Physical Chemistry
2nd Edition
ISBN: 9781133958437
Author: Ball, David W. (david Warren), BAER, Tomas
Publisher: Wadsworth Cengage Learning,
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Chapter 14, Problem 14.20E
Interpretation Introduction
Interpretation:
The degeneracy of rotational levels for symmetric tops is proved to be
Concept introduction:
In a molecule, the rotational energy level corresponds to the different probable ways in which the portion of a molecule rotates around the
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Students have asked these similar questions
Consider 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?
Calculate the ratio of the populations in the first two rotational energy levels of carbon monoxide, the lowest J=0 energy level and the higher J = 1 energy level, at 300 K if the energy difference between the levels is 3.8 cm-1and the degeneracies gJ of the two levels are g0 = 1 and g1 = 3, respectively. (You will see in Section 20.3 that there are 2J 1 1 rotational quantum states at each energy level EJ.)
the rotational constant for 1H35Cl is 10.6 cm-1 . What are the degeneracies, g, of the J=2, and J=3 rotational states?
Chapter 14 Solutions
Physical Chemistry
Ch. 14 - Prob. 14.1ECh. 14 - Determine if the following integrals can be...Ch. 14 - What is the frequency of light having the...Ch. 14 - What is the wavelength of light having the given...Ch. 14 - What is the energy of light having each...Ch. 14 - The Cu(H2O)62+ complex has octahedral symmetry. Is...Ch. 14 - What are the wavelength, speed, and energy of a...Ch. 14 - Prob. 14.8ECh. 14 - Prob. 14.9ECh. 14 - Prob. 14.10E
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Similar questions
- (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_forwardThe rotational constant for the molecule 1H35Cl is B = 10.60 cm-1. Using Boltzmann statistics, determine the most likely rotational state J that such a molecule would be expected to have at a temperature of 300 K.arrow_forwardCalculate the rotational energy of CO at J=2 given a bond length of 1.0 Å. unit in eV.arrow_forward
- Develop an expression for the value of J corresponding to the most highly populated rotational energy level of a diatomic rotor at a temperature T remembering that the degeneracy of each level is 2J + 1. Evaluate the expression for ICl (for which ᷉ B = 0.1142 cm−1) at 25 °C. Repeat the problem for the most highly populated level of a spherical rotor, taking note of the fact that each level is (2J + 1)2-fold degenerate. Evaluate the expression for CH4 (for which ᷉ B = 5.24 cm−1) at 25 °C. Hint: To develop the expression, recall that the first derivative of a function is zero when the function reaches either a maximum or minimum value.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_forwardJ.G. Dojahn et al. (J. Phys. Chem. 100, 9649 (1996)) characterized the potential energy curves of the ground and electronic states of homonuclear diatomic halogen anions. These anions have a 2Σu+ ground state and 2Πg, 2Πu, and 2Σg+ excited states. To which of the excited states are electric-dipole transitions allowed from the ground state? Explain your conclusion.arrow_forward
- (c) When a gas is expanded very rapidly, its temperature can fall to a few degrees Kelvin. At these low temperatures, unusual molecules like ArHCl (Argon weakly bonded to HCl) can form on mixing. For the isotopic species Ar H$CI, the following rotational transitions were observed: J (1 → 2): 6714.44 MHz J (2 → 3): 10068.90 MHz Assume the molecule can be treated as a linear diatomic molecule (ArCl). (i) Calculate the rotational constant (B) and centrifugal distortion (D) constant for this molecule.arrow_forwardA diatomic molecule has a rotational constant of 8.0 cm-1, and vibrational frequency of 1200 cm 1. What is the energy of the state with v = 1 and j = 6 relative to the lowest energy state, E = E(v=0,j=0)? 0arrow_forwardThe rotational constant of 12C16O is 57.65 GHz. Calculate the value of J for the most populated level at (a) 300 K and (b) 1000 K.arrow_forward
- Vibrational frequency of iodine molecule Br2 is 414 cm^-1. Calculate ratio populations of 1st excited to ground vibrational states in Br2arrow_forwardQ 1. Use the equipartition principle to estimate the value of γ = Cpm/CVm for gaseous CH3COOH. Do this calculation WITH the vibrational contribution to the energy.arrow_forwardP11B.10 The rotational terms of a symmetric top, allowing for centrifugal distortion, are commonly written F(J,K)= BJ(J+1)+(Ã-B)K²- Ď,J³(J+1)°–ϵJ(J+1)K²-Ď«K* (a) Develop an expression for the wavenumbers of the allowed rotational transitions. (b) The following transition frequencies (in gigahertz, GHz) were observed for CH,F: 51.0718 102.1426 102.1408 153.2103 153.2076 Evaluate as many constants in the expression for the rotational terms as these values permit.arrow_forward
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