Constants
k = 8.62×10-5 eV/(atom·K)
R = 8.31 J/(mol·K)
c = 3.00×108 m/s
h = 4.13×10-15 eV·s
NA = 6.022 × 1023 atoms/mol
F = 96,500. C/mol
e = 1.602×10-19 C
0 = 8.85×10-12 F/m
Polymers
Crystal
Structure
Formulae
𝜌=
𝑀𝐴𝑡𝑜𝑚 ∙ 𝑛
𝑉𝐶 ∙ 𝑁𝐴
𝐹𝐶𝐶: 4𝑅 = √2𝑎
𝐵𝐶𝐶: 4𝑅 = √3𝑎
̅̅̅̅
𝑀𝑛 = ∑(𝑥𝑖 ∙ 𝑀𝑖 )
𝑤𝑖 =
Electrical, Dielectric, Magnetic, &
Optical Properties
Phase Diagram
and Nucleation
Diffusion Mech.
& Defects Props
𝑖
𝜎𝑐 =
𝜎𝑐 = (
𝑄𝑣
)
𝑘𝑇
𝑖
𝑄𝐷
)
𝑅𝑇
ΔT
ΔG𝑉 = ΔH𝑚 ( )
𝑇𝑚
16 3
3  Gv 
̅̅̅̅
𝑀𝑤 = ∑(𝑤𝑖 ∙ 𝑀𝑖 )
2𝐸𝛾𝑠 ⁄2
)
𝜋𝑎
𝐷 = 𝐷𝑜 ∙ 𝑒𝑥𝑝 (−
P+F=C+2
or
P+F=C+1
G * 
(𝑥𝑖 ∙ 𝑀𝑖 )
∑𝑖 (𝑥𝑖 ∙ 𝑀𝑖 )
𝑑=
𝑎
(ℎ2 + 𝑘 2 + 𝑙 2 )1⁄2
̅̅̅̅̅
𝑀
𝑀𝑛
𝑀𝑛
𝑚
𝑃𝐷𝐼 = ̅̅̅̅̅𝑤 ;𝐷𝑃 =
1
𝐾𝐼𝐶
𝑌 ∙ (𝜋𝑎)1⁄2
𝑁𝑣 = 𝑁𝑜 ∙ 𝑒𝑥𝑝 (−
𝑛𝜆 = 2𝑑 sin 𝜃
G * 
2
𝑉 = 𝐼𝑅; 𝐽 = 𝜎𝐸
𝑅=𝜌
𝜎 = 𝐸𝜀 & 𝜈 = −
x2 = 2·D·t
𝐽 = −𝐷
𝐿 1𝐿
=
𝐴 𝜎𝐴
𝜀𝑎𝑥𝑖𝑎𝑙
𝜕𝐶
𝜕𝑥
W  (C  C0 ) / C  C )
2 Tm
H m (Tm  T )
𝑦 = 1 − 𝑒𝑥𝑝(−𝑘 ∙ 𝑡 𝑛 )
𝜎metal = 𝑛 ∙ |𝑒| ∙ 𝜇
↓Electrochemical ↓
r* 
2
𝜀𝑙𝑎𝑡𝑒𝑟𝑎𝑙
2
Gv
r*  
16 3Tm 2
3H f 2 Tm  T 
𝜏 = 𝜎 cos 𝜙 ∙ cos 𝜆
At 25 ˚C:
𝜎semiconductor = 𝑛|𝑒|𝜇𝑒
+ 𝑝|𝑒|𝜇ℎ
𝑉
𝐸=
𝑙
𝑣𝑑 = 𝜇𝐸
V  (V  V10 ) 
0
2
[ prod ]
0.0592
log
n
[react ]

𝑛𝑖 = 𝑛0 𝑒𝑥𝑝 (−
𝐶=
𝐸𝑔
)
2𝑘𝑇
𝑄
𝑉
C
𝐸𝑔 = ℎ ∙ 𝜈 =
 r  0 A A

l
l
𝑃 = (𝜀𝑟 − 1)𝜀0 ∙ 𝐸
X–ray Diffraction Reflection Rules
SC:
No restrictions
FCC:
h,k,l all odd or all even
BCC:
h+k+l even
Radius Ratio (r/R) Rules
0.225 < 𝑟⁄𝑅 < 0.414
⟹
CN = 4
0.414 < 𝑟⁄𝑅 < 0.732
⟹
CN = 6
0.732 < 𝑟⁄𝑅 < 1 ⟹
ℎ∙𝑐
𝜆
M =H
CN = 8
i/12
∆𝑉 = (𝑉2𝑜 − 𝑉10 ) −
𝑉 = 𝑉𝑜 +
𝑅𝑇 [𝑝𝑟𝑜𝑑]
𝑙𝑛
𝑛𝐹 [𝑟𝑒𝑎𝑐𝑡]
𝑘𝑇 [𝑀𝑛+ ]
𝑙𝑛
𝑛𝑒
[1𝑀]
YOU MAY TEAR THIS SHEET OFF
1
2
H
He
1.0079
4.0026
3
4
5
6
7
8
9
10
C
N
O
F Ne
Li Be
B
6.94
9.01
10.81 12.011 14.01 16.00 19.00 20.18
11
12
13
14
15
16
17
Na Mg
Al Si
P
S
Cl Ar
22.99 24.31
26.98 28.09 30.97 32.06 35.45 39.95
19
20
21
22
K Ca Sc Ti
23
24
25
26
27
28
29
30
31
32
33
34
35
18
36
V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
39.10 40.08 44.96 47.88 50.94 52.00 54.94 55.85 58.93 58.71 63.54 65.31 69.72 72.59 74.92 78.96 79.91 83.80
37
38
39
Rb Sr Y
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te
I
Xe
85.47 87.62 88.91 91.22 92.91 95.94 98.91 101.07 102.91 106.4 107.87 112.40 114.82 118.69 121.75 127.60 126.90 131.30
55
56
71
72
73
74
75
76
77
