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Unformatted text preview: Chemistry 1000 Lecture 5: Hydrogenic orbitals Marc R. Roussel Heisenberg uncertainty principle Fundamental limitation to simultaneous measurements of position and momentum: Δ x Δ p x ≥ 1 2 ~ with ~ = h 2 π . I Uncertainty is, roughly, the experimental precision of the measurement. I Position and momentum can’t simultaneously both be known to arbitrary accuracy. Why not? I Suppose that we want to locate an object in a microscope. I Photons reflect (or refract) from the sample. I Photons have momentum so they give the object a “kick” (i.e. change the momentum) during interaction with an object. I Resolution Δ x ∼ λ Kick Δ p x ∼ h /λ Δ x Δ p x ∼ h > h 4 π Example: Suppose that we use Xrays to determine the position of an electron to within 10 10 m (diameter of a hydrogen atom). Since Δ x Δ p x ≥ 1 2 ~ , we have Δ p x ≥ ~ 2Δ x = 5 × 10 25 kg ms 1 , or Δ v ≥ Δ p x m e = 6 × 10 5 m / s . Important consequence: I Bohr theory has orbits of fixed r , i.e. Δ, i....
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This note was uploaded on 03/03/2012 for the course CHEM 1000 taught by Professor Marc during the Fall '06 term at Lethbridge College.
 Fall '06
 Marc
 Chemistry

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