lOMoARcPSD|54878315
UNIVERSITY EXAMINATIONS
JANUARY/FEBRUARY 2023
PHY3707
Solid State Physics
100 Marks
Duration 4 Hours
Welcome to the PHY3707 exam.
Examiner name: Dr M M Tibane (UNISA)
Internal moderator name: Prof B M Mothudi (UNISA)
External moderator name: Prof ARE Prinsloo (UJ)
This paper consists of 4 pages.
Instructions:
• You have 4 hours to complete this closed book take home exam.
• Answer all the questions. Information sheet is given at the end of the paper.
• Please do not forget to make Honesty Declaration.
• This exam is invigilated using the IRIS tool to ensure its integrity. Students who have not
utilized IRIS will not get their results.
• Remember to submit your script at https://cset.myexams.unisa.ac.za.
Additional student instructions
1. Students must upload their answer scripts in a single PDF file (answer scripts must not be
password protected or uploaded as “read only” files)
2. Incorrect file format and uncollated answer scripts will not be considered.
3. NO emailed scripts will be accepted.
4. Students are advised to preview submissions (answer scripts) to ensure legibility and that the
correct answer script file has been uploaded.
5. Incorrect answer scripts and/or submissions made on unofficial examinations platforms will not
be marked and no opportunity will be granted for resubmission.
6. Mark awarded for incomplete submission will be the student’s final mark. No opportunity for
resubmission will be granted.
7. Mark awarded for illegible scanned submission will be the student’s final mark. No opportunity for
resubmission will be granted.
8. Submissions will only be accepted from registered student accounts.
9. Students who have not utilised invigilation or proctoring tools will be subjected to disciplinary
processes.
10. Students suspected of dishonest conduct during the examinations will be subjected to
disciplinary processes. UNISA has a zero tolerance for plagiarism and/or any other forms of
academic dishonesty.
11. Students are provided one hour to submit their answer scripts after the official examination
time. Submissions made after the official examination time will be rejected by the examination
regulations and will not be marked.
12. Students experiencing network or load shedding challenges are advised to apply together with
supporting evidence for an Aegrotat within 3 days of the examination session.
13. Students experiencing technical challenges, contact the SCSC 080 000 1870 or email
or refer to URL link for the list of additional contact numbers or
alternatively email your module lecturer. ONLY communication from your myLIfe account will be
considered.
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2 PHY3707
Jan/Feb 2023
1. (a) Define the term packing fraction. (2)
(b) Find the packing fraction for a simple cubic crystal structure. (5)
[7]
2. Use the following data to calculate the electron heat capacity at 1000 K in Au, K and
Sn metals using the following data:
Metal Electron density Fermi energy
n (x1028 m-3) εf (eV)
K 1.4 2.1
Au 5.9 5.5
Sn 14.8 10.2
Estimate what fraction of the total heat capacity it forms, assuming that 1000 K is well
above the Debye temperature in each case.
[18]
3. The lattice constants a, b and c of an orthorhombic crystal are related by a = 2b = 3c.
What is the interplanar separation between (1 2 1) planes?
[8]
4. Symbols 𝑟 < and 𝑟 > represent the radius of the smaller and bigger atom
respectively, in a crystal of diatomic basis. Show that the critical ratio,
𝑟> √3+1
= for the CsCl structure, and
𝑟< 2
𝑟>
= 2 + √6 for the zinc blende structure.
𝑟<
[20]
[TURN OVER]
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, lOMoARcPSD|54878315
PHY3707
Jan/Feb 2023
5. In potassium at 68 GHz three consecutive cyclotron resonance are observed at
magnetic fields of 0.74 T, 0.59 T and 0.49 T. What is the cyclotron resonance mass
of electrons in potassium? [10]
6. A weak periodic potential in the form of
𝑉(𝑥) = 𝑉0 cos(2𝑘𝐹 𝑥)
is created for one-dimensional electron system (kF is the Fermi wavenumber).
Calculate E(k) for the lowest energy band, and determine the total energy of the
system at zero temperature as a function of V0.
[15]
7. Derive an expression for the temperature at which the thermal lattice energy is equal
to the zero point energy in the Einstein model. Write down the corresponding
condition in the Debye model.
[22]
TOTAL: [100]
3 [TURN OVER]
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4 PHY3707
Jan/Feb 2023
Useful information
1
F (E) =
1 + exp[( E − E F ) / k B T ]
n
S g = f j exp(ig.r j )
j =1
e = 1.6022 10 −19 C
me = 9.1095 10−31 kg
k ~ 0 − − e ik .( r − r n m)
m
0 = 8.85 10−12 Farad/meter
1 1 d 2
=
m 2 dk 2
dN
D ( F ) =
d F
1
1
e
−1
x
+1
dx = 1
1 h2 + k 2 + l 2
=
d hkl a
sin = h2 + k 2 + l 2
2a
b c ca a b
a = 2 , b = 2 , c = 2
a.(b c ) a.(b c ) a.(b c )
A ( A B) = 0 for any two vectors A and B
ij = 1 if i = j , and ij = 0 if i j
L3
Reciprocal density of states:
8 3
©
UNISA 2023
Downloaded by Stephen ()
UNIVERSITY EXAMINATIONS
JANUARY/FEBRUARY 2023
PHY3707
Solid State Physics
100 Marks
Duration 4 Hours
Welcome to the PHY3707 exam.
