Chem111 Fall, 2005 23Wave- particle Duality••particles: specific location, velocity, mass; countable, distinct ••waves: delocalized; interference effects Æ2 particles cannot occupy the same space, but 2 waves can! So … when do light and matter act like particles and when do they act like waves? Light: depends on how we measure • λα1/νand E= hνÆhigh frequency (energy) radiation Æparticles low frequency (energy) radiation Æwaves •Atomic dimensions (0.5 to 2 Å= 0.5 to 2 x 10-19m ) λ> 10 Å Æwave behavior (radiowaves, IR, visible, ultraviolet) λ< 10 Å Æparticle behavior (gamma rays) Matter: de Broglie λ= h/p matter is composed of "wavicles" •λfor macroscopic objects is verysmall (< 10-30m) →definitely particle •on an atomic scale we see different behavior: •e- at 300 K (v~0.04% c)61Å Æwave behavior •e- at 3 x 105m/s (v~0.1% c)24 Å •e- at 3 x 107m/s (v~10% c)0.24 Å •He nucleus at 300K (v~0.04% c)0.72 Å Æparticle behavior Lecture 11: •Introduction to QM (continued) •The Schrödinger Equation •The Hydrogen Atom diffraction pattern (wavelike) no diffraction pattern (particle like)
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Chem111 Fall, 2005 24Heisenberg Uncertainty Principle •wave- particle duality places limitations on what can be measured (and the precision of the measurement ) problem of probabilities •another way to think about this … when the measurement process is on the same scale as the effect being measured, the effect is perturbed by the measurement ( i.e. don't know what the system is doing afterwards) consider a slit diffraction experiment: Δx = uncertainty in the knowledge of the position of the particle in x. Δpx= uncertainty in our knowledge of the velocity (momentum) of the particle in the x-direction before the screen after the screen Δx = infinity (we have no idea where the particle is in x) Δx = w Δpx= 0 (we know it's traveling in the y-direction) Δpx= 2h/w (geometry, interference conditions, de Broglie) microscopic particle travels in the y direction (vx= 0) we want to know its x position Æmeasure x by passing the particle through a slit x y w classical result = all particles with x value within w appear on the screen here quantum mechanical result = interference pattern (wave!) •what is the position? •clearly some particles have traveled in the x direction! (vx≠0 any more) we have learned something about x but at the expense of knowledge of px