Inorganic Chemistry: Solid State
3001. (Unit cells; Ch. 3 "Companion") Which
parallelograms in the figure below are unit cells?
A, B, C, D, E
After a unit cell is identified: What number of atoms belong to the unit
cell?
1, 2, other
3002. (Unit cells; Ch. 3 "Companion;" empirical
formula) Pictured below is an NaCl layer. Which of the squares are unit
cells?
A, B, C
Having identified B as a unit cell, for example, how many Na and Cl atoms
belong to it?
Na2Cl2, Na4Cl4, Na8Cl8
What is the empirical formula?
NaCl, Na2Cl, NaCl2
In terms of relative size, Na+ and Cl- would be represented, respectively,
by
small and large circles, large and small circles
3003. (Coordination number; Ch. 5 "Companion")
At-Seat Demonstration: Give students 10 pennies (students can share a set
of ten) and ask them to pack them at their desks to determine the largest
coordination number in two dimensions.
4, 6, 8, 9
3004. (Unit cells, layer sequences; Ch. 3 "Companion")
In the figures below, how many atoms per unit cell are present?
3005. (Close packed spheres, holes; Ch. 5 "Companion")
In the zinc blende layer sequence below, what fraction of the tetrahedral
holes are filled?
1/8, 1/4, 1/2, all
3006. (Close packed spheres, holes; Ch. 5 "Companion")
C60 (buckyball) is cubic closest packed (face-centered cubic)
in its crystalline form. If you insert potassium atoms into all the tetrahedral
and octahedral holes of the C60 structure, the formula would
become KxC60. What is the value of x?
1, 2, 3, other
3007. (Close packed spheres, holes; Ch. 5 "Companion")
In the solid compound Cu2HgI4, cations occupy tetrahedral
holes in a close packed anion lattice. What fraction of tetrahedral holes
are filled?
1/4, 3/8, 3/4
3008. (Bands; Ch. 7 "Companion") The 3s band
of solid Na will have as many orbitals (each delocalized over the entire
solid) as the number of 3s orbitals from Na atoms in the sample. If each
orbital of the band can hold two, spin-paired 3s valence electrons, to what
extent will the band be filled?
completely empty, half filled, completely filled
To what extent will the Na 2s band be filled?
completely empty, half filled, completely filled
Which is the best electronic band population for good electrical conductivity
(metallic behavior), if a net flow of electrons through a band is needed?
Demonstration 7.1 "Companion": A requirement for electrical
conductivity is net electron flow in a particular direction in a sample.
At what capacity should the band be filled with electrons to best promote
electrical conductivity? Have three jars sealed tightly: one empty (represents
empty band), one partially-filled (represents partially filled band) and
one completely filled (represents filled band). If the filler (sand or packing
peanuts, e.g.) represents electrons and tipping the jar represents the application
of a voltage, which jar(s) will exhibit net motion of the filler?
empty, partially filled, filled
In which part of the filled portion of the band is net motion greatest?
top, middle, bottom
3009. (Bands, metallic bonding; Ch. 7 "Companion")
What charge carrier concentration do you expect for Na if most of its valence
electrons are ionized?
105, 1015, 1022
3010. (Thermal conductivity; Ch. 7 "Companion")
If students have a seat/desk with metal and wooden parts that are not in
direct contact with their bodies, ask about the relative temperature: Which
is colder? Demonstration: Measure the temperature of each part with a digital
thermometer.
wood, metal, both are at the same temperature
(Tie in with thermal equilibrium and the calculated value of ambient
thermal energy as RT.)
If the temperature of the room goes from 20 degrees C to 40 degrees C, the
ambient thermal energy
doubles, is halved, increases by less than 10%
At-Seat Demonstration 7.5 "Companion": Touch the wood
and metal part of the desk. Which material conducts heat better and thus
has a higher thermal conductivity?
wood, metal, the two materials are the same
3011. (Bands; Ch. 7 "Companion") Which of these
band diagrams is consistent with diamond being an electrical insulator?
A, B, C
Another approach is to have students determine which bands are filled
to which extent, and then decide if each band scenario in turn (A, B, then
C) corresponds correctly to diamond's being an electrical insulator rather
than a conductor (metal). The s, p combination band can be related to sp3
hybrid orbitals if desired.
3012. (Isoelectronic structures, periodic properties;
Ch. 7 "Companion") Ge is a semiconductor. If half of the Ge atoms
of a sample of Ge are replaced with Ga atoms, with what element should the
other half of the Ga atoms be replaced in order for this new compound to
be isoelectronic with Ge?
Sn, As, Se
3013. (Band gap energy, spectroscopy, semiconductors;
Ch. 7 "Companion") Setup: Band gap energy has been introduced
in a localized picture: it can be defined as the energy needed to remove
an electron from a bond in the solid, enabling the electron to move freely
through the solid to conduct electricity. When itinerant electrons return
to such a one-electron bond, the band gap energy can be released as a photon.
The band gap energy is to a first approximation expected to increase as
the bonds become stronger and shorter and the electrons are held more tightly.
