Chem 113A HW5 - Solutions - Chem 113A HW5 Solutions...

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Chem 113A HW5 Solutions Wednesday, May 4, 2016 1:09 PM New Section 1 Page 1
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7) The far-infrared spectrum of H ±²³ I consists of a series of equally spaced absorption peaks which are evenly spaced, with Δ´ µ = 12.8 cm ¶± . What is the bond length of H ±²³ I? ·´ µ = 2¸ ¹ ¸ ¹ = 6.4º» ¶± ¸ ¹ = ² º½ = ² º¾¿ ² ¿ = À ² º¾¸ ¹ = 1.63 Å 8) When discussing the energy levels of a rigid rotor-harmonic oscillator, it is typical to express the energy levels as: Á ¹ v,J = ´ µ Âv + 1 2 à + ¸ ¹ v Ä(Ä + 1) a. Why do we add the extra “v” subscript to the rotational constant of the molecule? Because it changes depending on the vibrational state of the molecule b. Why does ¸ ¹ v decrease with increasing v? Because the internuclear distance increases in higher vibrational states and ¸ ¹ v is inversely proportional to ½ = ¾Å ² c. Consider the following spectroscopic data of H ÆÇ Cl: v 0 1 2 3 ¸ ¹ v (cm ¶± ) 10.410 10.115 9.820 9.524 Using this data, determine ¸ ¹ È and É Ê È for H ÆÇ Cl. How close are your values to those
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