The moment of inertia for an axis through the center of mass of a diatomic molecule calculated from the wavelength emitted in an l = 19 → l = 18 transition is different from the moment of inertia calculated from the wavelength of the photon emitted in an l = l → l = 0 transition. Explain this difference. Which transition corresponds to the larger moment of inertia?
Want to see the full answer?
Check out a sample textbook solutionChapter 42 Solutions
University Physics with Modern Physics, Volume 1 (Chs. 1-20) (14th Edition)
Additional Science Textbook Solutions
Physics for Scientists and Engineers with Modern Physics
Introduction to Electrodynamics
Physics: Principles with Applications
College Physics: A Strategic Approach (4th Edition)
College Physics: A Strategic Approach (3rd Edition)
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
- A diatomic F2 molecule is in the l = 1 state, (a) What is the energy of the molecule? (b) How much energy is radiated in a transition from a l =2 to a l = l state?arrow_forwardIn a physics lab, you measure the vibrational- rotational spectrum of HCl. The estimated separation between absorption peaks is f5.51011Hz . The central frequency of the band is f0=9.01013Hz . (a) What is the moment of inertia (I)? (b) What is the energy of vibration for the molecule?arrow_forwardAs an alternative to Equation 42.1, another useful model for the potential energy of a diatomic molecule is the Morse potential U(r)=B[ea(rr0)1]2 where B, a, and r0 are parameters used to adjust the shape of the potential and its depth. (a) What is the equilibrium separation of the nuclei? (b) What is the depth of the potential well, defined as the difference in energy between the potentials minimum value and its asymptote as r approaches infinity? (c) If is the reduced mass of the system of two nuclei and assuming the potential is nearly parabolic about the well minimum, what is the vibrational frequency of the diatomic molecule in its ground state? (d) What amount of energy needs to be supplied to the ground-state molecule to separate the two nuclei to infinity?arrow_forward
- A diatomic molecule consists of two atoms having masses m1 and m2 separated by a distance r. Show that the moment of inertia about an axis through the center of mass of the molecule is given by Equation 42.3, I = μr2.arrow_forwardSuppose the bond in a molecule is broken by photons of energy 5.0 eV. f = Submit Request Answer Part B Value X= Determine the wavelength of these photons. Express your answer with the appropriate units. Submit μA Value Units Request Answer Units www ?arrow_forwardAn empirical interatomic pair potential for xenon atoms, in units of eV, and nm, and the lattice parameter of Xenon is equal to 0.630 nm. V(r) = 12.6 X 10-7 31.8 X 10-4 712 The calculated interatomic separation (nearest-neighbour) distance is: A. 0.2227 nm. B. 0.3536 nm C. 0.4455 nm D. 1.414 nmarrow_forward
- 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 = 0.82i + 0.99j + 0.84k B = 1.09i + -1.01j + -0.97k What is the angle (in degrees) between the bonds based on this new data?arrow_forward3. Atomic vibrations in a metal. Consider point ions of mass M and charge e immersed in a uniform sea of conduction electrons. The ions are imagined to be in stable equilibrium when at regular lattice points. If one ion is displaced a small distance r from its equilibrium position, the restoring force is largely due to the electric charge within the sphere of radius r centered at the equilibrium position. Take the number density of ions (or of conduction electrons ) as 3/(47R³), which defines R. (a) Show that the frequency of a single ion set into oscillation is @= (e²/MR³) ¹/2. (b) Estimate the value of this frequency for sodium, roughly. (c) From (a), (b), and some common sense, estimate the order of magnitude of the velocity of sound in metal.arrow_forwardAn H2 molecule is in its vibrational and rotational ground states. It absorbs aphoton of wavelength 2.2112 µm and makes a transition to the ν = 1, J = 1energy level. It then drops to the ν = 0, J = 2 energy level while emitting6/9SIX1011a photon of wavelength 2.4054 µm. Calculate (i) the moment of inertia of theH2 molecule about an axis through its centre of mass and perpendicular tothe H − H bond, (ii) the vibrational frequency of the H2 molecule, and (iii) theequilibrium separation distance for this molecule.arrow_forward
- A hypothetical NH molecule makes a rotational-level transition from \= 3 to l = 1 and gives off a photon of wavelength 1.800 nm in doing SO. What is the separation between the two atoms in this molecule if we model them as point masses? The mass of hydrogen is kg. 1.67 * 10-2 kg, and the mass of nitrogen is 2.33 * 10 26 a) 6.52*10^{-13}m b) 5.69*10^{-13}m c) 5.70*10^{-14} m d) 5.69*10^{-12}m e) 5.62*10^{-13}marrow_forwardMolecular oxygen (O2) has a vibrational state transition energy of approximately 250 meV a) Calculate the relative populations of the vibrational ground state and first excited states of a collection of O2 molecules at 300 K. b) Calculate the probability of finding an O2 molecule in its vibrational ground state at 1200 Karrow_forwardA 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_forward
- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningUniversity Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax