Vladimir's material Flashcards
1
Q
Moseley’s Law
A
The atomic number is the number of protons. Moseley arrange the periodic table based off the atomic number.
2
Q
Periodic table
A
Mandeleev - arranged the PT based on atomic weights and reactivity. Predicted stable elements.
Moseley - arranged the PT based on atomic number. Predicted radioactive elements.
3
Q
Isotopes
A
Nuclei with the same number of protons but a different number of neutrons.
4
Q
Relative Atomic Mass (RAM)
A
The weighed mean of all masses of all naturally occurring isotopes.
RAM (Te) = 127.6 8 naturally occurring isotopes (heavier masses have higher proportions)
RAM (I) = 127 one naturally occurring isotope
5
Q
Radial Distribution Function (RDF)
A
As n increases (1s 2s 3s), max RDF increases (1s<2s<3s)
As l increases (3s 3p 3d), max RDF decreases (3s>3p>3d).
Total electron density decreases as l increases (3s>3p>3d).
6
Q
Normalised RDF
A
The integral of each curve equals 1
7
Q
Relative maxima
A
2p has a RDF max closer to the nucleus; however, 2s has a relative maxima within the core electrons, so it has better shielding and a higher Zeff.
8
Q
Zeff
A
The effective nuclear charge. A measure of an electron’s strength.
9
Q
Slater’s rules
A
n=n+1 orbitals - no effect on Zeff
n=n orbitals - shielding ability of 0.35
n=n-1 orbitals - shielding ability of 0.85
n=n-2 orbitals - shielding ability of 1
nd and nf orbitals with n=n-1 have a shielding ability of 1
10
Q
Clementi and Raimondi
A
Major change to Slater’s rules: electrons occupying orbitals with the same n but different l now have different Zeff.
- accounts for penetrating (s and p electrons feel different Zeff and Zeff increases down a group)
11
Q
Slater’s Rules - oversimplification
A
s and p electrons feel the same Zeff
Zeff doesn’t change much going down groups (slight changes from Al-Ga etc due to the d block)
12
Q
Trends - Zeff and Atomic radii
A
Greater Zeff = smaller radius
13
Q
Hund’s rule
A
Electrons first enter an empty orbital before they begin to pair up.
A pair of electrons with opposite spins occupies a smaller volume, leading to a greater repulsion. Electrons with parallel spins are stabilised (larger volume and less repulsion).
14
Q
Exchange energy (K)
A
K is the difference in energy between alternative configurations.
Electrons with parallel spins have greater volumes and less repulsion, making them more stable. Thus, half-filled and filled orbitals are more stable (3K).
15
Q
Aufbau Principle
A
Electrons fill up orbitals from lowest energy to highest energy (4s then 3d). Exceptions due to exchange energy: Cr = 3d5 4s1 Mo = 4d5 5s1 Cu = 3d10 4s1 Ag = 4d10 5s1 Au = 5d10 6s1 Pd = 4d10 5s0
16
Q
Pauli Exclusion Principle
A
No two electrons can have the same quantum numbers
17
Q
Ionisation energy (IE)
A
The amount of energy to remove an electron from a gaseous ion/atom
M (g,gs) + Min E -> M+ (g) + e- (g)
Measured in kJ/mol
18
Q
IE trends
A
Increases across the period and decreases down a group.
Exceptions - group 13: Ga introduces the d block and Tl inroduces the f block so they have higher IE
19
Q
IE interactions
A
IE is affected by the interaction of electrons with the nucleus, the formal charge of the atom, the shielding effect by other electrons, the atomic radii, interactions between electrons in the same orbitals, electron pair repulsion, and exchange energy interactions
20
Q
Electron Affinity (EA)
A
The amount of energy required for a gaseous atom/ion to gain an extra valence electron.
X(g) + e- (g) -> X-1 (g) + E released (Eeg1)
21
Q
EA trends
A
Increases across the period (Zeff) and decreases down the group (size)
22
Q
Transition metal IE trends
A
In transition-metal elements, electrons enter an inner-shell electron orbital (3d not 4s). In main-group elements, electrons enter outer-shell electron orbitals. As inner-shell electrons have a greater shielding effect than outer-shell electrons, transition metal elements have a smaller rate of increase in their IE than main-group elements.
23
Q
Bond Energy Approximation
A
Approximation of A-B bond energy = average of A-A and B-B. Averaged value would be lower than actual value since the resulting reduction in orbital overlap is overpowered by the increase in electrostatic interaction between them.
