION
EXPERIMENTAL
NY (1953).
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Katz,
L.
11.
Loevinger,
DOSIMETRY,
New York,
12.
Anderson,
D.W.,
Press,
Baltimore,
13.
ICRU
Report
Washington,
et
Inc.,
and Penfold,
2nd ed,
RADIATION
PROTECTION
DESIGN
ACCELERATOR
FACILITIES,
al,
Section
Englewood
A.S.,
Massachusetts
lOb,‘PHYSICAL
D.C. \1964).
and
Co.,
Inc.,
New
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OF
ASPECTS
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IONIZING
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Wiley
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G.L.,
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OF IRRADIATION,
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1, John
Institute
of Modern
NCRP Publi-
GUIDELINES
FOR O.lNCRP Publications,
4, PRINCIPLES
OF RADIATION
Cliffs,
NJ (1984).
Discrete
R.,
et
al,
edited
by Hine,
G.H.
NY (1956).
ABSORPTION
MD (1984).
Wiley
Year
NUCLEAR PHYSICS,
HEALTH
PHYSICS,
D.J.,
Cambridge,
MA (1967).
A.B.,
PHYSICS,
John
University
ICRU
Publications,
Park
Operational
Health
Physics
Training (Moe)
3-62
No.
38,
Bethesda,
14.
NCRP Report
Publications,
15.
Hubbell,
J.H.,
Photon
Cross
Energy
Absorption
Coefficients
U.S. Government
Printing
Office,
16.
and
Gamma
Evans,
R.D.,
X Ray
DOSIMETRY,
Vol.
1,
2nd ed, edited
Academic.
Press,
New York,
NY (1968).
17.
Shelien,
B.
RADIOLOGICAL
MD (1984).
18.
Chilton,
Prentice-Hall,
19.
Schaeffer,
TID-25951,
(1973).
A.B.,
PROTECTION
MD (1971).
AGAINST
NEUTRON
RADIATION,
Sections,
Attenuation
Coefficients
from 10 keV to 100 GeV, NSRDS-NBS
Washington,
D.C. (1969).
Ray
Interactions
by F. H. Attix
and
29,
in
RADIATION
and W. C. Roesch,
and
Terpilak,
M.S.,
Editors,
THE HEALTH PHYSICS AND
HEALTH
HANDBOOK,
Nucleon
Lectern
Assoc.,
Inc.,
Olney,
et
Inc.,
al, Section
Englewood
N.M.,
Editor,
NTIS,
U.S.
6, PRINCIPLES
OF RADIATION
Cliffs,
NJ (1984).
REACTOR SHIELDING
Department
of
NCRP Report
No.
23,
NEASUREMENT
OF
PHYSICAL
AND BIOLOGICAL
APPLICATIONS,
MD (1960).
21.
Cohen,
B.L.,
Nuclear
Cross
MEASUREMENT
AND PROTECTION,
Palm Beach,
FL (1978).
Sections,
edited
22.
Chilton,
Prentice-Hall,
8, PRINCIPLES
OF RADIATION
Cliffs,
NJ (1984).
et
Inc.,
al,
Section
Englewood
SHIELDING,
FOR NUCLEAR ENGINEERS,
Commerce,
Springfield,
20.
A.B.,
NCRP
VA
NEUTRON FLUX AND SPECTRA FOR
NCRP Publications,
Bethesda,
in
HANDBOOK OF RADIATION
by A. Brodsky,
CRC Press,
West
SHIELDING,
BIBLIOGRAPHY
Brodsky,
HANDBOOK
CRC Press,
A.B.,
X- and Gamma-ray
Absorption
and Scattering
coefficients,
in
OF RADIATION
MEASUREMENT
AND PROTECTION,
Edited
by A. Brodsky,
West Palm Beach,
FL (1978).
Morgan,
K.Z.
and Turner,
TION, John Wiley
and Sons,
Price,
W.J.,
NUCLEAR
New York,
NY (1964).
J.E.,
Editors,
Inc.,
New York,
RADIATION
PRINCIPLES
NY (1967).
DETECTION,
2nd ed,
Firedlander,
G., et al, NUCLEAR AND RADIOCHEMISTRY,
Sons, New York,
NY (1964).
