12. (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 е-Eл/kBT, where kÅ is the Boltzmann constant and T is the temperature in Kelvin. Because the J-th rotational level has degeneracy (2J + 1), we write, NJ = c(2J + 1)e¯ −BJ(J+1)/kT where we have used EJ = BJ(J+1). Plot NJ/No versus J for H35 C1 (В : 127135 Cl (B = 0.114 cm-1) at 300 K. = 10.60 cm-1) and 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.
12. (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 е-Eл/kBT, where kÅ is the Boltzmann constant and T is the temperature in Kelvin. Because the J-th rotational level has degeneracy (2J + 1), we write, NJ = c(2J + 1)e¯ −BJ(J+1)/kT where we have used EJ = BJ(J+1). Plot NJ/No versus J for H35 C1 (В : 127135 Cl (B = 0.114 cm-1) at 300 K. = 10.60 cm-1) and 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
Chapter1: Gases And The Zeroth Law Of Thermodynamics
Section: Chapter Questions
Problem 1.75E
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![12. (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 е-Eл/kBT, where kÅ is the Boltzmann constant and T is
the temperature in Kelvin. Because the J-th rotational level has degeneracy (2J + 1), we
write,
NJ = c(2J + 1)e¯
−BJ(J+1)/kT
where we have used EJ = BJ(J+1). Plot NJ/No versus J for H35 C1 (В :
127135 Cl (B = 0.114 cm-1) at 300 K.
=
10.60 cm-1) and
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d378848-bcd2-4fca-91fb-9e70c50f07a7%2Ff269ebf4-4804-4784-817a-df9205d8a257%2F9tdgyrb_processed.png&w=3840&q=75)
Transcribed Image Text:12. (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 е-Eл/kBT, where kÅ is the Boltzmann constant and T is
the temperature in Kelvin. Because the J-th rotational level has degeneracy (2J + 1), we
write,
NJ = c(2J + 1)e¯
−BJ(J+1)/kT
where we have used EJ = BJ(J+1). Plot NJ/No versus J for H35 C1 (В :
127135 Cl (B = 0.114 cm-1) at 300 K.
=
10.60 cm-1) and
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.
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