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solns21b-ps4-Jan11

# solns21b-ps4-Jan11 - Chemistry 21b Problem set 4 Out 26...

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Chemistry 21b Problem set # 4 Out: 26 January 2011 Due: 02 February 2011 Problems are worth: 1a=15, 1b=10; 2a=10, 2b=15; 3a=10, 3b=5, 3c=5, 3d=5; 4a-e=5 points each (for 25 points total). 1. A problem about simple symmetric tops. (a.) Prove the moment of inertia formulae for a symmetric top of form A 3 B can be written as: I bardbl = 2 m A (1 - cosθ ) R 2 I = m A (1 - cosθ ) R 2 + m A m B m (1 + 2 cosθ ) R 2 where R is the A-B bond length and θ the A-B-A bond angle. (b.) Treat AsCl 3 as a rigid rotor with transitions as follows: 75 As 35 Cl 3 has its J=4 5 transition at 21,472 MHz and 75 As 37 Cl 3 has its J=5 6 transition at 24,536 MHz. Fom these data calculate the geometry of the molecule, that is, R AsCl and θ ClAsCl . 2. Consider the molecule thioformaldehyde, H 2 CS. a) Using the asymmetric rotor energy level formulae given in Lecture #10 (Table 10.1 on p. 82), calculate the first few ( J =0, 1 and 2) rotational energy levels of the molecule. The rotational constants are A= 291291.641 MHz, B=17699.628 MHz, and C= 16651.83 MHz. Draw an energy level diagram. This molecule is a near-symmetric top. Which one (oblate or prolate)? b) The total permanent dipole moment of thioformaldehyde is 1.649 Debye. What are the projections of this dipole moment along the a , b , and c inertial axes? Using these results, and the selection rules also noted in Lecture #10, indicate in the energy level diagram which transitions are electric dipole allowed. Do the transitions lie in the centimeter, millimeter, submillimeter or far–infrared part of the spectrum? 3. a) From the following wave numbers of the P and R branches of the 1–0 infrared vibrational band of 1 H 127 I in the X 1 Σ + state, obtain values for the rotational constants B 0 , B 1 and B e (in cm 1 ), the band center ˜ ν 0 (in cm 1 ), the vibration–rotation interaction constant α e (in cm 1 ). v = 0 1 Rovibrational Transitions for 1 H 127 I Transition Frequency (cm 1 ) Transition Frequency (cm 1 ) R(0) 2242.087 P(1) 2216.723 R(1) 2254.257 P(2) 2203.541 R(2) 2266.071 P(3) 2190.025 R(3) 2277.510 P(4) 2176.168 b) What value results for the internuclear distance R e (in ˚ A)? How does the value for R e compare with the value R e =1.607775 ˚ A for 2 H

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solns21b-ps4-Jan11 - Chemistry 21b Problem set 4 Out 26...

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