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 7:30Performance Friday 8:00 Buskirk-Chumley

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.

Lecture 31Molecules and bonding

•Why do atoms combine together to form molecules, and what forces/conceptscontrol the way this happens?

•How do molecules behave?•Below we show a couple of model formulae used to describe molecular binding.

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?

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?

x~ 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 x 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!]

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

Lecture 31UV-Visible spectroscopy

http://www.sci.sdsu.edu/TFrey/Bio750/UV-VisSpectroscopy.html

Lecture 31Rotational/Vibrational Excitations

Evib = (n+1/2) hbar Erot = l(l+1) hbar2/2I

l=+/-1

Absorption of light by HCl in the region from nvib=0 to nvib=1.

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 to . 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.

Lecture 31Rotational/Vibrational Excitations

http://en.wikipedia.org/wiki/Infrared_spectroscopy

Lecture 32Rotational/Vibrational Excitations

•FTIR spectra of tissue from Normal and Tumor cells in human lungs

Lecture 32Ammonia Maser

http://ticc.mines.edu/csm/wiki/index.php/The_ammonia_Maser

From original paper Gordon ,Zeiger and Townes, Phys Rev. p282 (1954)

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 eV)., 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.

Lecture 32Stimulated emission

http://en.wikipedia.org/wiki/Stimulated_emission

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).

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.

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.gifNote that the excited He states are not populated directly but they are metastable (why?).

Lecture 32Laser

http://en.wikipedia.org/wiki/Laser

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)

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.

Building a more complex moleculeC2

Isolated impurities

From E. A. Moore: “Molecular Modelling and bonding”, Royal Soc. Chem.

Seee also : http://www.chemtube3d.com/orbitalsbenzene.htm

Lecture 33“Benzene”

organic.wsu.edu/files/348/Lectures/Lecture%2022.pp

Energy levels coming from a single atomic orbital (remember each carbon would have 4 such orbitals, ignoring spin)

Isolatedatoms

CondensedPhase

ConductionBand

ValenceBand

AvailableStates

No Statesavailable

1/R

E

Building a Semiconductor

Valence band

Conduction band

Isolated impurities

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.

Localized states near impurities; These control the properties of the semiconductor

Building a solid Graphite/Diamond

Isolated impurities

From W. A. Harrison: “Electron Structure” Freeman.

Band structure and Impurties in Si and Ge

From S. SM .Sze “Physics of Semiconductor devices”, Wiley (1969))