dr. jie zouphy 13711 chapter 43 molecules and solids
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Dr. Jie Zou PHY 1371 1
Chapter 43
Molecules and Solids
Dr. Jie Zou PHY 1371 2
Outline Molecular bonds Bonding in solids Energy states and spectra of
molecules Free electron theory of metals Band theory of solids Electrical conduction in
metals, insulators, and semiconductors
Semiconductor devices and superconductivity
Dr. Jie Zou PHY 1371 3
Molecular bonds The bonding mechanisms in a molecule
are fundamentally due to electric forces between atoms (or ions).
Potential energy function that can be used to model a molecule:
r: internuclear separation distance between the two atoms
A and B are parameters that can be determined by experiments.
system atom- twoafor mn r
B
r
ArU
Dr. Jie Zou PHY 1371 4
Plot of U(r) ~ r for a two-atom system
Equilibrium separation: U(r) is a minimum and the two atoms are in stable equilibrium.
At large separation distance: the slope is positive, corresponding to a net attractive force.
At small separation distance: the slope is negative, corresponding to a net repulsive force.
Binding energy: The additional energy the system has to be given to break up the diatomic molecule (so that r = ).
Dr. Jie Zou PHY 1371 5
Classification of molecular bonding mechanisms
Ionic bonds Example: Sodium Chloride (NaCl)
Covalent bonds Example: H2 molecule
Van der Waals bonds Example: Condensation of inert gas
atoms into the liquid phase Hydrogen bonds
Example: DNA molecules
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Example: Covalent bonding
Ground-state wave functions 1(r) and 2(r) for two hydrogen atoms making a covalent bond ( )
(a) The atoms are far apart and their wave functions overlap minimally.
(b) The atoms are close together, forming a composite wave function 1(r) + 2(r) for the system. The probability amplitude for an electron to be between the atoms is high.
0/
30
1
1)( ar
s ea
r
Dr. Jie Zou PHY 1371 7
Bonding in solids A Crystalline solid consists of a large
number of atoms (ions) arranged in a regular array, forming a periodic structure.
Classification of bonding in solids: Ionic solids. Example: Sodium Chloride
(NaCl crystal) Covalent solids. Example: Diamond, silicon,
germanium Metallic solids. Example: Copper, silver,
sodium, etc.
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Examples of bonding in solids
NaCl Diamond Metal
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Energy states and spectra of molecules
Total energy of a molecule:E = Eel + Etrans + Erot + Evib
Rotational motion of molecules Vibrational motion of molecules Molecular spectra
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Rotational motion of molecules
Erot = (1/2) I2. I = r2, = m1m2/(m1 + m2), the
reduced mass of the molecule Quantization of the magnitude of the
molecule’s angular momentum
J: rotational quantum number Allowed values of rotational energy:
Energy separation between adjacent rotational levels:
,..., , J JJIL 210 )1(
...,, J JJI
Erot 210 )1(2
2
...,,JJI
hEEE JJ 321
4 2
2
1
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Allowed Rotational transitions
Selection rule: J = 1 For most molecules, transitions
between adjacent rotational energy levels result in radiation that lies in the microwave range of frequencies (f ~ 1011 Hz).
Example 43.1: The J = 0 to J = 1 rotational transition of the CO molecule occurs at a frequency of 1.15 x 1011 Hz.
(a) Find the Moment of inertia of the molecule.
(b) Find the bond length of the molecule.
Dr. Jie Zou PHY 1371 12
Vibrational motion of molecules
Frequency of vibration for the system:
Allowed values of vibrational energy:
Energy separation between successive vibrational levels:
k
f2
1
...,,vkh
vhfvEvib 210 2
)2
1()
2
1(
hfkh
Evib 2
Dr. Jie Zou PHY 1371 13
Allowed vibrational transitions
Selection rule: v = 1 Transitions between
vibrational levels are caused by absorption of photons in the infrared region of the spectrum.
Example 43.2: The frequency of the photon that causes the v = 0 to v = 1 transition in the CO molecule is 6.42 x 1013 Hz. Find the force constant k for
this molecule.
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Molecular spectra Total energy of the molecule:
Each energy level is indexed by the two quantum numbers v and J.
Absorptive transitions between the v = 0 and v = 1 vibrational states: (1) J = +1 and (2) J = -1
Energies of the absorbed photons:(1) E = hf + (ħ2/I)(J+1), J= 0,1,2,…(2) E = hf - (ħ2/I)J, J=1,2,3…
)1(2
)2
1(
2
JJI
hfvE
Dr. Jie Zou PHY 1371 15
Absorption spectrum of the HCl molecule
Quick Quiz: There is a gap between the two sets of peaks. Why?
Dr. Jie Zou PHY 1371 16
Homework
Chapter 43, P. 1434, Problems: #3, 8, 9, 14, 17.