Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Question
Chapter 11, Problem 5P
(a)
To determine
The wavelength and the frequency of the
(b)
To determine
The moment of inertia of the molecule.
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The 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.
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?
The effective spring constant associated with bonding in the N2 molecule is 2 297 N/m. The nitrogen atoms each have a mass of 2.32 x 10-26 kg, and their nuclei are 0.120 nm apart. Assume the molecule is rigid. The first excited vibrational state of the molecule is above the vibrational ground state by an energy difference ΔE. Calculate the J value of the rotational state that is above the rotational ground state by the same energy difference ΔE.
Chapter 11 Solutions
Modern Physics
Ch. 11.2 - Compare the effective force constant for the CO...Ch. 11 - Prob. 1QCh. 11 - Prob. 2QCh. 11 - Prob. 3QCh. 11 - Prob. 4QCh. 11 - Prob. 5QCh. 11 - Prob. 7QCh. 11 - Prob. 8QCh. 11 - Prob. 9QCh. 11 - Prob. 1P
Ch. 11 - Use the data in Table 11.2 to calculate the...Ch. 11 - The CO molecule undergoes a rotational transition...Ch. 11 - Prob. 4PCh. 11 - Prob. 5PCh. 11 - Prob. 6PCh. 11 - Prob. 7PCh. 11 - The v = 0 to v = 1 vibrational transition of the...Ch. 11 - Consider the HCl molecule, which consists of a...Ch. 11 - Prob. 10PCh. 11 - Prob. 11PCh. 11 - Prob. 12PCh. 11 - Prob. 13PCh. 11 - Prob. 14PCh. 11 - Prob. 15PCh. 11 - Prob. 18P
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- Consider the HCl molecule, which consists of a hydrogen atom of mass 1 u bound to a chlorine atom of mass 35 u. The equilibrium separation between the atoms is 0.128 nm, and it requires 0.15 eV of work to increase or decrease this separation by 0.01 nm. (a) Calculate the four lowest rotational energies (in eV) that are possible, assuming the molecule rotates rigidly. (b) Find the molecules spring constant and its classical frequency of vibration. (Hint: Recall that U=12Kx2.) (c) Find the two lowest vibrational energies and the classical amplitude of oscillation corresponding to each of these energies. (d) Determine the longest wavelength radiation that the molecule can emit in a pure rotational transition and in a pure vibrational transition.arrow_forwardThe CO molecule undergoes a rotational transition from the ℓ = 1 level to the ℓ = 2 level. Using Table 11.1, calculate the values of the reduced mass and the bond length of the molecule. Compare your results with those of Example 11.1.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
- Show 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_forwardConsider a CO molecule that is initially in the ground state of n = 0, l = 0. If the energy of a vibrational transition from the n = 0 state to the n = 1 state in CO could instead be absorbed in a rotational transition, what would be the value of l for the final state?arrow_forwardThe 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_forward
- The rotational temperature of the Oxygen molecule is 2.08 K. Estimate the molecular rotational partition function of Oxygen at 300K. a. 72.1 b.288.4 c.-144.2 d.none of the above e.144.2arrow_forwardThe CO molecule has a dipole moment of 0.480x10-30 C m. Given that its equilibrium bond distance is 212 pm, what is the magnitude of the effective charge that causes this dipole moment? Give your answer in units of the charge of an electronarrow_forwardThe figure above shows the absorption spectrum of the molecule HBr. Following the basic procedures of Section 9.6, find:(a) the energy of the “missing” transition;(b) the effective force constant k;(c) the rotational spacing 2B. Estimate the value of the rotational spacing expected for HBr and compare with the value deduced from the spectrum. Why are there only single lines and not double lines as in the case of HCl?arrow_forward
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