The group 14 elements illustrate this effect with diamond being an electrical
insulator, silicon and germanium (longer, weaker bonds in the same diamond
structure) being semiconductors, and a-tin being a metal. Demonstration
7.11 "Companion": A trio of related predictions: what will
happen to interatomic spacing, band gap energy, and the color of the light
emitted when an orange LED is cooled in liquid nitrogen. On cooling,
atoms of the semiconductor will get closer together, atoms will
get farther apart
band gap energy increases, band gap energy decreases
color of light will become more red, color of light will become more
yellow
3014. (Spectroscopy; Ch. 7 "Companion") Knowing
diamond is transparent, which curve best represents the absorption spectrum
of diamond (see below)?
A, B, C
3015. (Superconductors, periodic properties; Ch. 9 "Companion")
A major research breakthrough was the discovery that an oxide of La, Cu,
and Ba was superconducting. When this material was "squeezed,"
the high pressure raised the critical temperature at which it became superconducting.
Given this effect, which element should be tried as a +3 ion replacement
for La to raise the critical temperature without having to apply pressure?
Hf, Y, Ac
3016. (Elemental analysis, diffraction, solid solutions;
Ch. 3 & 4 "Companion") Sample A is an equimolar physical mixture
of Si and Ge. Sample B is a Si0.5Ge0.5 solid solution.
Which measurements will be identical and which different for the two samples?
elemental analysis: same, different
x-ray diffraction: same, different
absorption spectrum: same, different
3017. (Solid solutions, periodic properties; Ch. 7 "Companion")
Which of the following is a reasonable solid solution?
GaxAl1-xAs, GaPxAs1-x,
GaAlxAs1-x, GaxP1-xAs
3018. (Solid-state synthesis, solid solutions; Ch. 3 &
10 "Companion") Which synthetic methods would intimately mix Si
and Ge on the atomic scale to create SixGe1-x solid solutions?
co-grinding, co-melting and condensing, co-vaporizing and
condensing
3019. (Diffraction, optical transforms; Ch. 4 "Companion,"
Demonstration 4.1) The equation dx = lL defines the relationship
between incident wavelength l, spacing of repeating features d, spacing
between diffracted spots x, and distance between transform slide and screen
L. Consider which variables are directly and inversely related to predict
the following.
When the wavelength is decreased from red to green (demonstration with 633
and 543 nm HeNe lasers), should the spacing between diffraction spots
increase, decrease, stay the same
(This relationship can also be seen by having students view a point source
of white light through their personal transform slide, as described in Demonstration
4.1, and having them note which part of the full spectrum they observe for
each diffracted spot, violet or red, is giving rise to the largest spacing).
When the distance between slide and screen is increased, the spacing between
diffraction spots should
increase, decrease, stay the same
When the spacing between features on the transform slide increases, the
spacing between diffraction spots should
increase, decrease, stay the same
3020. (Equilibrium, Le Châtelier's principle; Ch.
5 & 9 "Companion") The body-centered cubic (bcc) phase of
a metal has a 68% packing efficiency, while the face-centered cubic (fcc)
phase of the same metal has a 74% packing efficiency. For the equilibrium
bcc metal<=>fcc metal
as pressure increases, the equilibrium
shifts to the left, shifts to the right, is unaffected
Consider also the effect of increasing pressure on the following equilibria
graphite<=>diamond
shifts to the left, shifts to the right, is unaffected
hcp<=>ccp
shifts to the left, shifts to the right, is unaffected
3021. (Unit cells, layer sequences, close packed spheres;
Ch. 3 & 5 "Companion") A layer sequence for an FCC = CCP metal
is shown below.
A face diagonal passes through the center of atom 4 and the center(s)
of which other atom(s)?
1, 2, 5, 11 Also correct: 8, 12 & 9,
10
A body diagonal passes through the center of atom 4 and the center(s) of
which other atom(s)?
2, 5, 11, 14
A close-packed plane is comprised of six atoms. If atoms 2, 4, 5 are three
of six atoms comprising a close-packed plane, which other three atoms are
included in the plane?
11, 13, 14; 6, 9, 13; 7, 8, 12; 6, 9,
10
3022. (Phase changes, Le Châtelier's principle;
Ch. 9 "Companion") Nickel titanium memory metal has a symmetric
cubic unit cell in its high temperature form and a less symmetric noncubic
unit cell in its low temperature form. Demonstration 9.6 "Companion":
By slightly changing the Ni to Ti ratio, a sample can have, at room temperature,
one or the other of these phases. Two small rods, one in the symmetric structure,
one in the less symmetric structure at room temperature are dropped on the
floor. One produces a ringing sound, the other a soft thud. Which gives
the ringing sound?
the symmetric high temperature phase, the less symmetric low
temperature phase
To cause the ring-sounding sample to give a thudding sound,
heat it, cool it
Demonstration: Cool the sample with liquid nitrogen, remove it
and drop it to hear a thud. Rapid hand warming of the rod between repeated
drops will eventually restore the ring.
