S1801(a)
Semester 1, 2011
Page 1 of 12
THE UNIVERSITY OF SYDNEY
MRTY 1031 - MEDICAL RADIATION PHYSICS
JUNE 2011
Time allowed: TWO HOURS
Total marks: 80 MARKS
INSTRUCTIONS
•
•
•
All questions are to be answered.
Use the answer sheet provided for section A and the answer book for section B.
Hand in the answers to section A and B separately at the end of the examination.
DATA
Free fall acceleration at earth's surface
Speed of sound in dry air (0°C)
Speed of light in vacuum
Permittivity of free space
Permeability of free space
Elementary charge
Electron volt
Speed of light in vacuum
Planck’s constant
Boltzmann constant
Stefan-Boltzmann constant
Rydberg constant
Atomic mass unit
Rest masses - electron
- proton
- neutron
- hydrogen atom
-2
g = 9.8 m.s
-1
v = 331 m.s
8
-1
c = 2.998 × 10 m.s
-12 2 -1 -2
ε0 = 8.854 × 10 C .N .m
-7
-1
µ0 = 4π × 10 T.m.A
-19
e = 1.602 × 10 C
-19
1 eV = 1.602 × 10 J
8
-1
c = 2.998 × 10 m.s
-34
h = 6.626 × 10 J.s
-23
-1
k = 1.381 × 10 J.K
-8
-2
-4
σ = 5.671 × 10 W. m .K
7 -1
RH = 1.097 × 10 .m
-27
u = 1.66054 × 10 kg
-31
kg
-27
kg
-27
kg
-27
kg
me = 9.10938 × 10
mp = 1.67262 × 10
mn = 1.67493 × 10
mH = 1.67353 × 10
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Semester 1, 2011
Page 2 of 12
Formula Sheet
Fgravity = G
mEarth m
r2
F = mg
R=
W = Fd
1 2 p2
mv =
2
2m
V
I
1
1
1
=
+
+ ...
Rtotal R1 R2
λmin [ nm ] =
1.24
kVp
hfmax = KE final = eVp
1
f
E [ joule ]
= E [ eV ]
e
v = fλ
E = hf =
λmax
Wa→b Fe d
=
= ED
q0
q0
V2
P = VI = I R =
R
Rtotal = R1 + R2 + ...
GPE = mgh
T=
or U = q0V
2
W
t
KE =
U
q0
Vb − Va = −
F = ma
P=
V=
hfmax [ eV] = Vp [ volt ]
hc
λ
2.898 × 10 −3
=
T
I∝
1
x2
or
I1 x12 = I 2 x22
F = σT 4
I = I 0 e− µ x
⎛ 1
1
1 ⎞
= RH ⎜ 2 − 2 ⎟
λ
⎝ nlower nupper ⎠
⎛ I⎞
1
µ = − log e ⎜ ⎟
x
⎝ I0 ⎠
p=
h
λ
Fe = k
E=
Fe
q0
or λ =
h
p
q1q2
1 q1q2
=
2
d
4πε 0 d 2
or
Fe = qE
⎛µ
⎞
H = 1000 ⎜ medium − 1⎟
⎝ µwater
⎠
M.A.C. =
µ
ρ
Δλ = λ '− λ =
h
(1 − cos φ )
me c
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Semester 1, 2011
Page 3 of 12
Section A
Please use the answer sheet provided for this section.
20 multiple choice questions (1 mark each)
Question 1
Two ropes, one thick and heavy, the other thin and light, are connected to form one
long rope. A wave travels along the rope and passes the point where the two ropes are
connected. Which of the following pairs of parameters of the wave change at that
point?
(a) frequency and propagation speed
(b) propagation speed and wavelength
(c) period and amplitude
(d) frequency and wavelength
Question 2
Which of the following statements about X rays and radio waves is not true?
(a) X rays travel through space faster than radio waves.
(b) X rays have higher frequency than radio waves.
(c) X rays have higher energy than radio waves.
(d) X rays and radio waves are both forms of light, or electromagnetic radiation.
