Quiz-4 - Quiz#4 Particle/Wave Duality Complete both of the...

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Unformatted text preview: Quiz #4: Particle/Wave Duality February 27, 2008 Complete both of the following problems. Show all of your work for full credit. Name: SOLUTIONS Problem 1: A beam of protons travels at velocity of 30 m/s and impinges on two narrow slits separated by 200 nm. Find the angle between the center line and 5th minimum of the resulting interference pattern. 1 where d - distance between slits, n = 5 for 5th minimum and n - = d sin , 2 h h hc 1240 eV nm = = = = = 13.2 nm 2 p mv ( mc ) ( v / c ) (938 106 eV)(30/(3 108 )) = sin -1 (n - 1/ 2) -1 4.5 13.2 nm = sin = 17.3 d 200 nm Problem 2: Photons with energy 40 eV impinge on a 100 nm-wide slit. Find the angle between the center line and 2nd minimum of the resulting diffraction pattern for the photons. n = a sin , where n = 2, a = 100 nm, and = hc 1240 eV nm = = 31 nm E 40 eV n -1 2 31 nm = 38.3 = sin a 100 nm = sin -1 ...
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