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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. Copyright © 2012 Pearson Education Inc. Visual Demonstration Copyright © 2012 Pearson Education Inc. 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 ? Copyright © 2012 Pearson Education Inc. 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. Copyright © 2012 Pearson Education Inc. 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. I=mr2,; E=L2/2I D. The high-energy levels are spaced farther apart than if the molecule did not stretch. Copyright © 2012 Pearson Education Inc. 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 A. greater for transition A. B. greater for transition B. C. the same for both transitions. D. any of the above, depending on circumstances. Copyright © 2012 Pearson Education Inc. 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 A. greater for transition A. B. greater for transition B. A. l(l+1)h2; [5(5+1)4(4+1)]h2=14h2; B. C. the same for both transitions. [2(2+1)-1(2)]h2=4h2 D. any of the above, depending on circumstances. Copyright © 2012 Pearson Education Inc. 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. Copyright © 2012 Pearson Education Inc. 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 Copyright © 2012 Pearson Education Inc. Types of crystals • Figure 42.15 (left) shows a metallic solid, and Figure 42.16 (right) shows an edge dislocation in two dimensions. Also note the contrast between crystals and amorphous materials (e.g. glass), no long range order Copyright © 2012 Pearson Education Inc. Energy bands Copyright © 2012 Pearson Education Inc. 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) Copyright © 2012 Pearson Education Inc. According to Pauli, when all states in a band are “full” cannot add more electrons. Energy bands Band gap of 5 eV or more Copyright © 2012 Pearson Education Inc. Small band gap e.g. 1.12 eV for Si, 0.67 for germanium Metallic sodium is an example, gap is 2.1 eV but even at T=0, conduction electrons. Semiconductors • A semiconductor has an electrical resistivity that is intermediate between those of good conductors and good insulators. Copyright © 2012 Pearson Education Inc. 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 Copyright © 2012 Pearson Education Inc. 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. Copyright © 2012 Pearson Education Inc. Question: What is the force on a charged particle in a uniform E field 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. Copyright © 2012 Pearson Education Inc. n-type and p-type semiconductors • Figure 42.26 (left) shows an n-type semiconductor, and Figure 42.27 (right) shows a p-type semiconductor. Copyright © 2012 Pearson Education Inc. 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. Copyright © 2012 Pearson Education Inc. 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. Copyright © 2012 Pearson Education Inc. 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) f (E) = 1 e (E-E f )/kBT +1 There is a different distribution for spin 1 (photons) and spin 0 particles [Bose-Einstein] Copyright © 2012 Pearson Education Inc. Look at the change with temperature 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. Copyright © 2012 Pearson Education Inc. 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. Copyright © 2012 Pearson Education Inc.