The first three absorption lines in the pure rotational spec-trum of gaseous 12C16O are found to have the frequencies1.15 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 rotationallevels of CO, measured from the J = 0 state (in joules)(c) The C-O bond length (in angstroms)

Given that, Frequencies are 1.15×1011s-1, 2.30×1011s-1 and 3.46×1011s-1 Average interval between…

Answered: The first three absorption lines in the…

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter15: Introduction To Electronic Spectroscopy And Structure

Section: Chapter Questions

Problem 15.58E

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(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 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.
(hydrogen iodide, the superscripts represent the atomic mass number) (a) How fast will HI molecules rotate at the quantized rotational state with the rotational quantun number J of 2, given the bond length of 0.161 nim? (b) Calculate the effective force constant of the vibrational mode of HI at a wavenumber of 2300 cm' measured by infrared absorption spectrum. (c) HI has the bond energy of 3.06 eV. Applying the parabolic approximation to estimate the longest distance in which H and I atoms can be stretched before the dissociation of the molecular bond
Consider 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?
Q/ The bond length of the C0O molecule is 112.8 pm. Calculate the following (a) The reduced mass. (b) The rotational constant of CO when moment of inertia (I) is 1.4486 x 1046 kg.m² (c) Calculate the wavelength of the photon absorbed when a CO molecule initially in the J=2 level. makes a transition to the J=3 level.
(a) Calculate the moment of inertia of (i) 1H2, (ii) 2H2, (iii) 12C16O2, (iv) 13CO2 . (b) Calculate the corresponding rotational constants, expressing your answers as a frequency in hertz (Hz) and as a wavenumber in reciprocal centimetres (cm-1).
(A) Explain why the spacings between the bands in the vibrational spectrum of a diatomic molecule would be expected to decrease with increasing vibrational quantum number. (B) Explain why a molecule with no dipole moment is microwave inactive but may show an infrared spectrum. (C) Explain the occurrence of P and R branches in the rotational fine structure of a vibrational transition of a diatomic molecule such as HCl or CO.
3. ^14N^16O (the superscripts represent the atomic mass number) (a) NO molecules rotate at an angular velocity of 2.01x10^12 rev/s, at the quantized rotational state with the rotational quantum number J of 3. Calculate the bond length of NO molecules. (b) Can NO molecules rotate under light irradiation? Explain your answer. (c) Calculate the effective force constant of the vibrational mode of NO at a frequency of 5.63x10^13 Hz measured by the infrared absorption spectrum. (d) NO has a bond energy of 6.29 eV. Applying the parabolic approximation to estimate the longest distance in which N and O atoms can be stretched before the dissociation of the molecular bond
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.
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.
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.
Calculate the wavenumber of the first overtone transition w ith v = 2 ~ 0 in nitric oxide. NO. given that the valueof the vibrational wavenumber is v = 1904.03 em·' and theanharmonicity constant is x, = 0.0073.

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