1153_Physics ProblemsTechnical Physics

1153_Physics ProblemsTechnical Physics - 494 Quantum...

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494 Quantum Mechanics (b) When the electron falls from state 2 to state 1, it puts out energy Eh f hc =− == = 151 37 7 113 eV eV eV . λ into emitting a photon of wavelength ×⋅× × = hc E 6 626 10 10 113 1 60 10 11 0 34 8 19 . . . J s 3.00 m s eV J eV nm ej e j af . The wavelengths of the other spectral lines we find similarly: Transition 4 3 42 41 32 31 21 E eV 264 452 565 188 302 113 nm 4.71 2.75 2.20 6.60 4.12 11.0 P41.6 = 2 D for the lowest energy state K p m h m h mD p hh D = = ×⋅ ×× = == = × −− 2 2 2 2 2 34 2 27 14 2 14 34 14 20 2 28 6626 10 8 4 1 66 10 1 00 10 827 10 0517 2 331 10 . .. . . Js kg m J M e V .00 10 m kg m s e j P41.7 E hc h mL h ee F H G I K J −= 2 2 22 2 2 8 3 8 L h mc e × = 3 8 793 10 0793 10 m n m P41.8 E hc h h F H G I K J 2 2 2 2 8 3 8 so L h e = 3 8 P41.9 The confined proton can be described in the same way as a standing wave on a string. At level 1, the node-to-node distance of the standing
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