The difference between the measured body energy and calculated purely covalent value is proportional to the difference in EN.
24
Q
Pauling - EN
A
The ability of an atom to attract electron density towards itself in a molecule
25
Pauling - pros and cons
Pros - predictive power, determine bond dissociation energy
| Cons - requires bond energy (only possible for reactive compounds - noble gases are not reactive)
26
Allen - EN
The average one-electron energy of the valence-shell electrons in ground-state free atoms.
X = (mEp + nEs)/(m+n)
- m and n is the number of electrons in the p and s orbitals, respectively
- Ep and Es is the IE of the p and s orbital electrons, respectively
27
Allen - pros and cons
Pros - predictive power, uses spectroscopy to precisely determine EN, uses free atoms (can determine EN of noble gases)
Cons - only deals with s and p electrons, cannot predict bond energies
28
Alfred and Rochow
Based on the force exerted by the atom on its s and p electrons. EN defined in terms of Zeff and the covalent radius.
29
Mulliken
Average of the IE and Ea
30
EN trends
Increases across the PT and decreases down groups.
Reactivity of N and Cl depends on the scale (Pauling Cl>N; others N>Cl).
d- and f- contraction - increase in EN for Ga and Tl
31
EN and charge separation
The greater the difference in En, the greater the ionic character of the bond.
X<0.5 - fully covalent (equal contribution of electron density)
X=0.5-1.8 polar covalent to polarized ionic
X>1.8 - ionic
32
Van Arkel Diagram
```
Y-axis - the difference in EN
X-axis - the average of their EN. Ranges from Cs(0.75) to F(3.98).
Bonding - Be (1.57) and H (2.2) lines separate ionic, metallic, semimetals and covalent bonding.
EN (C) = 2.55
EN (Si) = 1.9
EN (Br) = 2.96
EN (Cl) = 3.16
EN (N) = 3.04
EN (O) = 3.44
```
33
Polarizability
Anions tendency to become polarized. Charge . V
Large anions with low EN are easily polarised (soft).
Small anions with high EN are no easily polarised (hard).
Polarisability of anions increases down groups and decreases across the periods.
34
Polarizing power
Cations ability to polarise an anion (pull electron cloud toward itself). Charge/V.
Polarising power of cations increases across periods and decreases down groups.
35
Polarising trends
Smaller cations with greater polarizing powers induce more covalent character (CC)
LiF>NaF>KF
Larger anions with greater polarizability induce more CC
NaI>NaBr>NaCl
Larger charges on both the cation and anion have more CC
AlN>MgO>NaCl (+/-3 > +/-2 > +/-1)
36
Sigma bond
On the line between 2 atoms. Orbitals have no nodes
37
Pi bond
On both sides of a connecting line. One orbital nodal plane.
38
Delta bond
On four sides of a connecting line. d orbitals.
39
Homonuclear bonds
pi and sigma contributions decrease down the group.
Small, compact orbitals give rise to stronger bonds (top of PT)
Large, diffuse orbitals of the heavy elements overlap at greater distances from the nuclei and less electron density is present in the area of overlap, leading to weaker bonds.
Weakness of N2-F2 sigma bonds - short bonds and repulsion between lone pairs significant.
40
Graphite - C
Close balance between sigma and pi.
Layers of hexagonal rings. Conjugation of p-atomic orbitals leads to conductivity. Strong bonds within layers but weak Van Der Waals interactions between layers.
41
Diamond - C
Close balance between sigma and pi.
| Lattice structure in which the C atoms are sp3 hybridised. Insulator and very hard material.
42
Other group 14 elements
Expect sigma bonding to dominate (larger). Distorted diamond-like structure.
43
Nitrogen
pi bonding will dominate. Strong triple bond explains N's use as a high E rocket fuel (exothermic and explosive)
44
Phosphorus
Expect sigma bonding to dominate. Only forms sigma-bonded allotropes.
45
Oxygen
pi bonding will dominate
46
Sulfur
sigma bonding will dominate.
47
Group 17 - halogens
No pi bonding.
F and Cl - smaller, more compact; weak Van der Waals interactions -> gases
Br and I - larger orbitals, stronger Van der Waals interactions -> liquid and solid respectively
48
Catenation
The preference of elements to engage in sigma bonding. Difference between 2nd row (pi) and later periods (sigma).