Which phase is more mechanically flexible?
the symmetric high temperature phase, the less symmetric low temperature
phase
When nickel titanium memory metal interconverts between the symmetric
high temperature form and the less symmetric low temperature form, which
of the following changes?
elemental analysis, X-ray diffraction pattern, hardness
When a sample of nickel-titanium in the high temperature phase is bent,
as pictured, the atoms that are under compression and thus favored by Le
Châtelier's principle to convert to the denser low-temperature phase
are those
at the bottom of the bend, in the middle of the bend, at the
top of the bend
Demonstration 9.5 "Companion": Bend memory metal eyeglass
frames and show that they return to their original shape. Then cool with
liquid nitrogen to show that when the eyeglass frames are in the more flexible
low temperature phase they stay bent until they return to room temperature,
where they regain their original shape.
3023. (Semiconductors, bands; Ch.8 "Companion")
Pictured below is an energy band diagram for silicon.
When doped into Si, Al is a(n)
donor, acceptor
When doped into Si, P is a(n)
donor, acceptor
Which energy level corresponds to Al?
A, B
Which energy level corresponds to P?
A, B
3024. (Semiconductors, doping; Ch 8 "Companion")
Which is a weaker acceptor (analogous to weaker acid)
In, Cu
Which is a weaker donor (analogous to weaker base)?
As, Mn
3025. (Close packed spheres, holes) Demonstration:
Which is a smaller hole?
One formed by a tetrahedron of identical spheres, one formed
by an octahedron of identical spheres
A sphere that fits snugly into an octahedron can be shown not to fit
into a tetrahedral hole.
3026. (Doping, equilibrium, autoionization; Ch. 8 "Companion")
KSi=[h+]x[e-]=pxn=1020 cm-6 For this endothermic autoionization
reaction, as temperature increases, KSi
increases, decreases, remains constant
3027. (Plastic deformation, slip planes; Ch. 6 "Companion")
Which situation allows easiest slippage of planes of atoms past one another,
as sketched below?
identical spheres in both layers, a layer with a large impurity
atom, a layer with a small impurity atom
Which of the two impurities acts like a "speed bump" and which
like a "pothole," in impeding movement along slip planes?
3028. (Electronegativity, bonding, band gap energy; Ch.
7 "Companion") The atoms below have the following electronegativities:
Zn Ga Ge As Se
1.6 1.7 1.9 2.1 2.4
The three isoelectronic semiconductors Ge, GaAs, and ZnSe all have roughly
the same size unit cell and internuclear separation (exclusively Ge-Ge,
Ga-As, and Zn-Se bonds, respectively). If under these conditions, band gap
energy increases with ionic character of bonding, which isoelectronic solid
should have the largest band gap energy?
Ge, GaAs, ZnSe
3029. (Equilibrium, semiconductors, doping; Ch. 8 "Companion;"
LeChâtelier's principle) When doped into Si, Cu is a weak acceptor,
Cu ==> Cu- + h+. To convert most of the copper to Cu-, dope with
a strong acceptor like aluminum, a strong donor like phosphorus,
a weak donor like manganese
3030. (Solar cells, band gap energy; Ch. 8 "Companion")
Two solar cells are to be used by stacking one atop the other. Solar cell
A has a band gap energy of 2 eV; solar cell B's band gap energy is 1 eV.
Either alone will absorb all the light above its band gap energy. But which
one must be on top (nearest the sun) for both to function simultaneously?
A, B
3031. (Semiconductors, equilibrium; Ch. 8 "Companion")
Given the graph below, unlabelled, and knowing that the band gap energies
Ge Si GaAs, label the graph. Compare the number of carriers per cm3
in Ge and water at room temperature from the graph below.
108 times more in Ge, equal numbers, 108 times
more in water
3032. (Solid solutions; Ch. 3 "Companion") The
following trio of metals all form the BCC structure.
Metal Atomic Radius
V 1.31 Angstroms
Mo 1.36 Angstroms
Na 1.86 Angstroms
Which two metals are most likely to form a solid solution?
V and Mo, V and Na, Mo and Na
Additional example: Group 14 Element Cubic Unit Cell Length
Metal Atomic Radius
C 3.57 Angstroms
Si 5.43 Angstroms
Ge 5.66 Angstroms
Which two elements are most likely to form a solid solution?
C and Si, C and Ge, Si and Ge
3033. (Diffraction, optical transforms, layer sequences;
Ch. 3 & 4 "Companion" Experiment 4) When looking down onto
a face of the FCC and BCC cubic unit cells, the two arrangements of atoms
shown below are seen by superimposing layer sequences. Which corresponds
to the FCC structure?
A, B
Which X-ray diffraction pattern corresponds to the FCC structure?
A, B
3034. (Miller indices) What are the Miller indices for
the plane represented by the line on the 2-D array of 'atoms' below?
(3 1 0), (2 1 0), (1 2 0)
(Unit cells; Ch. 3 "Companion;" Miller indices) Select the
Miller indices corresponding to the described planes of atoms in the FCC
structure:
Contains cubic unit cell face (100) (110) (111)
Perpendicular to cubic unit cell body diagonals (100) (110) (111)
Contains parallel cubic unit cell face diagonals (100) (110) (111)
Contains close packed planes of atoms (100) (110) (111)
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