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Lecture

# de Broglie wavelength, Heisenburg uncertainty principle, quantum mechanics, quantum numbers, s/p/d orbitals

5 Pages
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Department
Chemistry
Course Code
CHEM 111
Professor
Dana Johnson

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Description
15 September Announcements Exam tonight (7 – 9 pm) Double check Clark room Only pencil, calculator (TI-30Xa only) and ID No hats and no bathroom breaks Cell phones must be off Reflection exercise Recitation grade about your study skills Accessible through RamCT Can access 9 pm tonight through 6 pm Friday You have 2 hours to finish Grades posted after de Broglie wavelength All matter shows wave properties de Broglie wavelength is calculated using the following: λ = h / mν λ = wavelength h = Planck’s constant m = mass of the object (in kg) u = speed of the object (in m/s) Planck’s constant in different units J = kg * m / s 2 So, h = J * s = kg * m / s Clicker question Can you see the de Broglie wavelength of a football when you throw it? No Heisenberg uncertainty principle Macroscopic particle / wave distinction easy Moving particle has definite location Predictable motion Microscopic: difficult to distinguish properties Moving particle spread out like a wave Becomes impossible to know both speed and location Uncertainty principle results: Δx*mΔu ≥ h / 4π Δx = uncertainty in position Δu = uncertainty in speed m = mass (in kg) h = Planck’s constant (in kg*m / s) Example with uncertainty How accurately can an umpire know the position of a baseball (m = 0.142 kg) moving at 100.0 mi/h ± 1.00% (44.7 m/s ± 1.00%)? Δx*mΔu ≥ h / 4π → Δx ≥ h / mΔu4π Δu = 44.7*0.0100 = 0.447 m/s Δx ≥ 6.626 x 10 -3kg*m /s / 0.142 kg * 0.447 m/s * 4π ≥ 8.31 x 10 -3m Small number → low uncertainty Quantum mechanics Relatively new field: developed out of the particle – wave duality and Heisenberg’s uncertainty principle Makes statements about wave – like objects at the atomic level whose positions are impossible to know exactly Shrödinger’s equation describes the position of the electron in 3 – dimensions: HΨ = EΨ H = Hamiltonian operator E = Energy of the atom Ψ = Wave function, description of the electron Each solution is a different “orbital”: each is a different energy state, completely different than the Bohr “orbit” 2 Ψ vs. Ψ Ψ Wave function Mathem
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