- Principles of Chemistry I: Honors
Fall 2017, Unique 50135
Lecture Summary, 28 September 2017
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
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.