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Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford
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(a) Use the result of calculate the equilibrium separation

Chapter 42, Problem 41P

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QUESTION:

Problem 41P

(a) Use the result of Problem to calculate the equilibrium separation of the atoms in an HCI molecule. The mass of a chlorine atom is 5.81 × 10–26 kg, and the mass of a hydrogen atom is 1.67 ×10–27 kg. (b) The value of l changes by ± 1 in rotational transitions. What is the value of l for the upper level of the transition that gives rise to each of the wavelengths listed in Problem? (c) What is the longest-wavelength line in the rotational spectrum of HCls? (d) Calculate the wavelengths of the emitted light for the corresponding transitions in the deuterium chloride (DCl) molecule. In this molecule the hydrogen atom in HCl is replaced by an atom of deuterium, an isotope of hydrogen with a mass of 3.34 ×10–27 kg. Assume that the equilibrium separation between the atoms is the same as for HCl.

Problem:

The rotational spectrum of HCl contains the following wavelengths (among others): 60.4 µm, 69.0 µm, 80.4 µm, 96.4 µm, and 120.4 µm. Use this spectrum to find the moment of inertia of the HCl molecule about an axis through the center of mass and perpendicular to the line joining the two nuclei.

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QUESTION:

Problem 41P

(a) Use the result of Problem to calculate the equilibrium separation of the atoms in an HCI molecule. The mass of a chlorine atom is 5.81 × 10–26 kg, and the mass of a hydrogen atom is 1.67 ×10–27 kg. (b) The value of l changes by ± 1 in rotational transitions. What is the value of l for the upper level of the transition that gives rise to each of the wavelengths listed in Problem? (c) What is the longest-wavelength line in the rotational spectrum of HCls? (d) Calculate the wavelengths of the emitted light for the corresponding transitions in the deuterium chloride (DCl) molecule. In this molecule the hydrogen atom in HCl is replaced by an atom of deuterium, an isotope of hydrogen with a mass of 3.34 ×10–27 kg. Assume that the equilibrium separation between the atoms is the same as for HCl.

Problem:

The rotational spectrum of HCl contains the following wavelengths (among others): 60.4 µm, 69.0 µm, 80.4 µm, 96.4 µm, and 120.4 µm. Use this spectrum to find the moment of inertia of the HCl molecule about an axis through the center of mass and perpendicular to the line joining the two nuclei.

ANSWER:

Solution 41P

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