(McQuarrie 6-44) In this problem, we'll calculate the fraction of diatomic molecules in a particular rotational level at a temperature T using the rigid rotor approximation. This fraction is governed by the Boltzmann distribution, which says that the number of molecules with energy EJ is proportional to e-Eл/kBT, where kB is the Boltzmann constant and T is the temperature in Kelvin. Because the J-th rotational level has degeneracy (2J + 1), we write, where we have used EJ. = NJ = c(2J+1)e-BJ(J+1)/kBT BJ(J+1). Plot NJ/No versus J for H35 Cl (B = 10.60 cm-1) and 127135 Cl (B = 0.114 cm-1) at 300 K. At approximately what rotational state J is the population ratio NJ/No a maximum in each case? Explain how this distribution of rotational state populations leads to the spectroscopic band structure of the sort seen in McQuarrie Figure 6.4 or in lecture.

(McQuarrie 6-44) In this problem, we'll calculate the fraction of diatomic molecules in a particular rotational level at a temperature T using the rigid rotor approximation. This fraction is governed by the Boltzmann distribution, which says that the number of molecules with energy EJ is proportional to e-Eл/kBT, where kB is the Boltzmann constant and T is the temperature in Kelvin. Because the J-th rotational level has degeneracy (2J + 1), we write, where we have used EJ. = NJ = c(2J+1)e-BJ(J+1)/kBT BJ(J+1). Plot NJ/No versus J for H35 Cl (B = 10.60 cm-1) and 127135 Cl (B = 0.114 cm-1) at 300 K. At approximately what rotational state J is the population ratio NJ/No a maximum in each case? Explain how this distribution of rotational state populations leads to the spectroscopic band structure of the sort seen in McQuarrie Figure 6.4 or in lecture.

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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