Essentials University Physics, Volume 1 and 2 - With Modified MasteringPhysics Access
3rd Edition
ISBN: 9780134235448
Author: Wolfson
Publisher: PEARSON
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Chapter 37, Problem 19E
To determine
The rotational inertia of the gas 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?
A 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?
Consider 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?
Chapter 37 Solutions
Essentials University Physics, Volume 1 and 2 - With Modified MasteringPhysics Access
Ch. 37.1 - Prob. 37.1GICh. 37.2 - If a scientist uses microwave technology to study...Ch. 37.3 - Prob. 37.3GICh. 37 - If you push two atoms together to form a molecule,...Ch. 37 - Prob. 2FTDCh. 37 - Prob. 3FTDCh. 37 - Does it make sense to distinguish individual NaCl...Ch. 37 - Prob. 5FTDCh. 37 - Prob. 6FTDCh. 37 - Radio astronomers have discovered many complex...
Ch. 37 - Prob. 8FTDCh. 37 - Prob. 9FTDCh. 37 - Prob. 10FTDCh. 37 - Prob. 11FTDCh. 37 - Prob. 12FTDCh. 37 - Prob. 13FTDCh. 37 - Prob. 14FTDCh. 37 - Prob. 15FTDCh. 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. 29PCh. 37 - Prob. 30PCh. 37 - Prob. 31PCh. 37 - Prob. 32PCh. 37 - Prob. 33PCh. 37 - Prob. 34PCh. 37 - Prob. 35PCh. 37 - Prob. 36PCh. 37 - Prob. 37PCh. 37 - Prob. 38PCh. 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 - Prob. 55PCh. 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 - Prob. 63PCh. 37 - Prob. 64PCh. 37 - Prob. 65PCh. 37 - Prob. 66PCh. 37 - Prob. 67PCh. 37 - Prob. 68PPCh. 37 - Prob. 69PPCh. 37 - Prob. 70PPCh. 37 - Prob. 71PP
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- 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_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_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
- 7. A diatomic molecule has 2.6 x 10-5 eV of rotational energy in the L = 2 quantum state. What is the rotational energy in the L = 1 quantum state? Find the wavelength for such transition, L = 2 to L = 1.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_forwardCold interstellar molecular clouds often contain the molecule cyanogen (CN), whose first rotational excited states have an energy of 4.7x 10-4 eV (above the ground state). There are actually three such excited states, all with the same energy. In 1941, studies of the absorption spectrum of starlight that passes through these molecular clouds showed that for every ten CN molecules that are in the ground state, approximately three others are in the three first excited states (that is, an average of one in each of these states). To account for this data, astronomers suggested that the molecules might be in thermal equilibrium with some "reservoir" with a well-defined temperature. What is that temperature?*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_forwardTo 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?arrow_forwardWhen are the rotational degrees of freedom of a diatomic molecule expected to contribute R to the molar constant volume heat capacity? When will a vibrational degree of freedom contribute R to the molar heat capacity?arrow_forward
- Although an ordinary H2 molecule consists of two identical atoms, this is not the case for the molecule HD, with one atom of deuterium (Le., heavy hydrogen, 2H). Because of its small moment of inertia, the HD molecule has a relatively large value of E: 0.0057 eV. At approximately what temperature would you expect the rotational heat capacity of a gas of HD molecules to "freeze out," that is, to fall significantly below the constant value predicted by the equipartition theorem?arrow_forwardEstimate kBT at room temperature, and convert this energy into electronvolts (eV). Using this result, answer the following: (a) Would you expect hydrogen atoms to be ionized at room temperature? (The binding energy of an electron in a hydrogen atom is 13.6 eV.) (b) Would you expect the rotational energy levels of diatomic molecules to be excited at room temperature? (It costs about 10−4 eV to promote such a system to an excited rotational energy level.)arrow_forwardThe intensities of spectroscopic transitions between the vibrational states of a molecule are proportional to the square of the integral ∫ψv′xψvdx over all space. Use the relations between Hermite polynomials given in Table 7E.1 to show that the only permitted transitions are those for which v′ = v ± 1 and evaluate the integral in these cases.arrow_forward
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