Glasstone,
S.,
Inc.,
Princeton,
SOURCE BOOK ON ATOMIC
NJ (1967).
ENERGY,
3rd
OF RADIATION
McGraw-Hill
2nd ed,
ed,
John
PROTEC-
Book
Wiley
D. Van Nostrand
Co.,
and
Co.,
Operational
Health
Physics
Training (Moe)
3-63
Auxier,
RADIATION
Academic
Law,
Hall,
R.E.
Inc.,
Goldstein,
Reading,
INTRODUCTION
H.,
England
(1983).
Bushong,
St.
S.C.,
Louis,
ASPECTS
SCIENCE
2nd
PHYSICS,
ELEMENTARY
2nd
PROTECTION,
RADIOLOGIC
MO (1984).
PHYSICS,
4th
OF REACTOR SHIELDING,
HEALTH
J.E.,
J.,
RADIATION
MA (1981).
and Penetration
in Tissue,
in
F. H. Attix
and W. C. Roesch,
NUCLEAR RADIATION
NJ (1972).
TO
G.S.
and
Turner,
New York,
NY (1969).
Shapiro,
Cambridge,
co. )
and Andrews,
H.L.,
Englewood
Cliffs,
H.,
FUNDAMENTAL
MA (1959).
Cember,
Oxford,
Hurst,
Sons,
Neutron
Interactions
J.A.,
et
al,
Edited
by
DOSIMETRY,
Vol.
1,
Press,
New York,
NY (1968).
FOR TECHNOLOGISTS,
Pergamon
PHYSICS,
Harvard
ed,
Prentice-
Addison-Wesley,
ed.,
RADIATION
ed,
Press,
Wiley
University
3rd
ed.,
and
Press,
C. V. Mosby
QUESTIONS
3.1
Name
health
type?
the
four
physics.
3.2
What
emitted
term
is
used
from a given
3.3
Although
scattering
along
their
path is
is
main
What
of radiation
radiations
of
a
scattering
which must be dealt
with
in
may be considered
as a single
that
the energies
are almost
identical?
to
indicate
radioisotope
particles
most
is
What
naturally
3.5
processes
what
two
BY
Describe
the processes.
3.6
What
value
ion pair
in
3.7
What
happens
substance?
3.8
Why
unit
3.9
Why should
an increased
particle
near the end of
do
of
infrequent,
to occur?
likely
range
of
most
energy
radioactive
atoms?
3.4
does
path
the
occurring
types
two
Q
Q particles
CYparticles
at what
particles
emitted
lose
their
an Q
length?
an
a
particle
particle
produce
its
ionization
path?
whose
a
energy
high
occur
is
entirely
number
of
for
a
by
energies?
defined
by the average
energy
required
to
is
for air?
a given
substance. 7 What is that value
to
point
create
lo&
ion
heavy
an
in
pairs
per
charged
a
Operational
Health
Physics
Training (Moe)
3-64
3.10
What
unit
term
is
used to indicate
of path length
as it passes
3.11
What
term
is
used
to
indicate
substance
divided
by the density
3.12
What
term
is
two substances
3.13
What
travel
3.14
The
that
used
divided
P;:
the
symbols
will
E
Make
that
s,
a radiation
of
to
the
(S/P),,
a
powers
particle
relating
P,
per
power
ratio
of the stopping
of that
substance?
distance
ze,
by a particle
material?
linear
stopping
substance?
are used in formulas
travel
in a medium:
ip,
W:ia,
the
that
of
to indicate
the
by the density
term
indicates
in matter?
following
an a particle
the loss of energy
through
a specific
of
will
distance
WA),,
R,,
as an external
hazard
P:’
up a table
to
indicate
the
3.15
Explain
the
relative
hazard
and as an internal
hazard.
3.16
How is
different
3.17
What
3.18
Name
passing
3.19
Why is
usually
3.20
With
what
part
of
an atom
interact
to produce
bremsstrahlung?
3.21
For
a particular
Z or atomic
number
bremsstrahlung?
3.22
Explain
materials
stopping
3.23
What
unit
3.24
Explain
the
relative
hazard
and as an internal
hazard.
