F2003-Final - PHYSICS 112 - EXAM 4 (first part of final...

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PHYSICS 112 - EXAM 4 (first part of final exam) - FALL 2003 Name _______________________________________ Section _________ Use only a right-handed coordinate system ( along thumb, forefinger, and Bß Cß D middle finger of your right hand when these three fingers are perpendicular to one another). Show your calculations to get full credit. Be sure to include correct units. 1. [6 points total] A two-slit system consists of two slits, each of width 3.00 m, whose . centers are separated by a distance of 12.0 m. Light of wavelength 0.600 m shines on .. the slits. (a) [2 points] Determine the numerical value of sin for the angle corresponding to the ) first diffraction minimum. (b) [2 points] Determine the numerical value of sin for the angle corresponding to the ) fourth interference maximum. (c) [2 points] What number interference maximum coincides with the second diffraction minimum? 2. [3 points] In a two-slit system the separation of the slits is three times their width. Make an approximate sketch of the light intensity pattern seen on a screen far past the slits when it is illuminated with monochromatic light. Show at least two diffraction minima on each side of the central maximum, and show which interference maxima appear to be missing.
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3. [10 points total] When white light is incident normally (perpendicularly) from air onto a thin film of oil with an index of refraction of 1.200 floating on water ( 1.33), it is found that there is constructive interference at a wavelength of 600 nm (this is the wavelength in air). (a) [2 points] Determine the phase change, if any, of the reflections at the top and bottom surfaces of the thin film. At the top: _________________________ At the bottom: ______________________ (b) [2 points] What is the wavelength of this same light in the oil film? (c) [4 points] What is the smallest possible thickness of the film (to have constructive interference for 600 nm)? - œ (d) [2 points] What is the longest wavelength (in air) of electromagnetic radiation for which there would be destructive interference for this same thickness of oil? (This is not necessarily visible light.)
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4. [4 points] Louis de Broglie in the early 20th century proposed that particles have wave properties and vice versa, and that their linear momentum and wavelength were : - related by the simple formula (where is Planck's constant). - œ2Î: 2 Use this equation to determine the formula for the linear momentum of a photon of : frequency in terms of , , and and also in terms of and . 02 - 0 I - In terms of , and : 2- 0 :œ In terms of and : I- : œ 5. [3 points] The three lowest energy levels of the hydrogen atom have energies 1.51 eV,  3.40 ev, and 13.6 eV. If a sample is prepared of hydrogen atoms in the highest of these levels, determine the energies (in eV) of all the possible photons that might be emitted as the atom decays (in any number of steps) to the lowest state.
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6. [2 points] All the energy levels of the hydrogen atom can be expressed by the formula (13.6 eV) where 1 2 3, etc. Iœ Î 8 8œßß 8 2 If a hydrogen atom in its lowest state ( 1) absorbs a photon, but the atom is not ionized (that is, the electron remains bound to the hydrogen nucleus), what is the maximum energy (in eV) the absorbed photon could have?
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F2003-Final - PHYSICS 112 - EXAM 4 (first part of final...

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