22104_Mid_Term_S_2002

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Nov 15, 2013 (3 years and 6 months ago)

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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