3.25
How is
the
energy
of
from the energy
high
speed
particle
is
three
ways
in
through
matter.
the
much
actual
greater
/3
of
meaning
of
of
a particles
particles
a particles?
identical
which
/3-
from
the
velocity
a particular
particles
lose
path
travelled
by
than the straight-through
does
energy
of
/I
of an absorbing
terms.
radioisotope
to B-?
a
an
/3
particle
material
why the
stopping
power
for
decreases
as the
Z number
ability
is essentially
a function
does
the
of thickness
these
their
electron
path?
particle
or electron,
affect
the
,9 particles
increases
of their
of
a wave related
j? particles
to
its
in
or /? particle
or
an electron
how does
production
the
of
or electrons
in
yet their
relative
density.
constant
fractional
decrease
in the
by /? particles
or electrons
define?
of
energy
ionization
as an external
wavelength?
per
hazard
Operational
Health
Physics
Training (Moe)
3-65
3.26
How is
3.27
Name
some
familiar
constitute
a hazard
3.28
What
term
radiation?
3.29
What
3.30
What
is
the
at a specific
name of
distance
3.31
What
does
term
3.32
What
are
3.33
Identify
a>
b)
the
is
period
of
is
to
constant?
the
to
a
single
What
frequency?
quantum
are
its
of
"isotropic"
two conditions
the
sources
Which
of
these
an electromagnetic
units?
the statement
relating
the
from an isotropic
source?
the
radiation
intensity
mean?
under
which
inverse-square
law
is valid?
of
continuous
characteristic
x ray spectrum,
x ray
the
highest
and
energy
3.34
Upon
what
depend?
does
3.35
What
rays?
of
3.36
interactions
Name the
three
common
rays or 7 rays are absorbed.
3.37
Which
part
the
radiations.
ionizing
power?
electromagnetic
because
of their
given
Planck's
the
the
a wave related
the
atom
electromagnetic
is
all
and
b)
The
radiation
energy
energy
of an electron
c)
the
radiation
orbital
electron
energy
photon?
3.38
What
are
3.39
What
is
of activity?
3.40
What
related
produced
responsible
interactions
a>
x ray
for
with
with
the
matter
matter
by an x ray
production
that
take
of 7
result
place
tube
when x
when:
energy
is given
to the work function
of
the
radiation
to the kinetic
energy
of an ejected
orbital
electron?
Auger
internal
is
to
the
the
to
is
given
and a positron?
energy
and
electrons?
is
the
production
and kinetic
given partially
to the ejection
of an
remaining
energy
continues
as a lower
When are
conversion?
the
4
they
Why is
minimum
energy
needed
rest mass of an electron?
produced?
it
for
important
in
the
pair
production?
measurement
How is
it
Operational
Health
Physics
Training (Moe)
3-66
3.41
Name
intensity
the
per
decrease
an absorbing
constant
fractional
unit
thickness
of
3.42
What
cient
value
by the
is
obtained
density
p of
3.43
What
travels
term
is
before
3.44
What
when
rays?
corrections
computing
why?
used
to
interacting?
by dividing
the absorber?
indicate
the
must
be made
the
absorption
distance
to the total
of
a wide
y rays
What
is
half
3.47
What
is
buildup
3.48
What
are
the
3.49
How is
the
source
strength
of an (a,n)
rated?
What are the hazards
associated
with
3.50
Explain
source.
3.51
What
type
a)
b)
c>
a highly
monoenergetic
neutron?
a large
supply
of a spectrum
of neutrons?
and
economically
neutrons
most
conveniently
laboratory?
Make
a chart
a>
neutron
terminology
based upon neutron
interactions
of neutrons
with matter.
layer?
What
constitute
is
tenth
of
neutrons?
value
principal
sources
,term
anisotropy
of neutron
sources
in
x
a photon
coefficient
rays or y
external
than
layer?
will
neutron
source
these sources?
relation
to
an
frequently
neutron
(a,n>
produce
for
a
small
indicating:
3.53
Why are
high
3.54
What
resonance
3.55
What
is meant
it predominant?