Cs Ba Lu Hf Ta W Re Os Ir
78
79
80
81
82
83
88
103
104
105
106
107
108
109
Fr Ra Lr Rf Db Sg Bh Hs Mt
223
226.03 262.1 261.11 262.11 263.12 262.12
265
85
86
Pt Au Hg Tl Pb Bi Po At Rn
132.91 137.34 174.97 178.49 180.95 183.85 186.2 190.2 192.2 195.09 196.97 200.59 204.37 207.19 208.98
87
84
266
YOU MAY TEAR THIS SHEET OFF
ii/12
210
210
222
ENGR/CHEM/ISCI/PHYS -1600
EXAM-1 (Fall 2023) (50 mins)
PLEASE PRINT
----------------------------------------------------------------------------------Last Name
First Name
Select section number and Instructor
_________Section 2 (Ullal, M/Th 10 am)
_________Section 1 (Shi, M/Th 2 pm)
You have 50 minutes to complete the quiz.
Please put your answers for multiple choice Question 1-20 on the Scantron answer sheet
provided. If you mark more than one answer (even if you have erased the other selections), in
order for you to be eligible to receive credit for that question you must write the letter you
finally selected next to the question number on your Scantron. If multiple letters are visible
for the same question or the letters are deemed illegible by the instructor, credit will not be
given for that question. Please note that ANSWER SHEETS ARE PHOTOCOPIED prior to being
returned to you.
WHEN DONE, TURN IN YOUR ANSWER SHEET AND EXAM TO YOUR TA or INSTRUCTOR. BE
PREPARED TO SHOW YOUR STUDENT ID.
3/12
Multiple Choice (5 points each; 100 points total) Input your answers for the following questions on
your Scantron form.
Q U E S TI O N 1
Of the following materials, which has the most ionic bonding character:
A) Silicon
B) Diamond
C) Germanium
D) Silicon dioxide
Q U E S TI O N 2
If the potential energy, E(r), described in terms of interatomic spacing, r, is given by the
following equation, where, A and B are positive constants, what is the equilibrium
interatomic spacing?
𝐴
𝐵
+ 12
𝑟
𝑟
𝐸 (𝑟) = −
(A)
(B)
(C)
(D)
(
(
(
𝐴
12𝐵
𝐵
12𝐴
)
12𝐵
𝐴
𝐵
( )
)
1
11
1
11
)
1
11
1
11
𝐴
Q U E S TI O N 3
You have an ionic compound AxBy where the radii of the cation and anion are 0.171 and
0.182 nm, respectively. What is the predicted coordination number of the cation?
