Calculate the energies, in Joules, of the v = 0, 1, 2, and 3 vibrational states for HCI (Mosc 2991 cm-1) and 12 (Mosc = 214.5 cm-1). Make a sketch of the energy levels on the same scale
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- Pure rotational Raman spectra of gaseous C6H6 and C6D6 yield the following rotational constants: ᷉ B(C6H6) = 0.189 60 cm−1, ᷉ B(C6D6) = 0.156 81 cm−1. The moments of inertia of the molecules about any axis perpendicular to the C6 axis were calculated from these data as I(C6H6) = 1.4759 × 10−45 kg m2, I(C6D6) = 1.7845 × 10−45 kgm2. Calculate the CC and CH bond lengths.For 16O2, Δ ᷉ G values for the transitions v = 1 ← 0, 2 ← 0, and 3 ← 0 are, respectively, 1556.22, 3088.28, and 4596.21 cm−1. Calculate ᷉v and xe. Assume ye to be zero.The vibrational levels of 23Na127I lie at the wavenumbers 142.81, 427.31, 710.31, and 991.81 cm−1. Show that they fit the expression (v + 1/2) ᷉v − (v + 1/2) 2xe ᷉v, and deduce the force constant, zero-point energy, and dissociation energy of the molecule.
- a.) The spacings of the rotational fine structure lines of carbon dioxide 12C16O2 are determined from IR spectroscopy to be 0.7604 cm-1. Calculate the C=O bond length of the molecule (given masses: m(12C) = 12 amu, m(16O) = 15.9949 amu).Ans = ______ Angstroms b.) Suppose that the wavenumber of the J = 1 ← 0 rotational transition of 1H79Br considered as a rigid rotor was measured to be 17.89 cm-1, what is the bond length? Ans = ____ Angstroms When the moment of interia is 3.132x10^-47 kg*m^2(Given the isotopic masses:(m(79Br) = 78.9183 amu, m(81Br) = 80.9163 amu)Calculate (i) the thermal wavelength, (ii) the translational partition function of a Ne atom in a cubic box of side 1.00 cm at 300 K and 3000 K.Suppose you were seeking the presence of (planar) S03 molecules in the microwave spectra of interstellar gas clouds. (a) You would need to know the rotational constants A and B. Calculate these parameters for 32S16O3, for which the S-O bond length is 143 pm. (b) Could you use microwavespectroscopy to distinguish the re lative abundances of 32S16O3 and 33S16O3?
- If the transverse relaxation time, T2, is 50ms, after what time will theenvelope of the free induction decay decrease to half its initial amplitude?Consider a methane molecule in the gas phase. The energy difference between the ground and the 1st excited vibrational state for the symmetric stretch vibrational mode is 2917 cm-1. a. How many vibrationalnormalmodes are there for CH4? b. Will any of these vibrational modes be Raman active? Explain your answer.Estimate the centrifugal distortion constant for 1H127I, for which ᷉ B = 6.511 cm−1 and ᷉v = 2308 cm−1. By what factor would the constant change when 2H is substituted for 1H?