Lecture Notes from CHM 1341
28 June 1996

Light and Matter

In the 19th Century, Maxwell concluded that light was a wave of self-propagating electric and magnetic waves. But long prior to that, light's vulnerability to refraction (bending) by optics made it's description as a wave pretty obvious. Take, for example, the diagram at right (from U.C.S.D.) which demonstrates the principle which underlies X-ray spectroscopy.

Crystal structures have very regular, repeating molecular patterns, and light of wavelengths comparable to those pattern unit sizes will be diffracted by them. The picture shows how the crests and troughs of light's (electromagnetic - EM) oscillations interfere with themselves as they scatter from a pattern; in this case, the "pattern" is 2 slits in an otherwise opaque wall. Where crest meets crest, the interference is constructive, and the light's double bright. Where crest meets trough, it is destructive, and the light vanishes!

An actual double slit experimental result is shown at left. Note the alternating bright and dark spots (of ruby red laser light) where constructive and destructive interference of the wave with a diffracted version of itself.

Of course, to be useful as a tool to probe crystal structures, the wavelength of the light must be known, since different wavelengths will respond to the same patterns to different degrees. Fortunately, both the wavelength (the distance between adjacent EM crests) and the oscillation period as the light wave passes any reference point are trivially related. If the Wavelength is L and the Time period is T, then the speed of light, c, is just c=L/T, as would be any speed...distance travelled per time travelled.

However for reasons which will soon become apparent, chemists focus not on the (tiny fraction of) seconds in a light oscillation period but rather it's inverse: the (vast) number of oscillations (or cycles) per second, that is, the frequency. We're going to call that "v" the Greek "nu" which is traditionally used for frequency. (There's no web version of the Greek lambda normally representing wavelength.) Since v=1/T (cycles-per-second is the inverse of seconds-per-cycle), the relation of light's frequency and wavelength too is simple: c=vL.

Visible light has wavelengths in a very narrow EM range, L=575 ± 175 nm. Not surprisingly, this is because by the time sunlight filters through the atmosphere most of it is in this range; so as visually-oriented animals, we've evolved to make the most of it.

Newton demonstrated these wavelengths by separating them from sunlight with a glass prism; I've done that at right with a thousand little water "prisms" from UTD's fountain. One can put even more "prisms" than that on a diffraction grating by scoring it with parallel steps, about 13,600 to the inch (or 1870 nm apart, a couple of visible wavelengths apart...check out that "double slit" picture at top again and notice the nice disturbance rendered when the slit separation is a couple of wavelengths). That kind of grating is in the handheld spectrometer we used today.

But this wavelength range is as nought compared to those possible for EM radiation...all the way from 5 Mm of 60 cycle AC to the picometers of cosmic radiation and beyond indefinitely in both directions! Chemists become quite conversant with several milestones on this continuum:

WAVELENGTHS   CHEMICAL UTILITY

 nanometers   molecular dimensioned X-rays for crystal spectroscopy

 100 nm       ultraviolet for electronic energy changes

micrometers   infrared for molecular vibration changes

millimeters   microwaves for molecular rotation changes

centimeters   for nuclear spin changes (and Magnetic Resonant Imaging too)

With all this attention paid to wavelength, I should hastily point out that frequency (v=c/L) is critically important too as a result of an astonishing discovery by Planck. In trying to make sense of the equilibrium energy exchange of light and matter, he was obliged to conclude that light acted on matter as if it were bundles of energy of value exactly hv, where v is light's frequency and h is Planck's constant,

h = 6.626x10-34 J s

But "chunks" of light sound like it's not a wave but rather a particle, and that conclusion was reinforced by photoelectric experiments of using ultraviolet (UV) light to eject electrons from alkali metals (in a vacuum). Were light a wave, one might expect increasing its intensity (amplitude) to encourage electron ejection, but above a critical wavelength (i.e., below a critical energy), that doesn't happen no matter what the intensity. Instead one needs photons (light particles) with individual energies at (or in excess of) the ionization energy (called Work Function, W) of the metal to see any electron ejection at all. Intensity only determines how many electrons eject not if they do so.