Examiner name: Dr M M Tibane (UNISA)
Internal moderator name: Prof B M Mothudi (UNISA)
External moderator name: Prof ARE Prinsloo (UJ)
This paper consists of 4 pages.
Instructions:
• You have 4 hours to complete this closed book take home exam.
• Answer all the questions. Information sheet is given at the end of the paper.
• Please do not forget to make Honesty Declaration.
• This exam is invigilated using the IRIS tool to ensure its integrity. Students who have not
utilized IRIS will not get their results.
• Remember to submit your script at https://cset.myexams.unisa.ac.za.
Additional student instructions
1. Students must upload their answer scripts in a single PDF file (answer scripts must not be
password protected or uploaded as “read only” files)
2. Incorrect file format and uncollated answer scripts will not be considered.
3. NO emailed scripts will be accepted.
4. Students are advised to preview submissions (answer scripts) to ensure legibility and that the
correct answer script file has been uploaded.
5. Incorrect answer scripts and/or submissions made on unofficial examinations platforms will not
be marked and no opportunity will be granted for resubmission.
6. Mark awarded for incomplete submission will be the student’s final mark. No opportunity for
resubmission will be granted.
7. Mark awarded for illegible scanned submission will be the student’s final mark. No opportunity for
resubmission will be granted.
8. Submissions will only be accepted from registered student accounts.
9. Students who have not utilised invigilation or proctoring tools will be subjected to disciplinary
processes.
10. Students suspected of dishonest conduct during the examinations will be subjected to
disciplinary processes. UNISA has a zero tolerance for plagiarism and/or any other forms of
academic dishonesty.
11. Students are provided one hour to submit their answer scripts after the official examination
time. Submissions made after the official examination time will be rejected by the examination
regulations and will not be marked.
12. Students experiencing network or load shedding challenges are advised to apply together with
supporting evidence for an Aegrotat within 3 days of the examination session.
13. Students experiencing technical challenges, contact the SCSC 080 000 1870 or email
or refer to URL link for the list of additional contact numbers or
alternatively email your module lecturer. ONLY communication from your myLIfe account will be
considered.
Downloaded by Stephen ()
, lOMoARcPSD|54878315
2 PHY3707
Jan/Feb 2023
1. (a) Define the term packing fraction. (2)
(b) Find the packing fraction for a simple cubic crystal structure. (5)
[7]
2. Use the following data to calculate the electron heat capacity at 1000 K in Au, K and
Sn metals using the following data:
Metal Electron density Fermi energy
n (x1028 m-3) εf (eV)
K 1.4 2.1
Au 5.9 5.5
Sn 14.8 10.2
Estimate what fraction of the total heat capacity it forms, assuming that 1000 K is well
above the Debye temperature in each case.
[18]
3. The lattice constants a, b and c of an orthorhombic crystal are related by a = 2b = 3c.
What is the interplanar separation between (1 2 1) planes?
[8]
4. Symbols 𝑟 < and 𝑟 > represent the radius of the smaller and bigger atom
respectively, in a crystal of diatomic basis. Show that the critical ratio,
𝑟> √3+1
= for the CsCl structure, and
𝑟< 2
𝑟>
= 2 + √6 for the zinc blende structure.
𝑟<
[20]
[TURN OVER]
Downloaded by Stephen ()
, lOMoARcPSD|54878315
PHY3707
Jan/Feb 2023
5. In potassium at 68 GHz three consecutive cyclotron resonance are observed at
magnetic fields of 0.74 T, 0.59 T and 0.49 T. What is the cyclotron resonance mass
of electrons in potassium? [10]
6. A weak periodic potential in the form of
𝑉(𝑥) = 𝑉0 cos(2𝑘𝐹 𝑥)
is created for one-dimensional electron system (kF is the Fermi wavenumber).
Calculate E(k) for the lowest energy band, and determine the total energy of the
system at zero temperature as a function of V0.
[15]
7. Derive an expression for the temperature at which the thermal lattice energy is equal
to the zero point energy in the Einstein model. Write down the corresponding
condition in the Debye model.
[22]
TOTAL: [100]
3 [TURN OVER]
Downloaded by Stephen ()
, lOMoARcPSD|54878315
4 PHY3707
Jan/Feb 2023
Useful information
1
F (E) =
1 + exp[( E − E F ) / k B T ]
n
S g = f j exp(ig.r j )
j =1
e = 1.6022 10 −19 C
me = 9.1095 10−31 kg
k ~ 0 − − e ik .( r − r n m)
m
0 = 8.85 10−12 Farad/meter
1 1 d 2
=
m 2 dk 2
dN
D ( F ) =
d F
1
1
e
−1
x
+1
dx = 1
1 h2 + k 2 + l 2
=
d hkl a
sin = h2 + k 2 + l 2
2a
b c ca a b
a = 2 , b = 2 , c = 2
a.(b c ) a.(b c ) a.(b c )
A ( A B) = 0 for any two vectors A and B
ij = 1 if i = j , and ij = 0 if i j
L3
Reciprocal density of states:
8 3
©
UNISA 2023
Downloaded by Stephen ()
