The rotationa l energy of a linear or spherical molecule with quantum number J is EJ = hBJ(J + 1 ). For a linear molecule. each rotational level has a degeneracy of (2J + 1 ). For a spherical molecule, the degeneracy is (2J + 1 )2 (a) Calculate the ratio of populations of CO2 molecules with J = 4 and J = 2 at 25 °C, given that the rotational constant of CO2 is B = 11.70 GHz. (b) Also calculate the ratio of populations of CH4 molecules with J = 4 and J = 2 at 25 °C, given that the rotational constant of CH4 is 157 GHz.

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Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

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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The rotationa l energy of a linear or spherical molecule with quantum number J is EJ = hBJ(J + 1 ). For a linear molecule. each rotational level has a degeneracy of (2J + 1 ). For a spherical molecule, the degeneracy is (2J + 1 )² (a) Calculate the ratio of populations of CO₂ molecules with J = 4 and J = 2 at 25 °C, given that the rotational constant of CO₂ is B = 11.70 GHz. (b) Also calculate the ratio of populations of CH₄ molecules with J = 4 and J = 2 at 25 °C, given that the rotational constant of CH₄ is 157 GHz.

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