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Semester 1 – End of Semester, 2020
PHYS3105/ 6105 Semester 1 Physics of Matter
This paper is for all students.
Reading Time: 15 minutes
Examination Duration: 120 minutes
Submission Grace Period: 15 minutes
Exam Conditions:
Online individual open-book examination.
Permitted Materials:
Any course-related materials.
Computer with suitable internet connection to access the course Wattle page.
Digital camera, tablet or other means of producing digital images of diagrams or mathematical workings and uploading
them to the course Wattle page.
Stationery to support working and production of diagrams.
Instructions To Students:
Before reading time, you should join the Zoom meeting via the link provided on the course Wattle page.
The staff will use Zoom to make announcements and you may use it to ask questions. You are to remain in Zoom until
the end of the exam in order to receive announcements as they occur. You may have your video camera and
microphone turned off.
At 2.30 pm, the exam paper will be released on Wattle, at which point, you have 15 min of reading time. Questions to
staff are preferred during this period.
Writing time commences at 2.45 pm. You are to prepare your answers in a way that they can be digitally submitted at
the end of the exam (ie scanned handwriting, typed text with images etc).
You are permitted to access materials of your choosing.
Do not submit text or images that are not your original work. All answers are to be your own work.
Do not communicate with any other person during the examination.
Writing time finishes at 4.45 pm. Between 4.45 pm and 5 pm you are to submit your answers via the dropbox on the
course Wattle page. Notify the staff via Zoom if you are having difficulty submitting your answers.
Students who require special exam arrangements are to follow the instructions of staff as discussed prior to the exam.
This examination has a total of 40 marks. Marks available for each question are as denoted. Attempt all questions of
the exam.
Semester 1 – End of Semester, 2020 PHYS3105 Semester 1 Physics of Matter
Page 2 of 5
Question 1 (11 marks)
Consider the atomic structure of Ba (Z=56). Ba has two valence electrons. The ground configuration of the
two valence electrons is 6s2
.
a) Identify the allowed electronic levels of the 6s2
, 6s5d, 6s6p and 5d2 configurations of Ba. Sketch the
gross energy level structure of these configurations and label the levels with their term symbols 2S+1L.
Justify how you have energetically ordered the levels. (3 marks)
b) The fine structure parameter of the 3
D level is !” = 23 meV. Sketch the fine structure of the 3
D level.
Label the sub-levels by their total electron angular momentum J. Label the energy differences between the
sub-levels. (3 marks)
c) In terms of the one-electron orbitals {| , , # $} and spin states {|↓ $, |↑ $}, where = 1 or 2 denotes
electron number, construct the two-electron states corresponding to the %
( ! = +2, & = +1) and
‘
( ! = +2, & = 0) states of the 6s5d configuration. Using your two-electron states, derive the direct
and exchange energies of the 6s5d configuration in terms of the one-electron orbitals. Explain how these
expressions are consistent with Hund’s rules. (3 marks)
d) What is configuration interaction Identify the allowed configuration interactions between the levels
you sketched above in a). (2 marks)
Question 2 (14 marks)
This question looks at the structure of 165Ho (Z=67) whose level scheme is shown below
a) Give two reasons why you expect that 165Ho (Z=67) is a deformed nucleus. The first reason should be
related to the proton and neutron numbers of 165Ho and the second should be related to the observed
level scheme. (2 marks)
b) The deformation of 165Ho is e2 0.22. Use the attached Nilsson diagram to determine the particle
configuration of the ground state. (1 mark)
c) The 3/2ˉ state at 515 keV and the 11/2ˉ state at 689 keV are both due to a particular form of collective
vibrational excitation coupled to the 7/2ˉ ground state. What is the nature of this collective vibration
and show why the coupling (angular momentum and parity) results in 3/2ˉ and 11/2ˉ states (2 marks)
Semester 1 – End of Semester, 2020 PHYS3105 Semester 1 Physics of Matter
Page 3 of 5
d) Ignoring internal conversion, evaluate the strength of the 515 keV transition that de-excites the 3/2ˉ
state from part c). You should get an answer of the order of 30 W.u. Explain how this strength supports
the fact that the 3/2ˉ state at 515 keV is a collective vibrational excitation. (2 marks)
e) Use the energy of the 689 keV state to estimate the frequency of the vibrational motion. Your answer
should be of order 1020 Hz. (1 mark)
f) Use the energy of the 9/2ˉ state at 95 keV to determine the moment of inertia, á, of 165Ho. Use
c=197.3 MeV.fm and your answer should be of order 106 MeV.fm2
/c2
. (2 marks)
g) Let us assume that the energy of the rotation is (semi-classically) E=áw2
/2, where á is the moment of
inertia and w is the angular frequency. Using this equation, the moment of inertia from f) and the
energy of the 9/2ˉ state, estimate the frequency of rotation in the 9/2ˉ state. You answer should be
order 1019 Hz. (1 mark)
h) The rotational and vibrational frequencies
in e) and g) are different to those in a
diatomic molecule in both their overall
magnitude and the ratio between them.