A) 2
B) 3
C) 4
D) 8
4/12
Q U E S TI O N 4
Based on the given potential energy vs. interatomic distance plot, which of the following
statements is TRUE regarding the magnitude of the attractive and repulsive forces?
A) At point 5, the attractive and repulsive forces are large.
B) At point 3, the attractive and repulsive forces are equal.
C) At point 1, the attractive force exceeds the repulsive force.
D) At point 2 the repulsive force is smaller than the attractive force.
Q U E S TI O N 5
How many atoms of oxygen (O2-) are there in the unit cell shown?
A) 1
B) 3
C) 4
D) 6
5/12
Q U E S TI O N 6
The atomic packing of a plane for the body centered cubic crystal structure is shown with the atoms
drawn to full size represented by the circles. What plane might this represent?
A) (100)
B) (110)
C) (111)
D ) (211)
Q U E S TI O N 7
Iron can crystallize in both FCC and BCC structures. If the atomic radius, r, remains the
same in both structures, the lattice parameter, a, ratio a(FCC)/a(BCC) will be,
2 2
A) (3)
2
B) √3
3 2
C) (2)
3
D) √2
6/12
Q U E S TI O N 8
The unit cell of a substance composed of atoms of A (black) and B (white) is shown
above and has the cesium chloride structure. The ionic radii of A and B are 0.170 nm
and 0.181 nm, respectively. The atomic weights of A and B are 132.91 g/mol and 35.45
g/mol, respectively. What is the theoretical density of AB (g/cm³)?
A) 2.84
B) 3.69
C) 4.20 D) 10.39
Q U E S TI O N 9
Examples of closest packed directions in SC and FCC, respectively, are:
A) [100] and [110]
B) [110] and [100]
C) [111] and [100]
D) [100] and [111]
7/12
U S E T HE FI G U R E B E L O W FO R Q U E S T I O N S 1 0 & 1 1
( The red circles represent the 1/2 position coordinates)
Q U E S TI O N 1 0
What are the Miller indices for the plane shown?
A) (2 2 1)
B) (1 2 1)
C) (2 2 1̅)
D) (1 1 2)
Q U E S TI O N 1 1
What are the Miller indices for the direction shown?
A) [0 2̅ 1]
B) [0 1̅ 2]
C) [0 1 2]
D) [0 2 1]
=================================================================
8/12
Q U E S TI O N 1 2
Find the Miller index for the plane shown in the figure below,
A) (½ 0 0)
B) (100)
C) (200)
D) (022)
Q U E S TI O N 1 3
9/12
Given the specific volume vs. temperature curves in the figure shown, which of the
following is TRUE:
A) Z is completely crystalline, X is completely amorphous
B) Z is completely crystalline, Y is amorphous
C) Y is completely crystalline, X is completely amorphous
D) Y is completely crystalline, Z is amorphous
Q U E S TI O N 1 4
A polymer consists of a mixture of three monodisperse polymers--25% by weight of A
(1,000g/mol), 25% of B (5,000 g/mol), 50% of C (20,000 g/mol). What is this polymer's
number averaged molecular weight (g/mol)?
A) 3077
B) 2759
C) 6750
D) 3875
Q U E S TI O N 1 5
For the chain length distributions of polymers I, II and III (shown below), which has
(have) the highest weight-averaged molecular weight?
10/12
A) Polymers I
B) Polymers II
C) Polymers III
D) Polymers II and III
Q U E S TI O N 1 6
What is the planar density of the {110} family of planes in simple cubic structure
where a is the unit cell edge length?
(A)
(B)
(C)
(D)
1
√2𝑎2
1
√3𝑎2
1
2𝑎2
2
√3𝑎2
11/12
Q U E S TI O N 1 7
For the lattices shown, which of the following does not show a possible unit cell?
[Answer is D]
Q U E S TI O N 1 8
In the superball lab, the minimum in bounce height corresponds to which of the
following:
A) Melting point
B) Glass transition temperature
C) Room temperature
D) Temperature at which there is maximum crosslinking
12/12
Q U E S TI O N 1 9
Which of the following schematics best represents semi-crystalline polyethylene:
[answer is B]
Q U E S TI O N 2 0
For the polymer structure formula shown, what is the number average degree of
polymerization if the number average molecular weight is 1500 g/mol? Atomic weight in
amu can be found in the periodic table.
A) 28
B) 54
C) 62
D) 5357
13/12