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class25 - Announcements Reading for Friday 6.5 6.7 No...

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Announcements • Reading for Friday: 6.5 – 6.7 • No written HW due this Friday Today’s class: Electron interference! Last Friday we found that if the electron were a little wave going around the nucleus its angular momentum ‘L’ would be quantized: L = n ħ 1 2 3 4 5 6 7 8 9 10 Case shown for n = 10 Can we just repeat light double slit experiment with electrons? A. Yes. (If so, what experimental results would If electrons really are waves, we should be able to see interference! Q1 you expect?) B. No. (If so, why not?) Interference Peaks align: ‘Constructive interference’ Interference Peaks don’t align: ‘Destructive interference’ Double-slit experiment Determining the space between bright regions (H) 0.5 mm =D r 1 r 2 θ H L bright bright r = r 2 -r 1 Screen far away so θ 1 ~ θ 2 ~ θ & small angle approx. sin θ θ r = D·sin( θ ) D θ = m λ θ 1 θ D θ 2 H = L·sin( θ ) L θ H=mL λ D bright r = m λ (where m=1,2,3…)

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Double-slit experiment Determining the space between bright regions (H) 5 x10 -4 m = D r 1 r 2 r = r 2 -r 1 θ H L r = m λ (where m=1,2,3…) r=m λ = Dsin( θ )= D θ =m λ H= L θ m = 1, λ = 500 nm, so angle to first bright portion: θ = λ /D = 500 x 10 -9 /(5 x 10 -4 ) = 0.001 rad if L = 3m, then H= 3 m x 0.001 = 3mm. Calculating pattern for light So what will pattern look like with electrons? How figure out? 2. plug into θ = λ /D = (hc/pc)(1/D), calculate angle (radians) Steps to predict pattern for debroglie electron wave.
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