Essential University Physics
4th Edition
ISBN: 9780134988566
Author: Wolfson, Richard
Publisher: Pearson Education,
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Question
Chapter 37, Problem 40P
(a)
To determine
The classical vibrational frequency of the oxygen molecule.
(b)
To determine
The rotational inertia of the molecule.
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For a certain diatomic molecule, the lowest-energy photon in the vibrational spectrum is 0.17 eV.What is the energy of a photon emitted in a transition from the 5th exited vibrational energy level to the 2nd exited vibrational energy level, assuming no change in the rotational energy?
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To determine the equilibrium separation of the atoms in the HCl molecule, you measure the rotational spectrum of HCl. You find that the spectrum contains these wavelengths (among others): 60.4 mm, 69.0 mm, 80.4 mm, 96.4 mm, and 120.4 mm. (a) Use your measured wavelengths to find the moment of inertia of the HCl molecule about an axis through the center of mass and perpendicular to the line joining the two nuclei. (b) The value of l changes by +-1 in rotational transitions. What value of l for the upper level of the transition gives rise to each of these wavelengths? (c) Use your result of part (a) to calculate the equilibrium separation of the atoms in the HCl molecule. The mass of a chlorine atom is 5.81 * 10-26 kg, and the mass of a hydrogen atom is 1.67 * 10-27 kg. (d) What is the longest-wavelength line in the rotational spectrum of HCl?
Chapter 37 Solutions
Essential University Physics
Ch. 37.1 - Prob. 37.1GICh. 37.2 - If a scientist uses microwave technology to study...Ch. 37.3 - Prob. 37.3GICh. 37 - Prob. 1FTDCh. 37 - Prob. 2FTDCh. 37 - Prob. 3FTDCh. 37 - Prob. 4FTDCh. 37 - Prob. 5FTDCh. 37 - Prob. 6FTDCh. 37 - Prob. 7FTD
Ch. 37 - Prob. 8FTDCh. 37 - Prob. 9FTDCh. 37 - Prob. 10FTDCh. 37 - Prob. 11ECh. 37 - Prob. 12ECh. 37 - Prob. 13ECh. 37 - Prob. 14ECh. 37 - Prob. 15ECh. 37 - Prob. 16ECh. 37 - Prob. 17ECh. 37 - Prob. 18ECh. 37 - Prob. 19ECh. 37 - Prob. 20ECh. 37 - Prob. 21ECh. 37 - Prob. 22ECh. 37 - Prob. 23ECh. 37 - Prob. 24ECh. 37 - Prob. 25ECh. 37 - Prob. 26ECh. 37 - Prob. 27ECh. 37 - Prob. 28ECh. 37 - Prob. 29ECh. 37 - Prob. 30ECh. 37 - Prob. 31PCh. 37 - Prob. 32PCh. 37 - Prob. 33PCh. 37 - Prob. 34PCh. 37 - Prob. 35PCh. 37 - Prob. 36PCh. 37 - Prob. 37PCh. 37 - Prob. 39PCh. 37 - Prob. 40PCh. 37 - Prob. 41PCh. 37 - Prob. 42PCh. 37 - Prob. 43PCh. 37 - Prob. 44PCh. 37 - Prob. 45PCh. 37 - Prob. 46PCh. 37 - Prob. 47PCh. 37 - Prob. 48PCh. 37 - Prob. 49PCh. 37 - Prob. 50PCh. 37 - Prob. 51PCh. 37 - Prob. 52PCh. 37 - Prob. 53PCh. 37 - Prob. 54PCh. 37 - The critical field in a niobium-titanium...Ch. 37 - The transition from the ground state to the first...Ch. 37 - Prob. 57PCh. 37 - Prob. 58PCh. 37 - Youre troubled that Example 37.1 neglects the mass...Ch. 37 - Prob. 60PCh. 37 - The Madelung constant (Section 37.3) is...Ch. 37 - Prob. 62PCh. 37 - (a) Count the number of electron states N(E) with...Ch. 37 - Prob. 64PCh. 37 - Prob. 65PCh. 37 - Prob. 66PCh. 37 - Prob. 67PPCh. 37 - Prob. 68PPCh. 37 - Prob. 69PPCh. 37 - Prob. 70PP
