Question number
1
of
7
Mid

Term Exam 22.09/104
19 March 2002
2 hours
closed book
NaI scintillators are often used for the detection of
rays. Assume the efficiency of light
conversion in NaI is ~ 12%, i.e. about 12% of the energy deposited in the NaI is converted to
visible light photons.
a)
Estimate the energy resolution of an NaI sc
intillation detector (scintillator plus
phototube) at
1.3 MeV. State and justify any assumptions that you use in your
calculation
b)
I
n order to measure attenuation coefficients accurately and to limit the effects of
scattered radiation, collimation is ofte
n used to limit the acceptance angle of
detectors.
Alternatively, one can rely on the energy resolution of the detector to
eliminate scattered
’s. Assuming
energy
resolution given by (a), what is the
effective acceptance angle for
the radiation from a p
encil beam of
1.3 MeV
’s incident on a slab of material? Recall
the Compton relationship
between scattering angle and energy:
cos
1
1
2
'
c
m
E
E
E
e
Question number
2
of
7
The number of ions collected by a cylindrical single wire gas detector as a
function of voltage
applied between anode and cathode is shown below.
a)
There are five operating regions shown on the plot. For each region, explain the
shape of the curve and the
physical
process occurring in that region.
b)
Assuming the initial ionization
occurs at a
single
point within the detector, how
would the signal observed in each operating region depend on the position of this initial
ionization?
c)
Suppose the detector were a parallel plate detector instead of a cylindrical detector.
How would your a
nswers to a) and b) change, if at all?
Question number
3
of
7
You are scattering radiation from an object, which you think, might be polarized, that is
the amount of radiation scattered up and down is different. Let U be the number of
counts up and D the number of
counts scattered down. If the asymmetry index
is
defined as:
a)
What is the
error
in measuring
in terms of U and D?
b)
What is
the
error when
is small?
D
U
D
U
Question number
4
of
7
Match up Figures (a)
–
(d) with the following radiation source/detector pairs. Explain
you
r choices.
a)
5
MeV
neutrons, NE

213 organic scintillator
b)
1
MeV
ray, NaI scintillator
c)
5 MeV
, surface barrier detector
d)
1 MeV
electron
, plastic scintillator
Question number
5
of
7
a)
What is the origin of the
three
numbered features in the figure below? Using the
expressi
on for the energy of a Compton scattered gamma ray
b)
E
xplain why the energy of the backscatter peak is not very
dependent
on the gamma ray
energy.
Question number
6
of
7
A cylinder of diameter D with linear absorption coefficient
( units of inverse length)
and
density
is to be meas
ured in thickness by measuring the attenuation of a beam of well
collimated gamma rays through the diameter and detecting the beam with a well collimated
detector, i.e. a “good geometry” experiment. Assume the source and detector are well shielded
so any
background and scattering into the detector can be ignored. Assume the count rate with
the cylinder removed (“open beam”) is N
0
and is fixed
a)
Find the optimum value of
which will minimize the uncertainty in the derived value
of
the
diameter for a fixed measurement time of 1 second.
b)
What is the lowest obtained fractional standard deviation for this case?
c)
Is this also the minimum absorbed dose case?
Question number
7
of
7
A
x

ray
source has a uni
f
o
r
m distr
i
bution of
x

rays as a function of energy as s
h
own
below
:
a)
For every x

ray pulse, a digital cir
c
uit give
s
a
fixed height and width
digital
pulse
and
y
ou count
the
total number of events and obta
in N
total
.
What is the
fractional variation in the
ob
tained
value of N?
b)
You notice that as the count rate
goes up, yo
ur digital counter starts to miss
counts due
to dead time.
After a bit of thinking, you decide to
be clever and
do
the
whole thing
in an
analog
way
by integrating the x

ray pulse signals to pr
oduce
a total charge
,
i.e.
for each pulse, there is a
charge propo
rtional to the energy of
the x

ray and you in
tegrate the charge
per event
.
What is the fractional variation
in total c
harge and how does it compare to the digital
result?
c)
Suppose the distribution of pulse height were
as below. Would that c
hange
your results
from
a
)
and b
)
?
d
N/
dE
E
E
ma
x
d
N/
dE
E
E
ma
x
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