7.14 The moment of inertia of CH can be calculated from the expression /= mчR² where R = 109 pm is the CH bond length. Calculate the minimum rotational energy (other than zero) of the molecule and the degeneracy of that rotational state.
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7.14
Before solving the problem please also give a brief explanation of the concept or associated equation(s) and variables.
Believe answer should be something like 2.1 x 10-22 J
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- What is the physical explanation of the difference between a particle having the 3-D rotational wavefunction 3,2 and an identical particle having the wavefunction 3,2?Rotational spectra are affected slightly by the fact that different isotopes have different masses. Suppose a sample of the common isotope 1H35Cl is changed to 1H37Cl. (a) By what fraction is the molecule’s rotational inertia different? (The bond length is 0.127 nm in each case.) (b) What is the change in energy of theℓ = 1 to theℓ = 0 transition if the isotope is changed?7E.3 Before solving the problem please also give a brief explanation of the concept or associated equation(s) and variables.
- Estimate the value of Erot for the lowest rotational energy state of N2, which has a bond length 0.110 nm.4) Calculate the energies E of the first three rotational levels (those giving the minimal energy) of 1H35Cl molecule that is free to rotate in three dimensions. For its moment of inertia I = μeffR2 use the effective mass with μeff = mH * mCl / (mH + mCl) and bond length R = 127 pm.P8.41) Calculate the moment of inertia, the magnitude of the rotational angular momentum, and the energy in the J = 6 14N2. Compare the energy to kgT at 298 K. rotational state for
- The cesium iodide (CsI) molecule has an atomic separationof 0.127 nm. (a) Determine the energy of thesecond excited rotational state, with J = 2. (b) Find thefrequency of the photon absorbed in the J =1 to J = 2transition.The rotation of a 1H127I molecule can be pictured as the orbital motion of the hydrogen atom at adistance of 160 pm from the stationary iodine atom. Suppose that the molecule rotates only in a plane.Calculate the minimum energy needed to excite the molecule into rotation. What, apart from 0, is theminimum angular momentum of the molecule?E rotational is 2.777×10−20 J
- An H2 molecule is in its vibrational and rotational ground states. It absorbs a photon of wavelength 2.211 2 μm and makes a transition to the υ = 1, J = 1 energy level. It then drops to the υ = 0, J = 2 energy level while emitting a photon of wavelength 2.405 4 mm. Calculate (a) the moment of inertia of the H2 molecule about an axis through its center of mass and perpendicular to the H–H bond, (b) the vibrational frequency of the H2 molecule, and (c) the equilibrium separation distance for this molecule.J.G. Dojahn et al. (J. Phys. Chem. 100, 9649 (1996)) characterized the potential energy curves of the ground and electronic states of homonuclear diatomic halogen anions. These anions have a 2Σu+ ground state and 2Πg, 2Πu, and 2Σg+ excited states. To which of the excited states are electric-dipole transitions allowed from the ground state? Explain your conclusion.The J = 0 to J = 1 rotational transition of the CO molecule occurs at a frequency of 1.15 x 1011 Hz.(A) Use this information to calculate the moment of inertia of the molecule. (B) Calculate the bond length of the molecule.