What are these differences and what are
the implications for how well the adiabatic
or Born-Oppenheimer approximation can
be applied in molecules and nuclei
(2 marks)
i) In the energy level diagram for a molecule
shown on the right, the electronic
excitation is drawn vertically. Explain the physical reason why it is drawn like this. (1 mark)
Question 3 (3 marks)
There are only a handful of stable odd-odd nuclei that occur in nature. Draw a diagram showing the
energetics of binding energies for beta-decay chains that illustrates why most odd-odd nuclei are not
stable. You should explain it with reference to a particular term of the SEMF formula. (3 marks)
Question 4 (3 marks)
One of the more probable ways in which thermal neutron-induced fission of 235U can occur is via:
n + 235U → 92Kr + 141Ba + 3n
The experimental mass excesses that are relevant to this fission channel are:
n 8.071 MeV/c2
235U 40.914 MeV/c2
92Kr -68.788 MeV/c2
141Ba -79.730 MeV/c2
a) Evaluate the Q value for this reaction in MeV. Is binding energy converted to kinetic energy in this
reaction (1 mark)
b) In a reactor with 1000 MW of thermal power and using uranium fuel enriched to be 5% 235U and 95%
238U, there are 3.6×1019 nuclei of 235U fissioning each second. Given the following cross-sections:
sfission(
235U) = 579 b scapture(
235U) = 52 b sfission(
238U) = 0 b scapture(
238U) = 2.72 b,
estimate how many kg of 238U are converted into 239U in a year of reactor operation. Your answer
should be of order tens of kg. (2 marks)
nuclear separation
energy
Semester 1 – End of Semester, 2020 PHYS3105 Semester 1 Physics of Matter
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Question 5 (9 marks)
You are doing an experiment directing a beam of 16O nuclei at a target made of 208Pb. You place a detector
at a scattering angle q from the beam direction (i.e. forward-going beam is at q=0o) that is capable of
measuring the number of scattered 16O nuclei and their energies.
a) Estimate the energy of the 16O beam in the lab frame that is required to overcome the Coulomb barrier
between 16O and 208Pb nuclei. (2 marks)
b) You decide to run with a 16O beam of 110 MeV, which is above the Coulomb barrier. When you place
your detector at q=15o, you measure 10000 16O nuclei hitting your detector every second. What will be
the rate of 16O nuclei detected when the detector is placed at q=30o (1 mark)
c) As you increase the detector angle q you will reach a point where the number of scattered 16O nuclei
suddenly drops to zero. Explain why this happens in terms of the reaction impact parameter and the
paths that the 16O nuclei follow relative to the 208Pb nuclei. (2 marks)
d) The energy spectrum for the 16O nuclei measured in your detector is shown below. Note the log scale.
With reference to the level scheme for 208Pb that is also shown below, explain the origins of the peaks
labelled A to D. (2 marks)
e) The level scheme also shows the gamma-ray transition strengths in 208Pb. With this information as a clue
to the underlying structure of the states in 208Pb, why is peak C observed with much more intensity than
peaks A and B (1 mark)
f) The 16O beam current is 109 particles per second, your 208Pb target is 20 μg/cm2 thick and the cross section for fusion is 300 mb. How many fusion reactions do you expect to occur each second Your
answer should be of order 20 s-1
. (1 mark)
END OF EXAMINATION
D
C
B
A
76 77 78 79 80 81
energy [MeV]
100
105
108
counts
Semester 1 – End of Semester, 2020 PHYS3105 Semester 1 Physics of Matter
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