- Principles of Chemistry I: Honors
Fall 2013, Unique 52195
Lecture Summary, 1 October 2013
The electromagnetic spectrum can be resolved
into components of vastly different frequency and
wavelength. Although the visible spectrum covers only
a tiny fraction of the electromagnetic spectrum(about 2.5
eV), because our eyes are sensitive to only this spectrum,
we spend a lot of time thinking about how matter interacts
with lightat these wavelengths. By discharing an
electrode into a pure gas, collisions between the free
electrons and the molecules of gas will provide energy to
move electrons in the gas to higher energy levels.
When that electron falls back (or "relaxes") to its
lowest energy(or "ground") state, it will emit energy in the
form of light. We looked at a few examples of noble
metel gasses that emit light in the visible region of the
spectrum, and saw that sometimes the gas will emit several
different wavelengths of light. You can perform
thisexperiment on your own using a PhET Java applet:
By the end of the 19th century, these spectra lines had been measured for many atoms, and it was known empirically that the energy (i.e. frequency) of light emitted in these experiments was quantized.
de Broglie Waves: We have already seen that light behaves as both a particle and a wave. de Broglie postulated that matter can behave both as a particle (familiar from classical physics) and a wave - in particular a standing wave. If the electron in an atom is behaving as a standing wave, then its wavelength is quantized to integral values of2(pi)r, and its energy is therefore quantized automatically. de Broglie derived an equation to describe the wavelength of this standing wave: it is Planck's constant divided by the momentum of the particle. We can in theory calculate a wavelength for any particle,including macroscopic particles like baseballs, but these wavelengths become vanishingsly small at large particle mass and low particle velocity.
Heisenberg Uncertainty Principle: Describing an electron in an atom as a standing de Broglie wave raised a surprising problem. Because it is a de Broglie wave, we can calculate its momentum to arbitrary precision (through the de Broglie equation). However, we know nothing about its position, because it can be at any amplitude allowed by the standing wave. Another way of saying this is that we have infinitely high uncertainty in its position. This uncertainty has nothing to do with experimental limitations of the measurement - it is much more profound than that. This uncertainty comes from the position being unknowable in and of itself.
Heisenberg formulated an expression for this, in which the product of the uncertainty of two linked parameters (momentum x length, energy x time), is always greater than or equal to Planck's constant over 2(pi). Thus, we can increase our knowledge of one parameter of our system to essentially arbitrary accuracy, but only by giving up knowledge about another parameter. One way that we deal with this is by substituting our exact answers with probabilities. We have to choose how accurately we must know a certain parameter, and then what knowledge we are going to have to give up to get there.
Schrodinger Equation: We began talking about the Schrodinger equation today, but I am going to put off summarizing that discussion until after our next class.