Problem_Set_5

# Problem_Set_5 - (3(b Show that the form of Morse potential...

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CHEM 370 P ROBLEM S ET 5 S PRING 2008 P ROBLEMS FROM M C Q UARRIE AND S IMON From Chapter 13/Molecular Spectroscopy Problem 13.4 (p. 537) Hint: Use Eq. (5.46) on page 175 with L J r to find the revolutions/sec 2 = ϖ π . Problem 13.12(p. 537) Compute e B and e ϖ % in 1 cm - . Then draw to scale the energy level diagram. Finally compute the wavenumbers ν for the first three R and P branch lines. Problem 13.15(p. 537) Problem 13.25(p. 538) Problem 13.33(p. 542) Additional Problem 1. The Morse potential is a model potential energy function for diatomic molecules of the form ( 29 ( 29 ( 29 { } M U r A exp 2a r - b 2exp a r - b = - - - (1) where the Morse parameters a, A , and b are chosen to fit ( 29 M U r to the diatomic molecule’s actual potential ( 29 U r . The most common way of making this fit is to require that ( 29 M U r satisfy the following three conditions: ( 29 ( 29 ( 29 ' ' 2 M e e M e M e U r D ,U r 0, and U r = - = = μϖ . (2) (a) Show that the three conditions imply the following relations between A, a, and b and the measurable properties of the diatomic e e D ,r , and ϖ : 1 2 2 e e e A D ,a , and b r 2D μϖ = = = .

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Unformatted text preview: (3) (b) Show that the form of Morse potential given in equation (1) is equivalent to that given at the bottom of page 164 of McQuarrie and Simon. 2. For the 1 81 H Br isotope of the HBr molecule, spectroscopic measurements give 1 e D 362.7kJ mol ,r 141.44pm-=-= , and 1 e 2 c 2648.98cm-ϖ = ϖ π = % . (a) From this data compute the values of the Morse parameters, A, a, and b for HBr (see problem 2). Given your result for A in 1 kJ mol--. (b) Using these values, plot ( 29 M U r for HBr. Use 1 kJ mol--as your energy unit. (c) One the same graph plot the harmonic oscillator potential for HBr. ( 29 ( 29 2 2 1 2 H0 e e e U r D r r = -+ μϖ-, and compare with ( 29 M U r . (d) Compute e e e D ,D ,r , and ϖ % for the 2 79 H Br isotope of HBr. Give your results for D and e D in 1 kJ mol--. (In this problem assume e D D 1 2 =-ϖ h for all isotopes of HBr.) 2 Due Monday March 24, 2008...
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## This note was uploaded on 06/27/2008 for the course CHEM 370 taught by Professor Oldsleepyman during the Fall '08 term at Purdue.

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Problem_Set_5 - (3(b Show that the form of Morse potential...

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