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Unformatted text preview: 24.1. Model: Balmers formula predicts a series of spectral lines in the hydrogen spectrum. Solve: Substituting into the formula for the Balmer series, = 91.18 nm 1 2 1 2 2 n = = 91.18 nm 410.3 nm 1 2 1 6 2 2 where n = 3, 4, 5, 6, and where we have used n = 6. Likewise for n = 8 and n = 10, = 389.0 nm and = 379.9 nm. 24.2. Model: Balmers formula predicts a series of spectral lines in the hydrogen spectrum. Solve: Balmers formula is = 91.18 nm 1 2 1 2 2 n n = 3, 4, 5, 6, As , Thus, 91.18 nm 364.7 nm n n n = ( ) = 1 4 2 . . 24.3. Model: Balmers formula predicts a series of spectral lines in the hydrogen spectrum. Solve: Using Balmers formula, = = = = 389.0 nm 91.18 nm 1 2 1 1 4 1 0 2344 8 2 2 2 n n n . 24.4. Model: The angles of incidence for which diffraction from parallel planes occurs satisfy the Bragg condition. Solve: The Bragg condition is 2 d m m cos = , where m = 1, 2, 3, For first and second order diffraction, 2 1 1 d cos = ( ) 2 2 2 d cos = ( ) Dividing these two equations, cos cos cos cos cos cos . 2 1 2 1 1 1 2 2 2 6 8 4 1 5 = = ( ) = ( ) = 24.5. Model: The angles of incidence for which diffraction from parallel planes occurs satisfy the Bragg condition. Solve: The Bragg condition is 2 d m m cos = . For m = 1 and for two different wavelengths, 2 1 1 1 d cos = ( ) 2 1 1 1 d cos = ( ) Dividing these two equations, cos cos cos cos cos . . = = = ( ) = 1 1 1 1 1 1 1 54 0 4408 63 8 0.15 nm 0.20 nm 24.6. Model: The angles corresponding to the various orders of diffraction satisfy the Bragg condition. Solve: The Bragg condition for m = 1 and m = 2 gives 2 1 2 2 1 2 d d cos cos = ( ) = ( ) Dividing these two equations, cos cos cos cos cos . 1 2 1 1 2 45 2 45 2 69 3 = = = = 24.7. Model: The angles corresponding to the various diffraction orders satisfy the Bragg condition. Solve: The Bragg condition is 2 d m m cos = , where m = 1, 2, 3, The maximum possible value of m is the number of possible diffraction orders. The maximum value of cos m is 1. Thus, 2 2 2 4 2 d m m d = = = ( ) ( ) = 0.180 nm 0.085 nm . We can observe up to the fourth diffraction order. 24.8. Model: Use the photon model of light. Solve: The energy of the photon is E h f h c photon Js m / s m J = = = ( ) = 6 63 10 3 0 10 500 10 3 98 10 34 8 9 19 . . . Assess: The energy of a single photon in the visible light region is extremely small. 24.9. Model: Use the photon model of light....
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 Spring '08
 Medvedev

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