Physical Chemistry
2nd Edition
ISBN: 9781133958437
Author: Ball, David W. (david Warren), BAER, Tomas
Publisher: Wadsworth Cengage Learning,
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Chapter 17, Problem 17.24E
What is the ratio of ground-state nickel atoms (in which
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J.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.
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.)
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Chapter 17 Solutions
Physical Chemistry
Ch. 17 - Prob. 17.1ECh. 17 - Prob. 17.2ECh. 17 - Prob. 17.3ECh. 17 - Prob. 17.4ECh. 17 - Prob. 17.5ECh. 17 - Prob. 17.6ECh. 17 - Prob. 17.7ECh. 17 - Prob. 17.8ECh. 17 - Prob. 17.9ECh. 17 - Prob. 17.10E
Ch. 17 - Prob. 17.11ECh. 17 - If the ni values are all the same, a shorthand way...Ch. 17 - Prob. 17.13ECh. 17 - Prob. 17.14ECh. 17 - Prob. 17.15ECh. 17 - Prob. 17.16ECh. 17 - Prob. 17.17ECh. 17 - Prob. 17.18ECh. 17 - Prob. 17.19ECh. 17 - Prob. 17.20ECh. 17 - Prob. 17.21ECh. 17 - Prob. 17.22ECh. 17 - Explain why q is a constant for a given system at...Ch. 17 - What is the ratio of ground-state nickel atoms in...Ch. 17 - Ti3+ has the following electronic energy levels:...Ch. 17 - Using the fact that =1/kT, show that equations...Ch. 17 - A one-dimensional particle-in-a-box has a length...Ch. 17 - Prob. 17.28ECh. 17 - Prob. 17.29ECh. 17 - Prob. 17.30ECh. 17 - Prob. 17.31ECh. 17 - What is the value of q at absolute zero? Is it the...Ch. 17 - Prob. 17.33ECh. 17 - Prob. 17.34ECh. 17 - Prob. 17.35ECh. 17 - Prob. 17.36ECh. 17 - Prob. 17.37ECh. 17 - Prob. 17.38ECh. 17 - Prob. 17.39ECh. 17 - Prob. 17.40ECh. 17 - Prob. 17.41ECh. 17 - Prob. 17.42ECh. 17 - What change is there in the Sackur-Tetrode...Ch. 17 - Prob. 17.44ECh. 17 - Prob. 17.45ECh. 17 - Prob. 17.46ECh. 17 - Calculate the thermal de Broglie wavelength of He...Ch. 17 - Prob. 17.48ECh. 17 - Prob. 17.49ECh. 17 - Prob. 17.50ECh. 17 - Prob. 17.51ECh. 17 - Prob. 17.52ECh. 17 - Prob. 17.53ECh. 17 - Use equation 17.56 to determine the change in...Ch. 17 - For an electron that has a velocity of 0.01c where...Ch. 17 - Use the Sackur-Tetrode equation to derive the...Ch. 17 - Prob. 17.57ECh. 17 - Prob. 17.58E
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- What is the physical explanation of the difference between a particle having the 3-D rotational wavefunction 3,2 and an identical particle having the wavefunction 3,2?arrow_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_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
- 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?arrow_forward2. What are the term symbols for the microstates possible for the 1s 2s2p' electronic configuration of boron?arrow_forwardUsing the rigid rotor model, calculate the energies in Joules of the first three rotational levels of HBr, using for its moment of inertia I = μR2, with μ = mHmX/(mH + mX) and equilibrium internuclear distance = 1.63 Å. To put these energies into units that make sense to us, convert energy to kJ/mol. (Simply estimate atomic masses from the average atomic weights of the elements given in the periodic table).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_forwardP8.41) Calculate the moment of inertia, the magnitude of the rotational angular momentum, and the energy in the J = 6 rotational state for 1"N2. Compare the energy to kBT at 298 K.arrow_forward16.2 Consider 1.00 x 1022 4He atoms in a box of dimensions 1.0 cm x 1.0 cm x 1.0 cm. Calculate the occupancy of the first excited level at 1.0 mK, 2.0 K, and 4.0 K. Do the same for ³He. What conclusions might you draw from the results of your calculations?arrow_forward
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