3.56
Explain
tion
in
3.57
is
defined
by the probability
What
term
act with
a nucleus
in terms of an area?
why
matter
ray
coeffi-
which
a greater
Y
factor?
the
is
or
attenuation
beam
of
3.46
value
and
average
ray
attenuation
Explain
internal
b)
rays
linear
3.45
3.52
why x
hazard.
the
.of
x
substance.
Z materials
poor
for
slowing
energy
and
down neutrons?
absorption?
by radiative
capture
produced
ionization
is secondary,
of
neutrons?
as the
result
that
At what
energies,
of neutron
a neutron
is
interac-
will
inter-
Operational
Health
Physics
Training (Moe)
3-67
3.58
What
is:
a)
the
the
the
b)
name of the unit,
and
size
of
the unit
that
preceding
item?
3.59
What
term is defined
with
a particular
substance?
3.60
Name the
3.61
What
does
define?
3.62
What
does
1 m2 cross
3.63
What
error
occurs
in calculating
broad
neutron
beam
that
could
effectiveness
of an absorber?
3.64
What
unit
energy
lost
3.65
What
atomic
3.66
What
term
neutron
that
3.67
What
two
rates
will
determine
of radioactive
atoms in neutron
3.68
Discuss
At and
three
by the
material
principal
the
of
the
the
what
term
Of
of?
3.70
By what
process
3.71
Explain
the
the
a>
is
difference
indicated
the
why?
neutron
lead
that
neutron
cross
unit
time
of neutron
do recoil
following
organs?
rate
protons
do to
lose
section
passing
their
large
absorbs
growth
of
an activation
the
human
of
body
energies?
reactions:
above,
which
b)
is most
large
important
organs?
for:
Zt
through
a
case of a
of the
amount
attenuation
b) ltN(n,p)liC
given
interact
of
the
of
the activity
symbol A,.
in
interaction.
is based upon the
with hydrogen?
neutrons
definition
absorption
in the
an overestimation
to
the net
activation?
between
by the
damage
reactions
small
per
the
a neutron
will
the
thickness
macroscopic
relationship
neutrons?
a> H(n,T)D
In
for
is used to indicate
that when a nucleus
the product
becomes radioactive?
3.69
3.72
for
the
for neutron
attenuation
by fast neutrons
colliding
approximate
Z for fast
that
of
sections
the
number
of
neutrons
section
of area define?
is
the
number
be used
probability
in
terms
cross
reciprocal
would
of
versus
a thermal
the
number
sample
a function
Operational
Health
Physics
Training (Moe)
3-68
3.73
Why are
3.74
What
added
3.75
Why are
neutrons
not
radiation
hazard?
neutrons
considered
as an internal
may
accompany
neutrons
more
hazardous
than
hazard?
and must
be considered
as an
y rays?
PROBLEMS
3.1
An a
0.069
particles
formed?
particle
m in
in
Answer:
3.2
a>
a)
b)
a)
Find
the
plutonium-239,
b)
Using
c>
What
Find
the
platinum-190,
Answer:
3.5
Find
26.98
Answer:
214P0,
has
a range of
polonium-214,
energy
of 7.68 MeV. If the W value
for a
eV/ip,
what
is
the average
ion pairs/m
power of a 50 MeV proton
as 5.67 MeV cm*/g.
it to SI units
and
the linear
stopping
the
is
9.072x101.03~10-~
l4 Jm*/kg
J/m.
range
air
"Rule
the
Answer:
3.4
by
an
35
ip/m
stopping
is given
convert
what is
Answer:
3.3
emitted
and
is
3.18~10~
The
mass
lo4 kg/m3)
b)
air
air
in
*izPu.
of
% error
Thumb"
1.77x10-*
the
range
and density
2.88~10~~
of
the
5.15
equation,
air
of
(density:
the
the
MeV a particle
find
1.13x
the
range.
Q
particle
emitted
by
emitted
by
two values?
3.72x10-*
3.94x10-*
- 6%
range
in
'PgPt.
lead
power?
between
a)
b)
c>
in
m
m
3.16
MeV
MeV o particle
kg/m3.
in
m
of
of
a 6
2.7~10~
m
aluminum,
atomic
weight
Operational
Health
Physics
Training (Moe)
3-69
3.6
Find
the
Use
1000
respectively
range
kg/m3
for
Answer:
3.7
3.41~10-~
What
is
the
a)
5.81
3.11
3.12
a 1.32
MeV /3- in
or 4.5
m of
of
energy
the absorber
(Z-13)
Pb (Z=82)?
