Concept explainers
(a)
Interpretation:
The expected ratios of molecules in odd rotational states to even rotational stated for given molecule is to be predicted.
Concept introduction:
The antisymmetric spin states represent the even rotational states while symmetric spin states represent the odd rotational states.
The odd rotational states are calculated by,
The even rotational states are calculated by,
Where,
•
(b)
Interpretation:
The expected ratios of molecules in odd rotational states to even rotational stated for given molecule is to be predicted.
Concept introduction:
The antisymmetric spin states represent the even rotational states while symmetric spin states represent the odd rotational states.
The odd rotational states are calculated by,
The even rotational states are calculated by,
Where,
•
Want to see the full answer?
Check out a sample textbook solutionChapter 18 Solutions
Physical Chemistry
- The rotational constant for CO is 1.9314 cm−1 and 1.6116 cm−1 in the ground and first excited vibrational states, respectively. By how much does the internuclear distance change as a result of this transition?arrow_forwardCalculate the rotational energy of CO at J=2 given a bond length of 1.0 Å. unit in eV.arrow_forwardA rotating methane molecule is described by the quantum numbers J, MJ, and K. (a) For methane, how many rotational states have an energy equal to hBJ(J + 1) with J= 8? (b) Now consider chloromethane. How many rotationalstates have an energy equal to hBJ(J + 1) with J = 8?arrow_forward
- Calculate the contribution of each normal mode to the molar vibrational heat capacity of H_2O (g) at 600 K.arrow_forwardThe NOF molecule is an asymmetric rotor with rotational constants 3.1752 cm−1, 0.3951 cm−1, and 0.3505 cm−1. Calculate the rotational partition function of the molecule at (i) 25 °C, (ii) 100 °C.arrow_forwardRotational spectra are affected slightly by the fact that different isotopes have different masses. Suppose a sample of the common isotope 1H35Cl is changed to 1H37Cl. (a) By what fraction is the molecule’s rotational inertia different? (The bond length is 0.127 nm in each case.) (b) What is the change in energy of theℓ = 1 to theℓ = 0 transition if the isotope is changed?arrow_forward
- The vibrational wavenumber of the oxygen molecule in its electronic ground state is 1580 cm−1, whereas that in the excited state (B 3Σu−), to which there is an allowed electronic transition, is 700 cm−1. Given that the separation in energy between the minima in their respective potential energy curves of these two electronic states is 6.175 eV, what is the wavenumber of the lowest energy transition in the band of transitions originating from the v = 0 vibrational state of the electronic ground state to this excited state? Ignore any rotational structure or anharmonicity.arrow_forwardThe moment of inertia of CH4 can be calculated from the expression I=8/3 mHR2 where R is the C-H bond length (109 angstrom or 109 x 1012 m). a. What is the lowest possible rotational energy of the CH4 molecule and what is the value of quantum number l associated with that rotational energy? b. Calculate the rotational energy of the molecule in the first excited state (when quantum number l = 1). c. Determine the degeneracy of the first excited state. Explain what is meant by rotational energy degeneracy.arrow_forwardEvaluate the rotational partition function at 298 K of (a) 1H35Cl. for which the rotational constant is 318 GHz, (b) 12C16O2, for which the rotational constant is 11.70 GHz.arrow_forward
- Knowing that the rotational constant of the heteronuclear diatomic molecule HCl is 10.4367 cm−1 , calculate its internuclear distance.arrow_forward5. For carbon monoxide at 298K, determine the fraction of molecules in the rotational levels for J=0, 5, 10, 15, and 20. The rotational constant (B) is 3.83x10^-23 Joules.arrow_forwardConsider the rotational spectrum of a linear molecule at 298 K with a moment of inertia of 1.23×10−461.23\times10^{-46}1.23×10−46 kg m2 . (a) What is the frequency for the transition from J = 2 to J = 3? (b) What is the most populated rotational level for this molecule? Would the transition in (a) give the most intense signal in the rotational spectrum?arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,Principles of Modern ChemistryChemistryISBN:9781305079113Author:David W. Oxtoby, H. Pat Gillis, Laurie J. ButlerPublisher:Cengage Learning