(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-EJ/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 C1 (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. P branch. R branch 2400 2500 2600 2700 v/cm¹
(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-EJ/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 C1 (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. P branch. R branch 2400 2500 2600 2700 v/cm¹
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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