(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.

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter14: Rotational And Vibrational Spectroscopy

Section: Chapter Questions

Problem 14.24E: Which of the following molecules should have pure rotational spectra? a Dimethyltriacetylene,...

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Which of the following molecules should have pure rotational spectra? a Dimethyltriacetylene, H3CCCCCCCCH3 b Cyanotetraacetylene, HCCCCCCCCCN Such molecules have been detected in intersteller space. c Nitric oxide, NO d Nitrogen dioxide, NO2 e Sulfur tetrafluoride, SF4 f Sulfur hexafluoride, SF6
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