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 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.
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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_forward(a) In an HCl molecule, take the Cl atom to be the isotope 35Cl. The equilibrium separation of the H and Cl atoms is 0.127 46 nm. The atomic mass of the H atom is 1.007 825 u and that of the 35Cl atom is 34.968 853 u. Calculate the longest wavelength in the rotational spectrum of this molecule. (b) What If? Repeat the calculation in part (a), but take the Cl atom to be the isotope 37Cl, which has atomic mass 36.965 903 u. The equilibrium separation distance is the same as in part (a). (c) Naturally occurring chlorine contains approximately three parts of 35Cl to one part of 37Cl. Because of the two different Cl masses, each line in the microwave rotational spectrum of HCl is split into a doublet as shown in Figure P42.11. Calculate the separation in wavelength between the doublet lines for the longest wavelength.arrow_forwardConsider a model of a diatomic molecule with pointmass atoms of mass m1 and m2, separated by a distance R. (a) Show that the rotational inertia of the molecule is I= μR2, where the reduced mass μ = m1 m2/(m1 +m2). (b) Compute the rotational inertia of NaCl, which has a bond length of 0.236 nm. Assume the most common isotopes of sodium and chlorine.arrow_forward
- A hypothetical NH molecule makes a rotational-level transition from l=3 to l=1 and gives off a photon of wavelength 1.800 nm in doing so. What is the seperation between the two atoms in this molecule if we model them as point masses? The mass of hydrogen 1.67 * 10^-27 kg, and the mass of nitrogen is 2.33 * 10^-26 kg.arrow_forwardThe CO molecule loses hv = 0.2690 eV of vibrational energy and gains 0.000479 eV of rotational energy. Hence the energy E that goes into the emitted photon equals 0.2690 eV less 0.000479 eV, or 0.2685 eV. The photon wavelength is?arrow_forwardAssume the distance between the protons in the H2 molecule is 0.750 x 10-10 m. (a) Find the energy of the first excited rotational state, with J = 1. (b) Find the wavelength of radiation emitted in the transition from J = 1 to J = 0.arrow_forward
- 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.arrow_forwardPhysics Let's look at the characteristic wavelength of radiation that is produced in molecular transitions. The separation between adjacent energy levels is typically a few eV for atomic energy levels, on the order of 0.1 eV for vibrational levels, and on the order of 10−3eV for rotational levels. Find the wavelength of the photon emitted during a transition in which the energy of the molecule decreases by 5.00 eV, 0.500 eV, and 5.00×10−3eV. In each case, in what region of the electromagnetic spectrum does the photon lie? What is the largest energy of a transition that produces a photon in the green region of the spectrum (495 nm to 570 nm)? Express your answer in electronvolts.arrow_forwardThe vibrational frequency of an HF molecule is 8.72 x 1013 Hz and the reduced mass of the molecule is 1.589 x 1027 kg. What is the ground state vibrational energy of an HF molecule? (1 eV = 1.60 x 10-19 J, h = 6.626 x 10 34 J.s) %3D 0.18 ev O 2.4 ev O 0.12 ev O 1.2 ev O 3 ev Clear my choice 10 searcharrow_forward
- The characteristic rotational energy for a diatomic molecule consisting of two idential atoms of mass 14 u (unified mass units) is 3.68 e-4 eV. Calculate the separation distance between the two atoms. Subarrow_forwardA CO molecule starts in the vibrational and rotational ground state with k = 900 N/m. Calculate the energy of the CO molecule.arrow_forwardThe 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.arrow_forward
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