Group 15/16 - N/O Si ~Ge > Sn ~Pb - form networks
B > Al > In > Ga - form cages
49
Heteronuclear bonds
Stronger bonding due to polarity (difference in EN) and size of atoms.
Si-F is the strongest heteronuclear bond due to the greater difference in EN (compared to C-F).
50
Heteronuclear bond trends
Group 1 - 2: increase due to formal change (stronger electrostatic interactions).
B-F forms a pi bond, as F donates electrons to electron deficient B, small atoms. Al-F forms a sigma bond, due to increased size of Al.
R-F bonds: strength decreases down group (size increases so weaker bond) and decreases across period due to smaller difference in EN.
N/O-F - lone pair repulsion (weaker bonds)
F2 - weakest bond due to lack of polarity
R-H bonds: decrease in bond strength down group and increase across period (smaller). EN less important than for R-F bonds.
F vs Cl bond - F is more EN, so will form a stronger bond than Cl
N-Cl: will be weak due to the similar EN (difference close to 0)
51
Oxidation state (OS)
The charge that would result if the electrons in each bond to that atom were assigned to the more EN atom.
Negative OS - the atom has gained electrons
Positive OS - the atom has lost electrons.
Not an individual property (OS of N vs Cl depends on EN scale). Formalism - high +/- charges are rarely observed experimentally
52
Formal OS
States that don't match up with valence state
53
Valence state
The number of valence electrons that are used in bonding around an atom
54
Enthalpy
To determine whether or not an OS is stable, we look at the enthalpy of formation (sum of enthalpies). Negative = favourable. High and positive = unfavourable.
NaCl example:
1) Start with ground-state atoms: Na Cl2
2) Atomise Na (s->g) and 1/2 bond dissociation for Cl
3) 1st IE for Na and EA for Cl
4) Lattice forms NaCl(s)
55
Group 1 trends
OS = +1 or -1 (fill their s orbital - ligands)
| Electropositive, so their OS are ionic.
56
Group 2 trends
OS = +2
| Electropositive, so their OS are ionic.
57
OS trends in the p-block
Multiple OS states possible, common OS differ in value by 2. Elements in their common OS normally contain no radicals (unpaired electrons). Radical species are rare (stability due to delocalisation).
58
OS trends in the d-block
Organometallics form dimers rather than paramagnetic radicals, as the unpaired electron readily forms strong bonds. Exception V(CO)6 - monomeric radical.
Metal-metal bonds form for OS up to +3. In higher OS, d-orbitals are too contracted. Metal-metal bonds are strong down groups.
59
Group 13 trends
VS = 1 and 3
OS - +1 (one unpaired p electron) and +3 (1 unpaired s electron and 2 unpaired p electrons). +2 OS is purely formal.
Positive OS - low EN (bonding with more EN element).
Tl prefers the +1 OS due to the inert pair effect.
60
Inert Pair Effect
Formation of molecules from individual atoms is a favourable overall process when energy released due to the formation of covalent bonds between atoms exceeds promotion energy (affecting other electrons). Effect more pronounced for heavy atoms due to spin-orbit coupling effects and increases with n and Z. Mismatch in energy and radial distribution of ns- and np- valence orbitals (p- only bonding). Weak bonds formed by heavy elements often do not release enough energy to compensate for higher promotion energy costs, leading to lower OS (paired s electrons -> inert s orbital). Ex: Pb and Tl.
61
Relativistic effects
Heavy elements have significantly higher velocities than light elements, leading to a mass increase (decrease E and radius). Requires a relativistic correction for the mass.
The direct relativistic orbital contraction has the greatest effect on s orbitals of heavier atoms (s orbital has penetrating ability - stablised), less so for p and very little for d and f. Inert pair effect
The indirect relativistic orbitals expansion is pronounced for d and f orbitals, better shielded by contracted s and p.
62
Group 14 trends
VS = 2, 4
+/-4 OS common. +2 OS common for Ge, Sn and Pb (inert pair effect)
Negative OS is combined with less EN element
+/-3 and +/-1 OS are formal
63
Group 15 trends
VS = 3, 5 (N can only have a VS of 3 since there is no accessible d-orbital for promotion).
OS - +/-3 and 5 common
As, Sb and Bi prefer +3 due to inert pair effect
64
Group 16 trends
```
VS = 2,4,6 (O can only have VS=2 as there is no accessible d-orbital).
OS = +/-2, 4, 6. +4 favourable for Se, Te and Po due to inert pair effect
```
65
Group 17 trends
VS = 1,3,5,7 (F can has VS=1 as there is no accessible d-orbital).
