PHYSICAL CHEMISTRY-STUDENT SOLN.MAN.
2nd Edition
ISBN: 9781285074788
Author: Ball
Publisher: CENGAGE L
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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-STUDENT SOLN.MAN.
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
Ch. 14 - Prob. 14.11ECh. 14 - Prob. 14.12ECh. 14 - Prob. 14.13ECh. 14 - Prob. 14.14ECh. 14 - Diatomic sulfur, S2, was detected in the tail of...Ch. 14 - Prob. 14.16ECh. 14 - Prob. 14.17ECh. 14 - Prob. 14.18ECh. 14 - Prob. 14.19ECh. 14 - Prob. 14.20ECh. 14 - Prob. 14.21ECh. 14 - Prob. 14.22ECh. 14 - Which of the following molecules should have pure...Ch. 14 - Which of the following molecules should have pure...Ch. 14 - The following are sets of rotational quantum...Ch. 14 - The following are sets of rotational quantum...Ch. 14 - Derive equation 14.21 from the E expression...Ch. 14 - Prob. 14.28ECh. 14 - Prob. 14.29ECh. 14 - Lithium hydride, 7Li1H, is a potential fuel for...Ch. 14 - Prob. 14.31ECh. 14 - Prob. 14.32ECh. 14 - Prob. 14.33ECh. 14 - Prob. 14.34ECh. 14 - Prob. 14.35ECh. 14 - Prob. 14.36ECh. 14 - From the data in Table 14.2, predict B for DCl D...Ch. 14 - A colleague states that the pure rotational...Ch. 14 - Prob. 14.39ECh. 14 - Prob. 14.40ECh. 14 - Prob. 14.41ECh. 14 - Prob. 14.42ECh. 14 - Prob. 14.43ECh. 14 - Determine E for J=20J=21 for HBr assuming it acts...Ch. 14 - Determine the number of total degrees of freedom...Ch. 14 - Determine the number of total degrees of freedom...Ch. 14 - Prob. 14.47ECh. 14 - Prob. 14.48ECh. 14 - Prob. 14.49ECh. 14 - Prob. 14.50ECh. 14 - Prob. 14.51ECh. 14 - Prob. 14.52ECh. 14 - Prob. 14.53ECh. 14 - Prob. 14.54ECh. 14 - Prob. 14.55ECh. 14 - Prob. 14.56ECh. 14 - Prob. 14.57ECh. 14 - Prob. 14.58ECh. 14 - Prob. 14.59ECh. 14 - Prob. 14.60ECh. 14 - Prob. 14.61ECh. 14 - Prob. 14.62ECh. 14 - Prob. 14.63ECh. 14 - Prob. 14.64ECh. 14 - Prob. 14.65ECh. 14 - Prob. 14.66ECh. 14 - Prob. 14.68ECh. 14 - Prob. 14.69ECh. 14 - Prob. 14.70ECh. 14 - Prob. 14.71ECh. 14 - Prob. 14.72ECh. 14 - Prob. 14.73ECh. 14 - Prob. 14.74ECh. 14 - Prob. 14.75ECh. 14 - Prob. 14.76ECh. 14 - Prob. 14.77ECh. 14 - Prob. 14.78ECh. 14 - Prob. 14.79ECh. 14 - Prob. 14.80ECh. 14 - Prob. 14.81ECh. 14 - Prob. 14.82ECh. 14 - Prob. 14.83ECh. 14 - Prob. 14.84ECh. 14 - Prob. 14.85ECh. 14 - Dioctyl sulfide, (C8H17)2S, and hexadecane,...Ch. 14 - Where would you expect vibrations for ethyl...Ch. 14 - Prob. 14.88ECh. 14 - Prob. 14.89ECh. 14 - Prob. 14.90ECh. 14 - Prob. 14.91ECh. 14 - Prob. 14.92ECh. 14 - Prob. 14.93ECh. 14 - Prob. 14.94ECh. 14 - The mutual exclusion rule states that for certain...Ch. 14 - Prob. 14.96ECh. 14 - Prob. 14.97ECh. 14 - Prob. 14.98ECh. 14 - Prob. 14.99ECh. 14 - Construct and compare the energy level diagrams...Ch. 14 - Prob. 14.101E
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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_forwardCalculate the energies of the first four rotational levels of 1H127I free to rotate in three dimensions; use for its moment of inertia I = μR2, with μ = mHmI/(mH + mI) and R = 160 pm. Use integer relative atomic masses for this estimate.arrow_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_forward
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