Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 10, Problem 56P
To determine
Toshow: The energy difference between one rotational state of a molecule and the next higher state is proportional to
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Discuss the differences between the rotational and vibrational energy levels of the deuterium (“heavy hydrogen”) molecule D2 and those of the ordinary hydrogen molecule H2. A deuterium atom has twice the mass of an ordinary hydrogen atom.
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The l = 2 rotational level of the hydrogen chloride (HCl) molecule has energy 7.90 meV. The mass of the most common hydrogen atom is 1.674 * 10-27 kg, and the mass of the most common chlorine atom is 5.807 * 10-26 kg. Find the reduced mass of the HCl molecule
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Physics for Scientists and Engineers
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- The l = 2 rotational level of the hydrogen chloride (HCl) molecule has energy 7.90 meV. The mass of the most common hydrogen atom is 1.674 * 10-27 kg, and the mass of the most common chlorine atom is 5.807 * 10-26 kg. Find the moment of inertia of the HCl molecule.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_forwardIn the methane molecule, CH4, each hydrogen atom is at the corner of a regular tetrahedron with the carbon atom at the center. If one of the C-H is in the direction of A= i-hat + j-hat + k-hat and an adjacent C-H bond is at the direction B= i-hat - j-hat - k-hat results to an angular bond of approximately 109o for a static frozen molecule. However, the molecule we can encounter everyday continuously vibrates and interact with the surrounding causing its bond vector to vary slightly. According to a new spectroscopy analysis, the adjacent bond vectors was found to be A = 0.96i + 0.87j + 0.8k B = 0.94i + -0.98j + -1.07k What is the angle (in degrees) between the bonds based on this new data?arrow_forward
- A solid sphere, a thin spherical shell, and a solid cylinder each have a radius of 3 cm and a mass of 5 kg. They each rotate about an axis that goes through their center at a rate of 10 rad/s, and remain in place. Rank the rotational kinetic energies of the objects. (a) Kshell=Ksphere=KcylKshell=Ksphere=Kcyl(b) Kshell>Kcyl>KsphereKshell>Kcyl>Ksphere (c) Kshell>Ksphere>KcylKshell>Ksphere>Kcyl(d) Ksphere>Kcyl>KshellKsphere>Kcyl>Kshell (e) Ksphere>Kshell>Kcylarrow_forwardThe energy spacing between consecutive rotational energy levels is generally less than that between consecutive translational energy levels. True Falsearrow_forwardIn the methane molecule, CH4, each hydrogen atom is at the corner of a regular tetrahedron with the carbon atom at the center. If one of the C-H is in the direction of A= i-hat + j-hat + k-hat and an adjacent C-H bond is at the direction B= i-hat - j-hat - k-hat results to an angular bond of approximately 109o for a static frozen molecule. However, the molecule we can encounter everyday continuously vibrates and interact with the surrounding causing its bond vector to vary slightly. According to a new spectroscopy analysis, the adjacent bond vectors was found to be A = 1.09i + 1.06j + 1.02k B = 1.01i + -0.89j + -1.02k What is the angle (in degrees) between the bonds based on this new data? Note: Only 1% of error is permitted for the correct answer.arrow_forward
- Consider the hydrogen molecule H₂ as a rigid rotor with distance of separation of H-atoms r = 1.0 Å. Compute the energy of J = 2 rotational level.arrow_forwardA diatomic molecule has 18 x 105 eV of rotational energy in the I = 7 quantum state. What is its rotational energy in the I = 0 quantum state? %3Darrow_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_forward
- 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_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_forwardGive an example of two polyatomic molecules that have different rotational contributions to internal energy. State the conditions in which the vibrational contribution to internal energy is proportional to the temperature.arrow_forward
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