1. Question on Van der Waals Interactions
Consulted with Professor Lam and Marfatia, who are more expert.
Indeed, by definition, Van der Waals binding arise from dipole-dipole interactions.
However, they can occur from induced dipoles in neutral atoms or molecules. In particular, a QM dipole fluctuation in one atom can induce a dipole in another atom and then produce a Van der Waals force/potential (also mentioned on p.1407 of the text).
So permanent dipole moments are not required at all. Also note Van der Waals binding is weak.

2. Visual Demonstration

3. Rotation and vibrational levels combined
Figure 42.8 (right) shows an energy-level diagram for rotational and vibrational energy levels of a diatomic molecule. Figure 42.9 (below) shows a typical molecular band spectrum.
Question: Do the n values label rotational or vibrational modes ?

4. Clicker question on rotational energy levels
When a diatomic molecule rotates very rapidly, the atoms that comprise the molecule move slightly farther apart (the molecule “stretches”). What effect does this have on the rotational energy levels of the molecule?
A. The low-energy levels are spaced closer together than if the molecule did not stretch.
B. The low-energy levels are spaced farther apart than if the molecule did not stretch.
C. The high-energy levels are spaced closer together than if the molecule did not stretch.
D. The high-energy levels are spaced farther apart than if the molecule did not stretch.
Answer: C

5. Clicker question on rotational modes
When a diatomic molecule rotates very rapidly, the atoms that comprise the molecule move slightly farther apart (the molecule “stretches”). What effect does this have on the rotational energy levels of the molecule?
A. The low-energy levels are spaced closer together than if the molecule did not stretch.
B. The low-energy levels are spaced farther apart than if the molecule did not stretch.
C. The high-energy levels are spaced closer together than if the molecule did not stretch.
D. The high-energy levels are spaced farther apart than if the molecule did not stretch.
I=mr2,; E=L2/2I

6. Clicker question on energy levels of a molecule
This diagram shows the vibrational and rotational energy levels of a diatomic molecule. Consider two possible transitions for this molecule:
A. n = 2, l = 5 to n = 1, l = 4
B. n = 2, l = 1 to n = 1, l = 0
The energy change is
greater for transition A.
greater for transition B.
C. the same for both transitions.
D. any of the above, depending on circumstances.
Answer: A

7. Clicker question on molecular energy levels
This diagram shows the vibrational and rotational energy levels of a diatomic molecule. Consider two possible transitions for this molecule:
A. n = 2, l = 5 to n = 1, l = 4
B. n = 2, l = 1 to n = 1, l = 0
The energy change is
greater for transition A.
greater for transition B.
C. the same for both transitions.
D. any of the above, depending on circumstances.
Answer: A
A. l(l+1)h2; [5(5+1)-4(4+1)]h2=14h2; B. [2(2+1)-1(2)]h2=4h2

8. Crystal lattices for crystalline solids
A crystal lattice is a repeating pattern of mathematical points. The figure (below) shows some common types of lattices.
Two common types of binding in crystals:
ionic and covalent.
Also “metallic crystal”, electrons are shared among many atoms.

9. Crystal lattices and structures
Important to note, the crystal lattice extends to infinity (repeating each element)
The figure (below) shows the diamond structure, covalent bonding

10. Types of crystals
Figure (left) shows a metallic solid, and Figure (right) shows an edge dislocation in two dimensions.
Also note the contrast between crystals and amorphous materials (e.g. glass), no long range order

11. Energy bands

12. Energy bands
Consider a solid with N identical atoms, push the atoms closer together. The wavefunctions of the valence electrons distort. By Heisenberg the wave functions are less localized and extend large distances if the energy is fixed.
This leads to formation of continuous energy bands. There can be discrete gaps between the energy bands (band gap)
According to Pauli, when all states in a band are “full” cannot add more electrons.

13. Energy bands Small band gap Band gap of 5 eV or more
Metallic sodium is an example, gap is 2.1 eV but even at T=0, conduction electrons.
Small band gap
e.g eV for Si, 0.67 for germanium
Band gap of 5 eV or more

14. Semiconductors
A semiconductor has an electrical resistivity that is intermediate between those of good conductors and good insulators.

15. Resistivity
One type of thermometer works by measuring the temperature dependent electrical resistivity of a sample.
Question: Which of the following types of material displays the greatest change in resistivity for a given temperature change ?
(i) insulator (ii) semiconductor (iii) resistor or (iv) superconductor.
Ans: semiconductor. The resistivity of conductors and insulators changes more gradually with temperature

16. Holes A hole is a vacancy in a semiconductor.
A hole in the valence band behaves like a positively charged particle.
The figure on the right shows the motions of electrons in the conduction band and holes in the valence band with an applied electric field.
Question: What is the force on a charged particle in a uniform E field

17. Doping is the deliberate addition of impurity elements.
Impurities
Doping is the deliberate addition of impurity elements.
In an n-type semiconductor, the conductivity is due mostly to negative charge (electron) motion.
In a p-type semiconductor, the conductivity is due mostly to positive charge (hole) motion.

18. n-type and p-type semiconductors
Figure (left) shows an n-type semiconductor, and Figure (right) shows a p-type semiconductor.

19. Clicker question on band gaps and materials
At absolute zero (T = 0 K), what is the difference between a semiconductor and an insulator?
A. The conduction band is empty in a semiconductor but partially filled in an insulator.
B. The conduction band is partially filled in a semiconductor but empty in an insulator.
C. The energy gap between the valence and conduction bands is large in a semiconductor but small in an insulator.
D. The energy gap between the valence and conduction bands is small in a semiconductor but large in an insulator.
Answer: D

20. A42.4
At absolute zero (T = 0 K), what is the difference between a semiconductor and an insulator?
A. The conduction band is empty in a semiconductor but partially filled in an insulator.
B. The conduction band is partially filled in a semiconductor but empty in an insulator.
C. The energy gap between the valence and conduction bands is large in a semiconductor but small in an insulator.
D. The energy gap between the valence and conduction bands is small in a semiconductor but large in an insulator.

21. Fermi-Dirac distribution
The Fermi-Dirac distribution f(E) is the probability that a state with energy E is occupied by an electron (identical spin ½ particles)
Look at the change with temperature
There is a different distribution for spin 1 (photons) and spin 0 particles [Bose-Einstein]

22. Clicker question on semiconductors
How would you expect the electric conductivity of a semiconductor to vary with increasing temperature?
A. It should increase, because more electrons are thermally excited from the valence band into the conduction band.
B. It should increase, because more electrons are removed from their parent atoms and added to the valence band.
C. It should decrease, because the added thermal energy breaks apart correlated electron pairs.
D. It should decrease, because the atoms in the crystal will vibrate more and thus block the flow of electrons.
Answer: A

23. A42.6
How would you expect the electric conductivity of a semiconductor to vary with increasing temperature?
A. It should increase, because more electrons are thermally excited from the valence band into the conduction band.
B. It should increase, because more electrons are removed from their parent atoms and added to the valence band.
C. It should decrease, because the added thermal energy breaks apart correlated electron pairs.
D. It should decrease, because the atoms in the crystal will vibrate more and thus block the flow of electrons.