Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 42, Problem 36AP
To determine
The magnitude of J.
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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.
When a hypothetical diamotic molecule having atoms 0.8890 nm
apart undergoes a rotational transition from the l=2 state to the next
lower state, it gives up a photon having energy 8.850 * 10^-4 eV. When
the molecule undergoes a vibrational transition from one energy state
to the next lower energy state, it gives up 0.2540 eV. Find the force
constant of this molecule.
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 42 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 42.1 - For each of the following atoms or molecules,...Ch. 42.2 - Prob. 42.2QQCh. 42.2 - Prob. 42.3QQCh. 42 - Prob. 1PCh. 42 - Prob. 2PCh. 42 - Prob. 3PCh. 42 - Prob. 4PCh. 42 - Prob. 5PCh. 42 - The photon frequency that would be absorbed by the...Ch. 42 - Prob. 8P
Ch. 42 - Prob. 9PCh. 42 - Prob. 10PCh. 42 - (a) In an HCl molecule, take the Cl atom to be the...Ch. 42 - Prob. 12PCh. 42 - Prob. 13PCh. 42 - Prob. 14PCh. 42 - Prob. 15PCh. 42 - Prob. 16PCh. 42 - Prob. 17PCh. 42 - Prob. 19PCh. 42 - Prob. 21PCh. 42 - Prob. 22PCh. 42 - Prob. 23PCh. 42 - Prob. 24PCh. 42 - Prob. 25PCh. 42 - Prob. 26PCh. 42 - Prob. 27PCh. 42 - Prob. 28PCh. 42 - Prob. 29PCh. 42 - Prob. 30PCh. 42 - Prob. 32PCh. 42 - Prob. 33PCh. 42 - Prob. 35PCh. 42 - Prob. 36APCh. 42 - Prob. 37APCh. 42 - Prob. 39APCh. 42 - Prob. 40APCh. 42 - As an alternative to Equation 42.1, another useful...
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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_forwardWhen a hypothetical diatomic molecule having atoms 0.8860 nm apart undergoes a rotational transition from the l = 2 state to the next lower state, it gives up a photon having energy 8.841 * 10-4 eV. When the molecule undergoes a vibrational transition from one energy state to the next lower energy state, it gives up 0.2560 eV. Find the force constant of this molecule.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 moment of inertia of water molecule about an axis bisecting the HOH angle is1.91x10-47 kg m2. Its minimum angular momentum about that axis (other than zero) is ℏ. Inclassical terms, how many revolutions per second do the hydrogen atoms make about the axiswhen in that state? Calculate the rotational constant (cm-1) and bond length of H2O. Does the bondlength seem reasonable?arrow_forwardThe separation between two hydrogen atoms in an H2 molecule is 75 pm. The mass of a hydrogen atom is 1.6735 x 1027 Kg. Find the energy of the rotational state of H2 with quantum number I = 9. Give your answer in unites of eV. Round your answer to 3 decimal places. Add your answerarrow_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 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 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 moleculearrow_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 force constant for the internuclear force in a hydrogen molecule (H2) is k′ = 576 N /m. A hydrogen atom has mass 1.67 * 10-27 kg. Calculate the zero-point vibrational energy for H2 (that is, the vibrational energy the molecule has in the n = 0 ground vibrational level). How does this energy compare in magnitude with the H2 bond energy of -4.48 eV ?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_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
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