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,
•
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Physical Chemistry
- b. The energy difference between consecutive vibrational states is 1.0 x 1020 J for a molecule. (i) Calculate the population ratio, n4/n¡, for this system at 298 K and discuss the significance of this ratio in terms of the distribution of molecules in the higher vibrational energy states. (ii) Estimate the vibrational partition function at 298 K. (iii) Estimate the fundamental vibration wave number for this molecule. h = 6.626 x 10-3ª J s k= 1.38 x 1023 J K' c = 2.998 x 10® m s''arrow_forwardConsider the diatomic molecule AB modeled as a rigid rotor (two masses separated by a fixed distance equal to the bond length of the molecule). The rotational constant of the diatomic AB is 25.5263 cm-1. (a) What is the difference in energy, expressed in wavenumbers, between the energy levels of AB with J = 10 and J = 6? (b) Consider now a diatomic A'B', for which the atomic masses are ma 0.85 mA and mB' 0.85 mB and for its bond length ra'B' = 0.913 rAB. What is the difference in energy, expressed in wavenumbers, between the energy levels of the A'B' molecule with J = 9 and J = 7?arrow_forwardCalculate the CO and CS bond lengths in OCS from the rotational constants B(16O12C32S) = 6081.5MHz, B(16O12C34S) = 5932.8MHz.arrow_forward
- (c) Consider the following rotational temperatures of diatomic molecules: qr(N2) = 2.9K, qr(HD) = 64.7K Assuming classical behaviour (i.e. continuum approximation): (i) Estimate the number of accessible rotational energy levels at 290 K for both moleculesarrow_forwardCalculate the rotational energy of CO at J=2 given a bond length of 1.0 Å. unit in eV.arrow_forwardA molecule in a gas undergoes about 1.0 × 109 collisions in each second. Suppose that (a) every collision is effective in deactivating the molecule rotationally and (b) that one collision in 10 is effective. Calculate the width (in cm³¹) of rotational transitions in the molecule.arrow_forward
- The vibrational temperature of a molecule prepared in a supersonic jet can be estimated from the observed popula- tions of its vibrational levels, assuming a Boltzmann distri- bution. The vibrational frequency of HgBr is 5.58 × 1012 s-1, and the ratio of the number of molecules in the n = 1 state to the number in the n = 0 state is 0.127. Estimate the vibra- tional temperature under these conditions.arrow_forwardDerive an expression for the mean energy of a collection of molecules that have three energy levels at 0, ε, and 3ε with degeneracies 1, 5, and 3, respectively.arrow_forwardthe rotational constant for 1H35Cl is 10.6 cm-1 . What are the degeneracies, g, of the J=2, and J=3 rotational states?arrow_forward
- The J = 0 to J = 1 rotational transition of the CO molecule occurs at a frequency of 1.15 x 1011 Hz.(A) Use this information to calculate the moment of inertia of the molecule. (B) Calculate the bond length of the molecule.arrow_forwardCalculate the relative number of molecules in the J = 1 and J = 2 rotational states of HCI at 27 \deg C. (I = 2.643 x 1047 kg m^2).arrow_forwardConsider the rotational temperatures of the following hetero diatomic molecules: θr(CO) = 2.1 K, θr(HF) = 30.2 K. In which case would the classical approximation be accurate? Justify your answer.arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,