OS:
F=-1 as it is the most EN
5,3,+/-1 OS common
Br prefers +5 OS due to inert pair effect.
Cl - +7 charge is purely formal
66
Group 18 trends
VS = 2,4,6,8
OS:
He and Ne - don't form OS as they are too stable
Ra - too heavy and too stable to undergo promotion so doesn't form OS
Ar and Kr - 2 or 0
Xe - 8-0
67
High OS - F and O
High electron E(promotion) required to reach high count of unpaired electrons, allowing formation of higher valence state must be offset by the total energies of the formed bonds. Small hard atoms (O,F - EN) are required to form many strong covalent bonds and offset high electron promotion energies.
68
Molecular solid (ex: I2)
Strong covalent bonds between atoms, but weak intermolecular interaction. Insulators
69
Covalent network structure (Si)
Strong covalent bonds. Insulators
70
Metals (Fe)
Metal cations are held together by delocalised electrons. Conductors when solid or liquid
71
Ionic solid (NaCl)
Ions are held together in a lattice by electrostatic interactions. Conduct when molten or aqueous
72
Crystalline vs Amorphous
Crystalline - well defined faces and edges (diffract x-rays)
| Amorphous - irregular faces (doesn't scatter x-rays). Disordered in terms of long range order.
73
X-Ray crystallography
X-ray hits a lattice, photons scatter in phase (some bounce off first layer, some bounce off second layer of atoms). Use Bragg equation to solve d. Determine unit cell (crystal structure).
74
Coordination number (CN)
How many atoms are bonded to the central atom in a crystalline solid.
75
Ionic Radii Trends
In ions, radius depends on CN and formal charge of ion. As CN increases, radius increases
As formal charge increases with ions with the same electronic configuration, the radius goes down.
76
Limiting Radius Ratio (LRR)
```
Minimum ratio allowed between the radius of the anion (r-) and cation (r+) in a solid in order to be stable (in contact).
r=r+/r-
Apply sine rule:
(r+ + r-)/sin 90 = r-/sinx
sin 90=1 so r+/r- = (1/sinx) -1
Can predict CN and shape.
```
77
Lattice energies - attractive contribution
ΔU=(-z(+)z(-)e^2)/4piɛ(0)r
ΔU=(-AN(A)z(+)z(-)e^2)/4piɛ(0)r
A=madelung constant (number of nearest neighbours) - unique, so you can determine the crystalline structure
eg: NaCl: AN(Z)zz = -6, +12, -8...
78
Lattice energies - repulsive contribution
E(rep) = B/r^n
- B=constant
- r=interionic distance
- n=Born exponent (5-12)
- (n+ + n-)/2
79
Born-Lande equation
```
Combination of attractive and repulsive interactions. Derivative of U = 0 (bottom of graph). Solve B. Determine ΔU
ΔU=AN(A)z(+)z(-)e^2)/(4piɛ(0)r)(1-1/n)
Need to know:
-Crystalline structure (A)
-Interionic distance (r)
-Specific ions (z and n)
```
80
Kapunstinskii Equation
ΔU=(kvz(+)z(-))/(r+ + r-)
A/v and r0 increases with increase CN, ~cancelling out
Need to know:
-the number of ions in a formula unit (v)
-individual radii (r)
Pros - don't need to know A or r0!
Note - k (constant) in ppm so r in ppm
Thermochemical R - estimates radius of polyatomic ions
81
Bonding in ionic solids
Covalent contribution to bonding - strongly polarizing cations and easily polarizable anions (eg: AgI has strong error). Born-Lande equation underestimates the lattice energy due to CC.
- small contribution due to van der Waals forces
- zero-point energy
82
Free electron model
Lattice composed of metal ions surrounded by a sea of delocalised electrons. Metals are fixed in position and electrons can move in any direction. Once a voltage is applied, the electrons move from high to low potential (producing a current).