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- The CO molecule makes a transition from the J = 1 to the J = 2 rotational state when it absorbs a photon of frequency 2.30 x 1011 Hz. (a) Find the moment of inertia of this molecule from these data.arrow_forwardA CO molecule is initially in the n = 2 vibrational level. If this molecule loses both vibrational and rotational energy and emits a photon, what are the photon wavelength and frequency if the initial angular momentum quantum number is l = 3?arrow_forwardSuppose that the wavenumber of the J = 1 ← 0 rotational transition of 1H81Br considered as a rigid rotor was measured to be 18.20 cm-1, what is (a) the moment of inertia of the molecule? _____________kg-m2 (b) the bond length? ________________Angstroms (Given the isotopic masses:(m(79Br) = 78.9183 amu, m(81Br) = 80.9163 amuarrow_forward
- Consider the NaCl molecule, for which the rotational inertia is 1.30x 10-45 kg*m2. If infrared radiation with wavelength 30 μ m is Raman-scattered from a free NaCl molecule, what are the allowed wavelengths of the scattered radiation?arrow_forwardIf the moment of inertia of 1H 127I is 4.31 x 10-47 kg m2. Determine the bond length of HI and the rotational energy at quantum number J=5 Please to respond quickly.arrow_forward2(6) Calculate the fundamental vibrational wavenumber (in cm-1) for HI molecule, if its angular vibrational frequency is 4.394×1014 s-1. Calculate the vibrational energy of the molecule in the ground state and the force constant. Assume the mass is the mass of a proton.arrow_forward
- If a sodium chloride (NaCl) molecule could undergo an n S n - 1 vibrational transition with no change in rotational quantum number, a photon with wavelength 20.0 mm would be emitted. The mass of a sodium atom is 3.82 * 10-26 kg, and the mass of a chlorine atom is 5.81 * 10-26 kg. Calculate the force constant k′ for the interatomic force in NaCl.arrow_forwardThe equilibrium separation between the two ions in the KCl molecule is 0.267 nm. (a) Assuming that the K+ and Cl- ions are point particles, compute the electric dipole moment of the molecule. (b) Compute the ratio of your result in (a) to the measured electric dipole moment of 5.41 x 10-29 C*m. This ratio is known as the fractional ionic character of the molecular bond.arrow_forwardWhen an OH molecule undergoes a transition from the n = 0 to the n = 1 vibrational level, its internal vibrational energy increases by 0.463 eV. Calculate the frequency of vibration and the force constant for the interatomic force. (The mass of an oxygen atom is 2.66 * 10-26 kg, and the mass of a hydrogen atom is 1.67 * 10-27 kg.)arrow_forward
- The vibrational frequency n for Br2 is 323 cm-1 and the energy difference between its two lowest rotational energy levels, J = 0 and J = 1, is 0.164 cm-1. Calculate the relative populations of the v = 1 and v = 0 vibrational energylevels and the relative populations of the two lowest rotational energy levels for Br2 at 300 K. Comment on your results.arrow_forwardThe first three absorption lines in the pure rotational spectrum of gaseous 12C16O are found to have the frequencies 1.15 × 1011, 2.30 × 1011, and 3.46 × 1011 s21. Calculate:(a) The moment of inertia I of CO (in kg m2)(b) The energies of the J 5 1, J 5 2, and J 5 3 rotational levels of CO, measured from the J 5 0 state (in joules)(c) The CUO bond length (in angstroms)arrow_forwardShow that the moment of inertia of a diatomic molecule composed of atoms of masses mA and mB and bond length R is equal to meffR2, where meff = mAmB/(mA+mB).arrow_forward
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