In the microwave spectrum of the 12C16O molecule, the following consecutive lines have been measured: 115271.68; 230539.21 and 345798.45 MHz. Deduce the transitions that have given rise to these lines.Data: Atomic masses C = 12.000 u; O = 15.999 u; NA = 6.0225×1023 mol-1; h = 6.626×10-34J s
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In the microwave spectrum of the 12C16O molecule, the following consecutive lines have been measured: 115271.68; 230539.21 and 345798.45 MHz. Deduce the transitions that have given rise to these lines.
Data: Atomic masses C = 12.000 u; O = 15.999 u; NA = 6.0225×1023 mol-1; h = 6.626×10-34J s
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- The first three absorption lines in the pure rotational spec- trum of gaseous 12C16O are found to have the frequencies 1.15 x 1011, 2.30 × 1011, and 3.46 × 1011 s-1. Calculate: (a) The moment of inertia I of CO (in kg m²) (b) The energies of the J = 1, J = 2, and J = 3 rotational levels of CO, measured from the J = 0 state (in joules) (c) The C-O bond length (in angstroms)When ultraviolet radiation of wavelength 400 nm passes through 2.50 mm of a solution of an absorbing substance at a concentration 0.717 mmol dm−3, the transmission is 61.5 per cent. Calculate the molar absorption coefficient of the solute at this wavelength. Express your answer in square centimetres per mole (cm2 mol−1).A molecule in a liquid undergoes about 1.0 × 1013 collisions in each second. Suppose that (i) every collision is effective in deactivating the molecule vibrationally and (ii) that one collision in 100 is effective. Calculate the width (in cm−1) of vibrational transitions in the molecule.
- (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.The vibrational wavenumber of the oxygen molecule in its electronic ground state is 1580 cm−1, whereas that in the excited state (B 3Σu−), to which there is an allowed electronic transition, is 700 cm−1. Given that the separation in energy between the minima in their respective potential energy curves of these two electronic states is 6.175 eV, what is the wavenumber of the lowest energy transition in the band of transitions originating from the v = 0 vibrational state of the electronic ground state to this excited state? Ignore any rotational structure or anharmonicity.The molar absorption coefficient of a solute at 540 nm is 386 dm3 mol−1 cm−1. When light of that wavelength passes through a 5.00 mm cell containing a solution of the solute, 38.5 per cent of the light was absorbed. What is the molar concentration of the solute?
- 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.Calculate the energies of the first four rotational levels of 1H127I free to rotate in three dimensions; use for its moment of inertia I = μR2, with μ = mHmI/(mH + mI) and R = 160 pm. Use integer relative atomic masses for this estimate.Predict the shape of the nitronium ion, NO2+, from its Lewis structure and the VSEPR model. It has one Raman active vibrational mode at 1400 cm−1, two strong IR active modes at 2360 and 540 cm−1, and one weak IR mode at 3735 cm−1. Are these data consistent with the predicted shape of the molecule? Assign the vibrational wavenumbers to the modes from which they arise.
- Calculate the frequency of the J = 3 2 transition in the pure rotational spectrum of 12C16O. The equilibrium bond length is 112.81 pm.The moment of inertial of 12 C-16 O is I = 1.454 × 10°46 kg*m². The molecule also has a force constant for the C-O bond of 1920N*m. Take the atomic masses of 12 C to be 12.00aμ and 160 to be 16.00aµμ and the conversion factor from 16 atomic mass unit to kg to be 1, 66054 x 1027 kμ. a) Calculate the bond length for the 12 C-1 O molecule b) Calculate a the reduced mass for the 12 C-16 O molecule c) Calculate the vibrational frequency of 12 C-160 d) Calculate the zero point vibrational energy of this molecule e) Calculate the moment of inertia for the molecule f) Calculate the rotational energy of the J = 1 and J = 2 energy levelsConsider the rotational spectrum of a linear molecule at 298 K with a moment of inertia of 1.23×10−461.23\times10^{-46}1.23×10−46 kg m2 . (a) What is the frequency for the transition from J = 2 to J = 3? (b) What is the most populated rotational level for this molecule? Would the transition in (a) give the most intense signal in the rotational spectrum?