Question 3
What forms of light would you expect to be emitted by gas heated to a temperature of
millions of degrees?
(a) mostly ultraviolet light.
(b) mostly radio waves.
(c) an equal amount of all wavelengths of light.
(d) mostly X rays.
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Semester 1, 2011
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Question 4
Photon P in the diagram (at right) moves an
electron from energy level n = 1 to energy level
n = 3. Soon after, the electron jumps to n = 2,
emitting photon S, and then jumps to n = 1,
emitting photon R. The spacing between energy
levels is drawn to scale.
What is the correct relationship among the
wavelengths λ of the photons?
(a)
(b)
(c)
(d)
λP < λS < λR
λR < λP < λS
λS < λP < λR
λP < λR < λS
Question 5
An electron has the same de Broglie wavelength as an 810 nm photon. Which of the
following values is closest to the speed of the electron?
(a) 260 m.s-1
(b) 620 m.s-1
(c) 900 m.s-1
(d) 990 m.s-1
Question 6
Which of the following correctly describes a valid electron state and shell
designation?
(a) 2s, K
(b) 1p, K
(c) 2p, L
(d) 1s, L
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Question 7
Five identical light bulbs are used to construct the three simple circuits 1, 2 and 3 as
shown below.
Which of the following listings of the circuits correctly ranks their total light output in
decreasing order of brightness – from brightest to dimmest?
(a) 1 – brighter than – 2 – brighter than – 3
(b) 1 – brighter than – 3 – brighter than – 2
(c) 2 – brighter than – 1 – brighter than – 3
(d) 3 – brighter than – 2 – brighter than – 1
Question 8
The diagram below shows a cross-section view of a high power X-ray tube. Various
‘items’ or ‘regions’ within the tube are labelled with numbers.
Which
tube?
(a)
(b)
(c)
(d)
of the following statements would be false during normal operation of the
Item 2 ensures that region 6 remains under vacuum
Thermionic emission takes place in item 3
Item 1 rotates to prevent the focal spot becoming too hot
Items 4 & 5 are more positive than item 3
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Semester 1, 2011
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Question 9
Each of three X-ray photons (of identical wavelength) is Compton scattered by a
single collision with nearly stationary electrons.
• Photon X is deviated through an angle of 90° from its original direction.
• Photon Y is scattered backwards towards the direction it came.
• Photon Z is slightly deviated by approximately 1° from its original direction.
Which of the following sequences correctly lists the photons in order of increasing
wavelength after Compton scattering?
(a) X, Y, Z
(b) Z, X, Y
(c) Z, Y, X
(d) Y, X, Z
Question 10
Which of the following statements is completely correct?
(a) A mammography tube is different from most other X-ray tubes because it is
designed to produce lower energy (i.e. higher quality) X-ray photons.
(b) In the photon spectrum of an X-ray tube, the sharp characteristic peaks are
caused by sudden deceleration of incident electrons by the nucleus of target
atoms. This process is called "Bremsstrahlung".
(c) Increasing the filament current in a normally-operating X-ray tube increases
the filament temperature and space charge around the filament and therefore
increases the tube current.
(d) An X-ray tube is normally operated in the ‘saturation region’ because that
way the tube voltage barely changes even if the current fluctuates and so the
tube's behaviour is more stable.
Question 11
Consider a beam of X-ray photons with an energy range from 10 keV to 1.02 MeV.
The beam is being attenuated by human tissue. Which of the following statements is
most correct?
(a) The lowest energy photons have a higher probability of being scattered by the
Compton effect than of being absorbed by the photoelectric effect.
(b) The lowest energy photons have a higher probability of being absorbed by
pair production than of being attenuated by the photoelectric effect.
(c) The lowest energy photons have a higher probability of being absorbed by
the photoelectric effect than of being scattered by the Compton effect.
(d) The highest energy photons have a higher probability of being absorbed by
the Compton effect than of being scattered by the photoelectric effect.
