The rigid rotor model is often used to study the rotation of diatomic molecules. In this case, there is often a spectroscopic transition from a state with angular momentum quantum number, J, to one with J+ 1 (absorption) or to one with J-1 (emission). (a) Using the expression for rigid rotor energy levels, derive an expression for the energy difference corresponding to an emission transition J→J-1 and equate this to hv, the energy of a photon. Report your result as a positive number (in emission, energy is lost). (On the quiz, you will be given values for J and, and asked to compute the value of v.) 21 (b) In spectroscopic experiments, one typically observes a series of absorption lines corresponding to the transitions originating in states with successive values of J. For one diatomic, one observes a set of lines equally spaced at Av = 1.1338 × 1012sec1. What is the moment of inertia for this molecule in units of kg-m?? (Note that since molecules have masses on the order of 10-27 kg and bond lengths on the order of 100 pm, this quantity should be about 10-47 kg-m². Report the number multiplying 10-47.)
The rigid rotor model is often used to study the rotation of diatomic molecules. In this case, there is often a spectroscopic transition from a state with angular momentum quantum number, J, to one with J+ 1 (absorption) or to one with J-1 (emission). (a) Using the expression for rigid rotor energy levels, derive an expression for the energy difference corresponding to an emission transition J→J-1 and equate this to hv, the energy of a photon. Report your result as a positive number (in emission, energy is lost). (On the quiz, you will be given values for J and, and asked to compute the value of v.) 21 (b) In spectroscopic experiments, one typically observes a series of absorption lines corresponding to the transitions originating in states with successive values of J. For one diatomic, one observes a set of lines equally spaced at Av = 1.1338 × 1012sec1. What is the moment of inertia for this molecule in units of kg-m?? (Note that since molecules have masses on the order of 10-27 kg and bond lengths on the order of 100 pm, this quantity should be about 10-47 kg-m². Report the number multiplying 10-47.)
Chemistry
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ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Transcribed Image Text:The rigid rotor model is often used to study the rotation of diatomic molecules. In this case,
there is often a spectroscopic transition from a state with angular momentum quantum
number, J, to one with J+ 1 (absorption) or to one with J-1 (emission).
(a) Using the expression for rigid rotor energy levels, derive an expression for the energy
difference corresponding to an emission transition J→J-1 and equate this to hv, the
energy of a photon. Report your result as a positive number (in emission, energy is lost).
(On the quiz, you will be given values for J and
and asked to compute the value of v.)
21
(b) In spectroscopic experiments, one typically observes a series of absorption lines
corresponding to the transitions originating in states with successive values of J. For one
diatomic, one observes a set of lines equally spaced at Av
is the moment of inertia for this molecule in units of kg-m?? (Note that since molecules
have masses on the order of 10-27 kg and bond lengths on the order of 100 pm, this
quantity should be about 10-47 kg-m². Report the number multiplying 10-47.)
= 1.1338 × 1012sec-1. What
(c) Suppose this diatomic is a hydride and its bond length has been determined by separate
means to be 96.97 pm. What is the mass of the other element in the molecule in Dalton
(atomic mass units)?
(d) Use your result in part (c) to determine the identity of the second element.
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