The last lecture

In which we say good-bye...and consider how a laser "amplifies" light.

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The truly dedicated student can build a laser by following the directions at Sam's Laser site. Lasers can be built from a number of different materials, including Jello.

Fiat Lux! Population inversion is the key to successful lasing

Population inversion is a key feature of a system which be used to construct a laser. A system in thermal equilibrium follows Boltzmann's statistics, in which the number of molecules in higher energy states is smaller than the number in the lowest energy state. Lasers require that you have a non-equilibrium situation established, in which more molecules are "stuck" in an excited state than are currently in a lower energy state. This phenomenon is called population inversion. A second feature of lasers is that the emission process(the release of a photon when a molecule or atom relaxes from an excited state to a lower energy state) can be stimulated, or enhanced by the emissions from other molecules. This is where the "se" in the name comes from! (LASER = Light Amplification by Stimulated Emission of Radiation).



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Lumos! The Quantum Mechanics of Harry Potter

We wrap up NMR and begin to consider the quantum mechanics behind lasers. Lasers are magic wands for chemists, making it possible to explore what happens in chemical processes on very short time scales. Lasers are ubiquitous tools in everyday life, too. Grocery store scanners and CD players use lasers to read information, an when you "burn" a CD, a laser is used to literally score the material.

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A Pocket NMR?

Could you build an NMR that could fit in your pocket? The effect of magnetic field on the splitting between nuclear spin states. What would happen if you walked through a very strong magnetic field? Say a million Tesla field? Are there such fields? We propose building a pocket-sized NMR from a cow magnet. It could be done, if you're not interested in very high resolution.

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A list of very strong magnetic fields, the strongest are found in rare stars.

Magnetic Personalities: NMR

The quantum mechanics of nuclear spins. How a magnetic field splits degenerate spin states of at nuclei, setting the stage for NMR.

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What's a cow magnet?
Accidents with MRIs

Degrees of Freedom

The vibrational spectra of most molecules is very complex. We considered how additional lines arise in diatomic spectra including isotopic substitution and "hot bands". There are many more vibrational modes available to polyatomic molecules. How many? 3N-6!

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Check out the vibrational modes of CO₂ at Purdue's site. You need CHIME for this.
Animations of infrared vibrational modes.
and more animations

A Matter of Moment

The rotational spectra of polyatomic molecules depend on the moments on inertia about the principal axes. We considered 4 cases: linear molecules, spherical tops, oblate symmetric tops and prolate symmetric tops.

We backtracked to vibration spectroscopy to discuss the Franck-Condon principle, or the principle of vertical excitation. It adds a third rule to our list: What goes up must come down; You can't always get there from here; When you go up, go straight up!

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Answers to the exercise to determine the type of molecular "top".

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Out of Tune: The Effects of Anharmonicity and Centrifigual Distortion on Rotational/Vibrational Spectra

We noted in our demonstration on Friday that rotation affected vibration. We quantified this, including a term in the energy to account for centrifugal distortion. The effect is small, but noticeable, as we saw with HCl. We consider the appearance of overtones in the vibrational spectrum, and the shifts in equilibrium bond length that occur as a result of the anharmonicity of the vibrational potential.

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Shake, Rattle and Roll: Simultaneous Excitation of Vibrational and Rotational States

Why are there all those lines in the HCl spectrum? Why is there no line at the fundamental frequency? We consider the interplay of rotation and vibration and their respective selection rules to see why.

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Pure Vibrational Spectroscopy

Using the harmonic oscillator to model vibrational energy transitions can be done, but has its limits. Consider the observed high resolution spectrum of gaseous HCl.



[Figure from hyperphysics.phy-astr.gsu.edu.]

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