Chemistry 204 Dr. Don DeCoste 3014 Chemistry Annex decoste@illinois.edu 12-1 pm MWF (after lecture) 10-11 am Tuesdays and Thursdays By appointment; open door policy

Particles or waves? Double slit experiment (“cannot explain…just tell”). Eddington: There was a time when we wanted to be told what an electron is. The question was never answered. No familiar conceptions can be woven around the electron; it belongs to the waiting list. [1928] A Tale of Two Nobels JJ Thomson: “proving” the electron is a particle. [1906] George Thomson (JJ’s son): “proving” the electron is a wave. [1937]

Werner Heisenberg “What we observe is not nature itself but nature exposed to our method of questioning.” “The act of measuring something creates the reality we observe; no elementary phenomenon is a phenomenon until it is a measured phenomenon.” The behavior we find depends on what we look for. That is, making an observation affects in the outcome. Twenty Questions

Heisenberg’s Uncertainty Principle Also known as Heisenberg’s Indeterminacy Principle. We simply cannot know what the electron is doing in the atom. Not merely because our devices to measure are not sophisticated enough. It is a fundamental property.

Heisenberg’s Uncertainty Principle If you measure the x-component of the momentum of an object with an uncertainty of p, you cannot know its x-position more accurately than x = h/p. Written mathematically as xp = h. Conjugate variables (time and frequency: musical notes) Not a coincidence that this uncertainty is the “atom of action”.

Heisenberg’s Uncertainty Principle Atomic level Electron “trapped” in a hydrogen atom (uncertainty in position is ~10-10 m). Uncertainty in momentum is ~6 x 10-24 kgm/s. Uncertainty in velocity ~7 x 106 m/s. ~2% the speed of light. ~16,000,000 mph. The electron is moving (but we don’t know how) because it is confined.

Heisenberg’s Uncertainty Principle Macro level Imagine a 4 ounce (100 g) ball “trapped” in a 1 foot (0.3 m) 1-D box. If h = 1 Uncertainty in velocity is ~30 m/s or ~70 mph. We would be accustomed to the “oddities” of quantum mechanics. But h ~10-34. Uncertainty in velocity ~10-32 m/s. It has moved <~10-23 m in your lifetime (~20 years), much (much) smaller than the size of an atom (~10-10 m).

HUP and Quantized Energy Gas particle trapped in a 1-D box of length L. Maximum uncertainty in position is L. Must be moving (confined). E = ½mv2, p = mv, so E = p2/2m. Max Δx = L, Δp = 2p (vector) and ΔxΔp = h p = h/2L (minimum), thus E = h2/8mL2. Zero point energy! Difference in momentum = h/2L, next is 2h/2L, 3h/2L, 4h/2L, etc. Thus, E = n2h2/8mL2.

HUP and Quantized Energy Some notes. n is the energy level (the lowest n is n = 1). E is related to n2 in this model. In the atom, E is inversely related to n2. E is quantized as a result of HUP, which is a fundamental property (a “rule” – this rule dictates what is true even though we cannot derive the rule). n is a quantum number. We need more than one quantum number for a hydrogen atom (3-D “box”), as we shall see.

HUP, Pauli, and Quantized Energy What if there is more than one particle? The area of the plot has to equal h. So, p = h/2L E = h2/8mL2.