Chem Lec 20100915

Chem Lec 20100915 - 8.5 Two New Ideas 8.5 Two New Ideas 8-5 Two ideas leading to a new quantum mechanics Louis de Broglie Werner Heisenberg 8.5 Two

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Unformatted text preview: 8.5 Two New Ideas 8.5 Two New Ideas 8-5 Two ideas leading to a new quantum mechanics Louis de Broglie Werner Heisenberg 8.5 Two New Ideas 8.5 Two New Ideas What about matter? Louis de Broglie (1892–1989) French Central idea: Einstein’s relativity E=mc 2 Matter & energy are related Louis de Broglie Louis de Broglie 8.5 Two New Ideas 8.5 Two New Ideas de Broglie started with Einstein’s eqn. Then he used Planck’s relationship 2 mc E = h ν E = h ν mc 2 = c h ν mc p = = Recall linear momentum: p = mu 8.5 Two New Ideas 8.5 Two New Ideas Next he used the eqn. c = λν c h ν mc p = = λν h ν mc p = = 8.5 Two New Ideas 8.5 Two New Ideas de Broglie arrived at the following eqn. mc h λ λ h mc p = = = or This is valid for light… What about matter? Note : Photons have zero “rest” mass but will have a relativistic mass and momentum 8.5 Two New Ideas 8.5 Two New Ideas de Broglie equation predicts that matter should have waves mu h λ λ h mu p = = = or de Broglie’s equation Einstein helped him get his Ph.D. thesis accepted! 8.5 Two New Ideas 8.5 Two New Ideas What is the wavelength of an e- traveling at 1.00 x 10 7 m . s-1 mu h λ = pm 72.7 m 7.27x10 s m 1.00x10 kg 9.109x10 s J 6.626x10 λ 11- 1- 7 31--34 or = ⋅ = [Note : 1.0 J = 1.0 kg . m 2. s-2 ] 8.5 Two New Ideas 8.5 Two New Ideas What is the wavelength of a baseball traveling at 44 m/s (mass = 0.145 kg) mu h λ = 8.5 Two New Ideas 8.5 Two New Ideas What is the wavelength of a baseball traveling at 44 m/s (mass = 0.145 kg) mu h λ = m 1.04x10 s m . 4 4 kg 0.145 s J 6.626x10 λ 34- 1--34 = ⋅ = [Note : 1.0 J = 1.0 kg . m 2. s-2 ] 8.5 Two New Ideas 8.5 Two New Ideas The Uncertainty Principle 4 π h p x ≥ Δ ⋅ Δ Uncertainty in position Uncertainty in momentum h = Planck’s constant Uncertainties are standard deviations 8.5 Two New Ideas 8.5 Two New Ideas The Uncertainty Principle: Implications 4 π h p x ≥ Δ ⋅ Δ Limits to what we can know Causality replaced with indeterminacy Einstein was deeply bothered by this as was Wien!!!! 8.5 Two New Ideas 8.5 Two New Ideas Heisenberg’s γ-Ray Microscope Thought experiment: Gedanken Microscope resolution is limited by λ of light Amoeba 8.5 Two New Ideas 8.5 Two New Ideas Heisenberg’s γ-Ray Microscope Thought experiment: Gedanken To measure position of an electron…Need very short wavelength light, i.e., γ-rays- Electron position? 8.5 Two New Ideas 8.5 Two New Ideas Heisenberg’s γ-Ray Microscope Thought experiment: Gedanken γ-ray ν = 10 22 s-1 E γ = h ν = 6.626 x 10-34 J s . 10 22 s-1 E γ = 6.626 x 10-12 J- Electron position? 8.5 Two New Ideas 8.5 Two New Ideas Heisenberg’s γ-Ray Microscope Thought experiment: Gedanken But…easily ionize the e- E IE = 2.179 x 10-18 J E γ = 6.626 x 10-12 J- Electron position?...
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This note was uploaded on 09/29/2010 for the course SCIENCE 120 taught by Professor Frenser during the Spring '10 term at McGill.

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Chem Lec 20100915 - 8.5 Two New Ideas 8.5 Two New Ideas 8-5 Two ideas leading to a new quantum mechanics Louis de Broglie Werner Heisenberg 8.5 Two

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