What
percent
x rays if it
of
is
the
preceding
problem?
air
the
above
p-
is
converted
to brems-
and
a)
Answer:
of
kg/m2
Al
Answer:
ip/m
range
What
percent
strahlung
if
b)
3.10
water,
H20.
of 1 and 16
m.
6.4~10~
Answer:
3.9
common
weights
The
mass
stopping
power
of
1.32
MeV /3 particles
emitted
from
potassium-40,
MeV m2/kg
in
air.
The
*OK
is
given
as 0.168
density
of
air
is
1.29
kg/m3.
If the W value
for betas
in air is
33.85 eV/ip,
how many ion pairs
per meter
are formed?
Answer:
3.8
of
a 5 MeV o particle
in
for
density
and
the
atomic
hydrogen
and oxygen.
0.57%
is
b)
of energy
absorbed
3.6%
of an electron
beam
by lead
(Z=82)?
of
5 MeV is
converted
to
electrons
in
MeV
m2/kg
lead
and
28.7%
The
collision
mass
stopping
(density
1.13x104
k/m3,
the total
mass stopping
power
power
Z-82)
is 0.83
a>
Find
the
collision
b)
What
% of
production?
electron
cl
If
to
the approximation
loss,
what would
ratio
loss.
one uses
collision
Answer:
a)
c>
Find
the
a maximum
range
energy
Answer:
14.1
5.01
85.4%
of
a
of 2.86
kg/m2
of
of
50 MeV
is
0.138
MeV m2/kg.
radiative
energy
is
energy
loss
lost
in
EZ/700
for
be-the
8.
b)
manganese-56,
MeV.
the
(bremsstrahlung)
the
ratio
to
bremsstrahlung
of
radiative
83.4%
i:Mn,
fl
particle
that
has
Operational
Health
Physics
Training (Moe)
3-70
3.13
3.14
Answer:
0.435
Find
a>
the
b)
the
frequency
2x10-l2
m.
radiation
in the
a)
b)
2.61~10~
1.5~10~~
Answer:
3.15
a)
b)
If
the
700 nm,
Find
137cs.
55
3.1
the
Answer:
3.18
The
7
source,
distance?
Answer:
3.19
Find
the
Answer:
3.20
wavelength
of
A point
an 1150
wavelength
signal
Js).
of
frequency
intensity,
MeV/m2
s.
MeV/m2
the
2.26~10~~
source
of
is
the
x ray
in
the
preceding
light
energy
is between
region
in
400 nm and
eV?
of
a
1.6~10~~
1.88~10-~~
Hz
0.662
MeV
"f
ray
from
m
0.06
What
m
is
from
the
an isotropic
intensity
at
source
in
problem
3.18.
1 m from
the
point
0.4
m
s
isotropic
MeV/s
137Cs
a>
Find
b)
At what
distance
initial
intensity?
c>
At what
the
and
visible
photon
Frequency:
Wavelength:
power
and
eV
and
1.125~10~~
signal,
MeV
1.8
radiation
is
5~10~~
radio
of
an x ray
whose
wavelength
velocity
of
electromagnetic
The
atmosphere
is 3x10* m/s.
region
of
corresponding
eV and
kHz
m
Hz.
4.75~10~~~
0.62 MeV
wavelength
what is the
Answer:
3.17
MeV.
Find
the
energy
of the radio
problem,
in MeV (h = 6.626~10~~~
Answers:
3.16
3x104
of
j3 particles
is
0.25 kg/m2,
the intensity
is
First,
p particle.
Hint:
The
original
intensity
of
a beam
cpm.
Upon
passing
through
a foil
of
1x104
cpm.
Find
the
energy
of
the
find
the mass attenuation
coefficient.
intensity
distance
emits
at
will
will
.2x104
a distance
the
intensity
MeV/s.
of
intensity
drop
source.
be reduced
by a factor
of
to half
lo?
the
Operational
Health
Physics
Training (Moe)
3-71
Answers:
3.21
b)
c>
of
202 eV
a
Compton electron
a)
b)
c>
3.04~10~l2 m
1.593 MeV
0.407 MeV
and
,~
- 42".
