lecture-11 - Chem111 Fall, 2005 Lecture 11: Introduction to...

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Chem111 Fall, 2005 23 Wave- particle Duality •• particles : specific location, velocity, mass; countable, distinct •• waves : delocalized; interference effects Æ 2 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 λ α 1/ ν and E= h ν Æ high frequency (energy) radiation Æ particles low frequency (energy) radiation Æ waves Atomic dimensions (0.5 to 2 Å= 0.5 to 2 x 10 -19 m ) λ > 10 Å Æ wave behavior (radiowaves, IR, visible, ultraviolet) λ < 10 Å Æ particle behavior (gamma rays) Matter : de Broglie λ = h/p matter is composed of "wavicles" λ for macroscopic objects is very small (< 10 -30 m) definitely particle on an atomic scale we see different behavior: e- at 300 K (v~0.04% c) 61Å Æ wave behavior e- at 3 x 10 5 m/s (v~0.1% c) 24 Å e- at 3 x 10 7 m/s (v~10% c) 0.24 Å He nucleus at 300K (v~0.04% c) 0.72 Å particle 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 24 Heisenberg 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: Δ x = uncertainty in the knowledge of the position of the particle in x. Δ p x = uncertainty in our knowledge of the velocity (momentum) of the particle in the x-direction before the screen after the screen Δ x = infinity (we have no idea where the particle is in x) Δ x = w Δ p x = 0 (we know it's traveling in the y-direction) Δ p x = 2h/w (geometry, interference conditions, de Broglie) microscopic particle travels in the y direction (v x = 0) we want to know its x position Æ measure 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! (v 0 any more) we have learned something about x but at the expense of knowledge of p
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Chem111 Fall, 2005 25 Æ It appears that we can never know both the position (x) and momentum (p x or velocity v x ) with exact precision consider … the product Δ x Δ p x Δ x Δ p = before screen Δ x Δ p = 2h after screen in Q.M. there is no situation where Δ x = Δ p = 0 ! certain pairs
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lecture-11 - Chem111 Fall, 2005 Lecture 11: Introduction to...

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