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Semester 1, 2011
Page 7 of 12
Question 12
An X-ray photon travelling through a material interacts with an atom. The photon is
absorbed completely, but most of its energy carried away by an electron that was
knocked out of the atom. What is this process called?
(a) Bremsstrahlung
(b) Compton effect
(c) Pair production
(d) Photoelectric effect
Question 13
As an X-ray beam containing a range of photon energies passes through a material, it
experiences ‘beam hardening’. How does this affect the X-ray beam?
(a) Beam quality increases because average photon energy decreases.
(b) Beam quality increases which also results in an intensity increase.
(c) Average photon energy increases, however beam intensity decreases.
(d) Average photon energy decreases, therefore beam intensity decreases.
Question 14
When does the conversion of a latent image into a visible image occur in film?
(a) When an electron activates the sensitivity centre
(b) When electrons are added to the silver ions at the sensitivity centre
(c) When the silver bromide crystals interact with a light photon
(d) When the silver ions migrate to the sensitivity centre
Question 15
An advantage of digital imaging over film imaging is the ability to “post-process” the
image. What is post processing?
(a) Altering the appearance of the image once it has been formed.
(b) Changing the speed of the developing cycle
(c) Use of a daylight processor to develop the image
(d) Reading out the latent image using a laser
Question 16
A magnification mammogram is taken with the compressed breast raised on a
platform 29 cm above the image receptor. The SID is 65 cm. A lump is seen on the
image with a diameter of 32 mm. What is the diameter of the lump within the breast?
(a) 14.3 mm
(b) 16.0 mm
(c) 17.7 mm
(d) 57.6 mm
S1801(a)
Semester 1, 2011
Page 8 of 12
Question 17
The diagram above illustrates a section of a parallel grid. What is the grid ratio of this
grid?
(a) 3:1
(b) 60:1
(c) 10:1
(d) 20:1
Question 18
What does the mA setting on an x-ray tube console control?
(a) The voltage applied across the tube filament
(b) The number of electrons produced by the tube filament
(c) The potential difference between the anode and cathode
(d) Which filament is used in the exposure
Question 19
Which of the following actions does not result in an increase in the percentage of
scatter reaching the detector?
(a) Increasing the field size
(b) Increasing the mA
(c) Removing the grid
(d) Increasing the kVp
Question 20
Which of the following statements is not true?
(a) Contrast resolution is the ability to distinguish between two areas of intensity
in an image
(b) Contrast is affected by the noise level in an image
(c) Contrast in an image is only due to photoelectric absorption
(d) Using small field sizes gives better contrast resolution
This is the end of Section A.
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Semester 1, 2011
Page 9 of 12
Section B
Please use the booklet provided for this section.
This section has six (6) questions (10 marks each)
ANSWER ALL QUESTIONS
Question 1
(a)
Briefly define or otherwise describe the following terms (two or three lines
each):
(i)
(ii)
(iii)
(iv)
(b)
Electron volt
Thermionic emission
Pair production absorption
Noise in an X-ray image
Fill in the blank spaces in the following paragraphs using the most correct
words or phrases from the following list:
attenuated
attenuation coefficient
absorb
absorbed
higher energy
lower energy
characteristic X-ray
beam hardening
dark
filament temperature
transmitted
transmit
reflected
Bremsstrahlung
tube voltage
work function
beam quality
ions
light
increasing
decreasing
scattered
kinetic energy
high
space charge
atoms
low
Don't use a word/phrase more than once. There are unused words/phrases in
the list. Don't write out the whole paragraph. Just list each of your answers
labelled this way:
A (i) word/phrase, (ii) word/phrase
B (i) word/phrase, (ii) etc.
A. In a normally operating X-ray tube, the tube current is increased by (i) _____
the (ii) _____.
B. A high speed electron can knock an inner shell electron out of an atom.
Another electron from a (i) _____ shell in the atom, can fall into the vacant
inner shell, losing its energy in the form of a (ii) _____ photon.
C. There are two classes of mechanism which attenuate X-ray or gamma photon
beams: either the photons are (i) _____ which means photons change
direction, or the photons are (ii) _____.
