Konopinski Lecture Tonight (7:30, Whittenberger)

1. Konopinski Lecture Tonight (7:30, Whittenberger) Also keep in mind the Patten lectures this week: Wendell Berry “The agriculture we have and the agriculture we need” Wed 7:30 : Ballentine 013 Readings in Rawles 100 T,R 7:30 Performance Friday 8:00 Buskirk-Chumley

2. Lecture 31Exam II: Avg 31.1/54=57.6% Note: a couple of exams were regraded, and there were some minor errors in the original histogram, so this is slightly different from what you originally saw in class.

3. Lecture 31Molecules and bonding • Why do atoms combine together to form molecules, and what forces/concepts • control the way this happens? • How do molecules behave? • Below we show a couple of model formulae used to describe molecular binding.

4. Lecture 31CALM What is the change in confinement energy for an electron in going from a hydrogen atom (where r=0.053 nm) to the H2+ ion (where the nuclei are separated by 0.1nm)? This question confused most of you, but my reason for asking it was to emphasize the simplistic nature of the book’s statement that “the attractive forces between atoms in molecules must be due to the Coulomb force, because the Coulomb force is the only one that has both the strength and range necessary…” How do we answer this?

5. Lecture 31CALM What is the change in confinement energy for an electron in going from a hydrogen atom (where r=0.053 nm) to the H2+ ion (where the nuclei are separated by 0.1nm)? This question confused most of you, but my reason for asking it was to emphasize the simplistic nature of the book’s statement that “the attractive forces between atoms in molecules must be due to the Coulomb force, because the Coulomb force is the only one that has both the strength and range necessary…” How do we answer this? Dx~ 0.053 nm suggests a minimum p and therefore a certain KE (3.4 eV), this is what we have previously referred to as “confinement energy”. Forming the molecule increases Dx to ~ 0.1-0.15 nm, and therefore lowers the “confinement energy” by about a factor of 4 to 9 (to ~0.9 to 0.4 eV). This suggests a difference of about 2.5 to 3 eV, just from letting the electron “spread out” more. [NOTE: the actual binding energy of H2+ is about 2.79 eV!]

6. Lecture 31Molecules and bonding • The Morse Potential is useful for describing vibrations because it does include • anharmonic effects, and it more closely represents the real potential than • a pure harmonic potential • http://wapedia.mobi/en/Morse_potential

7. Lecture 31UV-Visible spectroscopy http://www.sci.sdsu.edu/TFrey/Bio750/UV-VisSpectroscopy.html

8. Lecture 31Rotational/Vibrational Excitations Absorption of light by HCl in the region from nvib=0 to nvib=1. Evib = (n+1/2) hbar w Erot = l(l+1) hbar2/2I Dl=+/-1

9. Lecture 32Rotational motion The wave functions relevant to rotational motion are our friends the spherical harmonics. For homo-nuclear diatomic molecules (e.g. H2, D2, N2, O2 etc. ) the symmetry of these functions becomes important due to the spin-statistics theorem. In such a molecule, “exchanging the two particles” is equivalent to changing r for –r which is equivalent to adding p to q. in spherical polar coordinates. Note that if l is even (0,2, …) the Ylm is even under this transformation, but if l is odd, the function changes sign upon the transformation. This produces strong correlations between the totao spin and the orbital angular momentum for such molecules.

10. Lecture 31Rotational/Vibrational Excitations http://en.wikipedia.org/wiki/Infrared_spectroscopy

11. Lecture 32Rotational/Vibrational Excitations • FTIR spectra of tissue from Normal and Tumor cells in human lungs

12. Lecture 32Ammonia Maser Energy difference between the symmetric and antisymmetric combinations of the two states on the left (nitrogen atom on left or right of the 3 H atoms) are separated in energy by 24 GHz (about 10 meV)., the quadrupole “focusser” was set to focus beam molecules in the state of higher energy into the cavity and defocus the beam for the lower energy state, which produced a population inversion inside the cavity. http://ticc.mines.edu/csm/wiki/index.php/The_ammonia_Maser From original paper Gordon ,Zeiger and Townes, Phys Rev. p282 (1954)

13. Lecture 32Stimulated emission http://en.wikipedia.org/wiki/Stimulated_emission

14. Lecture 32“Forbidden Transitions” Transitions we have called “forbidden” (i.e. disobey a selection rule) really are simply less likely to occur than the ones that follow the selection rules. This can lead to “metastable states” that last a reasonably long period of time. Having such states allows one to create a “population inversion” (where the excited state is more populated than the lower energy state).

15. Lecture 32“4-level system for lasers” In this scheme you avoid the process where by the coherent photons get absorbed by a transition from the ground state back up to the metastable state.

16. Lecture 32“He-Ne laser energy scheme” In this scheme you excite the Helium atoms directly, and then use those atoms to excite Neon atoms that perform the lasing. Fig. on the right is from: http://www1.union.edu/newmanj/lasers/LaserTypes/HeNeTransitions.gif Note that the excited He states are not populated directly but they are metastable (why?).

17. Lecture 32Laser http://en.wikipedia.org/wiki/Laser

18. Lecture 33“X-ray sources through the ages” From a talk on inverse Compton x-ray sources by David Moncton, founding director of the Advanced Photon Source (shown below)

19. Lecture 33“Free Electron Lasers” Strictly speaking, these devices use “undulator” magnets rather than “wigglers” (the difference is only technical and has to do with the ratio of the electron’s cyclotron frequency (eB/m) to the frequency c/lu (where lu is the undulator’s spatial period). If this ratio is small, you get coherent effects.

20. Building a more complex molecule C2 Isolated impurities From E. A. Moore: “Molecular Modelling and bonding”, Royal Soc. Chem.

21. Lecture 33“Benzene” Energy levels coming from a single atomic orbital (remember each carbon would have 4 such orbitals, ignoring spin) organic.wsu.edu/files/348/Lectures/Lecture%2022.pp Seee also : http://www.chemtube3d.com/orbitalsbenzene.htm

22. E 1/R Building a Semiconductor Fill up the states with electrons just like you fill up atomic or molecular states, fill from the lower energy up being careful to abide by Pauli. The material properties are dominated at by the highest energy states that are occupied. Isolated atoms Condensed Phase Conduction Band Available States No States available Valence Band Conduction band Localized states near impurities; These control the properties of the semiconductor Isolated impurities Valence band

23. Building a solid Graphite/Diamond Isolated impurities From W. A. Harrison: “Electron Structure” Freeman.

24. Band structure and Impurties in Si and Ge From S. SM .Sze “Physics of Semiconductor devices”, Wiley (1969))