83
Simple Cubic Cell (SCC)
CN=6
1 atom per unit cell (1/8 of cell in 8 corners)
Cell volume = a³=8r³
Occupied V = 4pir³/3
Fraction of V occupied = O/C= pi/6 = 0.524
52.4% efficient packing
84
Body-centred cubic cell (BCC)
```
CN = 8
2 atoms per unit cell (1 centre atom + 8*1/8)
Cell V = a³=(4r/√3)³
-b²=a²+a²
-c²=a²+b²=3a²
-c=√3a=4r
Occupied V = 2(4pir³/3)
Fraction V occupied = pi√3/8 = 0.680
68% efficient packing
```
85
Face-centred cubic cell (FCC)
```
CN=12
4 atoms per unit cell (6*1/2 + 8*1/8)
Cell V = a³= (√8r)³
-b=4r
-b² = a² + a²=16r²
-a=√8r
Occupied V = 4(4pir³/3)
Fraction V occupied = 2pi/3√8=0.740
74% efficient packing
```
86
HCP
Change in packing of 2D layer. Third layer goes above holes in second layer.
fcc and hcp have 6 nearest neighbours within layer. scc and bcc have 4 nearest neighbours within layer.
HCP: Third layer goes directly above the first layer. CN=12
87
Density
d=m/V=nM/Na³
| -need cell edge length (a), molar mass (M), and number of atoms per cell (n).
88
Band theory
In a metallic solid, the orbitals interact. As more atoms interact, the molecular energies get closer together until they merge into a band. The unfilled antibonding orbitals have higher energy. In ground state (0K), electrons present in low energy bonding orbitals and can be excited to antibonding orbitals. Add some energy, the electrons can freely move (conduct). Eqm point shows which energy levels electrons can be found at. Form a closely packed lattice.
Band gap - electrons cannot enter this region
Band structures depend on element and eqm interactomic spacing (core-like orbitals don't interact with valence orbitals)
89
Conductors
Empty state directely above filled states for electrons to readily jump to.
Cu - Filled state, empty state, band gap, empty band
Mg - Filled band overlaps with empty band forming empty states.
In freeze out, all electrons are in the filled state. Adding any energy will allow the electrons to freely move
90
Insulators
Filled valence band, band gap and empty conduction band. Large band gaps >4eV
-diamond
91
Intrinsic Semiconductor
Filled valence band, band gap and empty conduction band. Small band gap (<4eV)
-Ge
92
Conductivity in metals
Electron conduction by thermal energy and free electron model. Continuum - cannot differentiate between E levels. Resistivity - lattice and defects as scattering centres for electrons.
Resistivity increase with T (so conductivity decreases) as the lattice starts vibrating, interfering with and breaking up the flow of electrons (scattering events).
93
Defects
Mechanical properties: resistivity and malleability
Boundary between crystals - more resistivity
Edge dislocation effect - one row of atoms is terminated
Point Defects: boundaries fuse together with time
Vacancy - gap in the structure
Substitutional atom - there is a different atom taking another atom's place in the structure
Interstitial atom - there is a small atom inserted into a cavity of a lattice
Diffusion - position of interstitial atom moves
94
Conduction in intrinsic semiconductors
Both the electrons (-) and holes (+) are major current carriers. Small band gap, so not much energy is required to excite electrons into the conduction band.
Changing the T changes the concentration of charge carriers.
Smaller band gap - for any given T, Ge will have a higher concentration of charge carriers than Si.
Point defects due to impurities - interstitial impurity and substitutions impurity.
95
Doping
Adding impurities into the lattice. Concentration of charge carrier relies on concentration of dopant.
- Donor state - dopant has an extra electron position just below the conduction band, which can readily jump. n-doped
- Acceptor state - dopant has one less electron, so there is a hole jump above the valence band, which electrons can jump into. p-doped
96
n-doped semiconductor
Donor state.
| Only electrons are charge carriers.
97
p-doped semiconductor
Acceptor state.
| Only holes are charge carriers
98
Extrinsic semiconductor benefits
Type - n-dopant or p-dopant
Concentration - <1% dopant so you need a super pure matrix. Concentration of dopant controls the number of acceptor and donor state.
Concentration is stable over a wider T range - better for technology
99
Extrinsic semiconductors
Freeze-out region - electrons are promoted from donor states or into acceptor states
Extrinsic region - concentration of electron/holes proportional to concentration of dopant.
Intrinsic region - correlates to matrix as electrons in valence band/acceptor states can be promoted into the conduction band, electrons and holes are charge carriers.
100
Modification
Increase the width of the extrinsic region
- decrease the gap between the donor/acceptor states and the conduction/valence band (less energy required to promote electrons - electrons promoted at lower T in freeze-out region)
- Change the matrix to get a larger band gap - electrons will require a higher T to be promoted from the valence band/acceptor state to the conduction band.
101
LEDs
Electrons over holes, emits a particular wavelength of light.
Pros - durable, small, shock resistant, different colours, energy efficient.