D. (i) _____, average photon energy and half value layer are all examples of
ways of characterising (ii) _____.
E. In a developed X-ray film, an area of (i) ____ optical density has a large
number of silver (ii) ____ present which (iii) _____ most of the light. This
results from a high level of x-ray exposure and makes that area of the film
appear (iv) ____ when it is held up to a viewing box.
(10 marks)
S1801(a)
Semester 1, 2011
Page 10 of 12
Question 2
In 1913 Niels Bohr proposed a modification to Rutherford’s nuclear model of the
atom. He suggested that electrons occupy discrete energy levels (or ‘shells’)
surrounding the nucleus.
(a)
Explain what is meant by “discrete energy levels” in this context.
(b)
Describe the experimental evidence that indicates there are discrete energy
levels in atoms.
(c)
Would you expect the energy levels of a neutral helium atom to be the same,
similar or very different to a neutral hydrogen atom? Explain your reasoning.
(d)
Would you expect the energy levels of a singly-ionised helium atom (i.e. with
only one electron) to be the same, similar or very different to a neutral
hydrogen atom? Explain your reasoning.
(10 marks)
Question 3
The graph above is a spectrum of photon energies from a filtered X-ray tube.
Consider the four quantities indicated in the graph: the size of the area under the curve
N and the horizontal positions of features labelled M, O and P.
(a)
(b)
For each of the following conditions listed below, identify which of the four
quantities will change. Where possible, state if the change is an increase or
decrease. If possible, quote values for the new quantities (with any relevant
units). You are not required to provide an explanation why.
(i)
You increase the acceleration voltage to 120 kV.
(ii)
You reduce the thickness of the filter.
(iii)
You decrease the tube current to one quarter (1/4) of its original value.
(i)
What is the name given to the features labelled O?
(ii)
Name any changes that would need to be made to the tube to affect the
horizontal positions of the features labelled O.
(10 marks)
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Semester 1, 2011
Page 11 of 12
Question 4
(a)
A 300 kV X-ray tube with a 6 mm aluminium filter, produces a beam with an
linear attenuation coefficient in copper of 0.707 mm-1.
Calculate the half value thickness (HVT) in copper for this beam. Identify the
main assumptions or approximations you employed.
(b)
You have used a plastic phantom to test an X-ray CT machine. By analysing
the CT image, you find that the CT number for the plastic is -40 HU. For the
same X-ray beam, calculate the linear attenuation coefficient for the plastic
expressed as a percentage of the linear attenuation coefficient of water.
(c)
For each of the following two tissue types (i) and (ii), identify which
attenuation mechanism (Compton or photoelectric) is most responsible for
radiographic contrast and very briefly explain why. Give one example of each
kind of tissue.
(i)
Variable density tissues of roughly uniform atomic number Z
(ii)
Roughly uniform density tissues with high Z compared to soft tissue
(10 marks)
Question 5
In mammographic imaging the breast tissue is compressed. This means that during
imaging the tissue is put under pressure between two plates.
(a)
(i)
One of the things this does is reduce the thickness of the tissue. How
does this affect the image quality?
(ii)
How does this affect the patient dose?
(b)
Compressing the tissue also reduces the distance between more of the tissue
and the image receptor. How does this affect the image quality?
(c)
Compressing the tissue also reduces the movement of the tissue. How does
this affect the image quality?
(10 marks)
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Semester 1, 2011
Page 12 of 12
Question 6
The penumbra is the partial shadow outside the darkest portion of the shadow of an
opaque object. In an X-ray image the penumbra is caused by the size of the focal
spot.
(a)
Draw a diagram to illustrate how the size of the penumbra of an object is
affected by the size of the focal spot.
(b)
What effect does the size of the focal spot have on the quality of an image?
Explain your answer.
(c)
What effect does the size of the focal spot have on the magnification in an
image? Explain your answer.
(d)
Describe one imaging situation in which you would use a fine (small) focal
spot.
(10 marks)
This is the end of your questions.