This is because intensity simply measures the number of photons incident per unit time...it's a flux...whereas frequency, v, determines the energy of each photon as E=hv. If v is so high that it exceeds the metal's work function, W, the excess energy goes directly into kinetic energy in the electron; it flies off faster. Since we know the electronic mass, the relationship between input and output energies in a photoelectric expermiment is simple:

(Input) hv = W + ½ m_ev² (Output)

But electrons don't have to abandon their atom to absorb light. Instead they can become more energetic within the atom. Indeed that change can be reversed; energetic electrons in an atom may reduce their energy by emitting a photon of light, and that photon's frequency will tell us immediately just how much energy the electron lost. These are the bases of spectroscopy. We see emissions with we jostle atoms as in a flame or a star! We see absorptions by the simple fact that objects are colored; their molecules have selected some light frequencies and not others not to reflect...absorbing them and causing internal energy changes instead.

In either case, however, what frequencies electrons (or intramolecular motions) choose to absorb or emit give rise to an astounding conclusion. In many cases, only particular wavelengths are involved suggesting that electrons (for example) cannot have arbitrary energies but only particular energy levels separated by the energies (of photons) associated with those unique wavelengths! So atomic spectra (there only electrons can be excited) are line spectra! Thus the very structure of an atom denies its electrons arbitrary energies and instead enforces a strict heirarchical energy scheme.

These discrete energy levels are measured even more simply than in the photoelectric experiment because the electrons have no free flight kinetic energy since they've not escaped the atom. So the "input/output" accounting we did before is simpler now:

(Input) hv = E_upper - E_lower (Output)

where that energy difference is that between the electron's state before and after absorbing the photon. Note that both here and in the photoelectric effect, it's not possible to absorb part of a photon and decline the rest...it comes as lump, like it or lump it.

When this strategy was turned to the emissions (reverse input and output above) of the hydrogen atom, a startling simplicity was discovered for those electronic energy levels. They were all perfectly described by

E_n = - 2.18 n^-2 aJ (where an attoJoule is 10^-18 J)

where n can take on any value from 1 to infinity...and at infinity, that expression rises from negative (bound energies) to zero (no electron binding) implying that the electron is free. So the work function for ejecting hydrogen's single electron from its (n=1) ground state is exactly 2.18 aJ per atom (or 1.31 MJ per mol of atoms).
So the wavelengths studied from H atom emission between states m and n, say, should be found from:

hc/L = -2.18 ( m^-2 - n^-2 ) aJ

And when m=1, transitions from any n (larger than 1, of course) yield photons with L in the ultraviolet...invisible to us. But when m=2, transitions from n=3 and above start with visible wavelengths...indeed that very red-orange line you see in the diagram. Emissions from 4 to 2 must be higher in energy than 3 to 2, so the next line is blue-green. The 5 to 2 emission is right on the edge of the visible spectrum; try to make out that weak purple line at the far right of the figure! And from 6 on up, we're back into (invisible but photographable and otherwise recordable) UV.

Any physicist (or chemist) seeing those lines knows she's looking at hydrogen. Not surprisingly, those lines are prominent in stellar spectra since stars react hydrogen in their nuclear furnaces in order to shine. But one sees many other lines in stellar spectra corresponding to other atoms. So the study of off-Earth chemistry is old hat in that sense. Until the astronomer Hubble, however, the red-shifted spectral lines from distant galaxies was inexplicable. But Hubble pointed out that since all galaxies are fleeing one another following some ancient Big Bang which appears to have created the Universe. Those red-shifts are the spectral equivalent of the Doppler shift you here when a fire engine's siren appears to lower its pitch (frequency) as it passes you. The fire engine runs from you at some small fraction of the speed of sound; distant galaxies are receding at some fraction of the speed of light instead! Thus their light frequencies lower and spectra are "red-shifted."

So not only can we do stellar chemistry from afar, we can even measure how fast a star is moving via its spectral lines! Spectroscopy has not only given us chemical analysis, it's given us our current cosmology as well!

Chris Parr
University of Texas at Dallas
Programs in Chemistry, Room BE3.506
P.O. Box 830688  M/S BE2.6 (for snailmail)
Richardson, TX  75083-0688

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