Find the linear
attenuation
coefficient
when the intensity
narrow
gamma beam is reduced
to ti of its original
intensity
passing through 0.05 m of a substance.
Answer:
3.27
work function
is 4 eV, what is the energy
when the photon energy was 206 eV?
m
In problem
3.23, if the Compton electron
is found to have an energy
of 1.0 MeV, in what direction
is the scattered
photon emitted?
Answer:
3.26
by
What is the wavelength
of the scattered
photon?
What is the energy of the Compton electron?
What is the energy of the scattered
photon?
Answer:
3.25
can be produced
A 2 MeV photon
causes the emission
of
scatters
at an angle of 90" from its path.
a>
3.24
2.07~10~l1
If
the photoelectric
the emitted photoelectron
Answer:
3.23
1.59x103 MeV/m2 s
1.414 m
3.162 m
What is the shortest wavelength
of x ray (m) that
an electron
accelerated
by 60,000 volts?
Answer:
3.22
a)
b)
c>
of a
upon
27.7 m-l
the
mass
attenuation
coefficient,
Pm, when the linear
Find
is 50/m and the density of the substance is
attenuation
coefficient
4.1~10~ kg/m3.
Answer:
1.22~10~~
Find:
a>
b)
when the linear
Answers:
a)
b)
m2/kg
half value layer and
tenth value layer
attenuation
1.386~10~~ m
4.6~10~~ m
coefficient
is 50 m-1
Operational
Health
Physics
Training (Moe)
3-72
3.28
Find
the
15 m-l.
X
when
What
is
the
buildup
factor
and the calculated
one is 5~10~
when
cpm?
Answer:
3.29
Assuming
a buildup
factor
of 1.2,
of
20 m-l
and
a thickness
of
emerging
beam
fluence
rate
when
9x108 r/m2 s.
Find
10,000
kg-
1.46~10~
Find
tions.
3.33
If
the
will
3.35
in
mass
linear
the
true
factor
is
reading
is
6~10~
cpm
of
1.283~10~
a neutron
moving
at
to
be 1.6747~10~~~
a 100 MeV neutron.
Hint:
Use relativistic
equa-
m/s
Cact
cross
1741
for
natural
section
for
kg/m3.
Hint:
magnesium,
activation
use
same
m-l
4.26~10~~
1.2~10~
of
eV
speed
0.272
volts
neutron
n/m2
of
a material
is
80 m-l and
2~10~~
m, what
fluence
rate
rate
is 5~10'~
n/m2 s?
s
A 1~10~~
kg
carbon
sample
is
bombarded
beam
for
6 hours.
What
activity
is
to
the
end
of irradiation?
The reaction
cross
irradiating
flux
is
1012
particles/m2
llC is 20.4 m.
Answer:
attenuation
a linear
attenuation
coefficient
material
as 0.1
m,
find
the
the
original
fluence
rate
is
electron
of
a
the
macroscopic
cross
section
thickness
of
the
material
is
result
when the original
fluence
Answer:
the
s
Find
the
macroscopic
cross
section
atomic
weight
24.3,
microscopic
0.063
barns,
and
density
aact
form used for finding
Et.
Answer:
3.34
0.523
the
Answer:
r/m2
the
kinetic
energy
m/s.
Assume
the
Answer:
3.32
path
1.2
Answer:
3.31
free
6.67~10-~
Answer:
3.30
mean
Bq
with
a 50 MeV proton
be expected
from llC at
section
is 24 mb and the
s? The
half
life
of
Operational
Health
Physics
Training (Moe)
3-73
3.36
A thin
gold
foil
flux
of
9x10g
irradiation?
Data
section
98.8 barns,
kg was irradiated
6 days by a
weighing
1~10-~
n/m2
s.
What
was its
activity
3 days
after
atomic
weight
197,
activation
cross
for
Gold:
and T% = 2.7 days.
Answer:
Bq or 5.934x10'
9.89x102
dis/min.
Operational
Health
Physics
Training (Moe)
3-74