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The spacing of lines in the microwave spectrum of 27Al1H is 12.604 cm−1; calculate the moment of inertia and bond length of the molecule.
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- 15. The far-infrared spectrum of HI consists of a series of equally spaced lines with Δν(bar) = 12.8 ^-1 cm. What are (a) the moment of inertia and (b) the internuclear distance?A space probe was designed to see 13CO in the atmosphere of Saturn by looking for lines in its rotational spectrum. If the bond length of CO is 112.8 pm, at what wave number do the first three rotational transitions appear?Using the rigid rotor model, calculate the energies in Joules of the first three rotational levels of HBr, using for its moment of inertia I = μR2, with μ = mHmX/(mH + mX) and equilibrium internuclear distance = 1.63 Å. To put these energies into units that make sense to us, convert energy to kJ/mol. (Simply estimate atomic masses from the average atomic weights of the elements given in the periodic table).
- Assume that the states of the π electrons of a conjugated molecule can be approximated by the wavefunctions of a particle in a one-dimensional box, and that the magnitude of the dipole moment can be related to the displacement along this length by μ = −ex. Show that the transition probability for the transition n = 1 → n = 2 is non-zero, whereas that for n = 1 → n = 3 is zero. Hints: The following relation will be useful: sin x sin y = 1/2cos(x − y) − 1/2cos(x + y). Relevant integrals are given in the Resource section.(a) Express the moment of inertia of an octahedral AB6 molecule in terms of its bond lengths and the masses of the B atoms. (b) Calculate the rotational constant of 32S19F6 , for which the S—F bond length is 158 pm..Assuming reasonable bond lengths, estimate the frequency of the J=15 – 14 transition in the linear molecule N≡C-(C≡C)6-H. In which region of the electromagnetic spectrum does it lie
- 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.Explain how the bond length of a diatomic molecule may be determined from the measured spacing between the lines observed in its microwave spectrum.The moment of inertia of an SF6 molecule is 3.07 × 10−45 kg m2. What is the minimum energy needed to start it rotating?