P11C.9 Provided higher order terms are neglected, eqn 11C.9b for the vibrational wavenumbers of an anharmonic oscillator, e AĞv+1/2 = Ỹ −2(v +1)x¸ỹ+…, is the equation of a straight line when the left- hand side is plotted against v + 1. Use the following data on CO to determine the values of ỹ and x¸ỹ for CO: V AĞ+1/2/cm-¹ 0 1 2143.1 2116.1 2 3 2088.9 2061.3 2033.5

P11C.9 Provided higher order terms are neglected, eqn 11C.9b for the vibrational wavenumbers of an anharmonic oscillator, e AĞv+1/2 = Ỹ −2(v +1)x¸ỹ+…, is the equation of a straight line when the left- hand side is plotted against v + 1. Use the following data on CO to determine the values of ỹ and x¸ỹ for CO: V AĞ+1/2/cm-¹ 0 1 2143.1 2116.1 2 3 2088.9 2061.3 2033.5

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

See similar textbooks

Similar questions

E11C.2(a) Calculate the percentage difference in the fundamental vibrational wavenumbers of "Na Cl and "Na"Cl on the assumption that their force constants are the same. The mass of "Na is 22.9898m..
(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.
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?
Suppose an oxygen atom (m = 15.9949mu) is adsorbed on the surface of a nickel nanoparticle by a bond of force constant 544 N m-1. Calculate the wavelength of a photon needed to excite a transition between its neighbouring vibrational energy levels.
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.
(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).
Calculate the frequency and wavenumber of the J = 3 ← 2 transition in the pure rotational spectrum of 14N16O. The equilibrium bond length is 115 pm. Would the frequency increase or decrease if centrifugal distortion is considered?
The wavenumber of the fundamental vibrational transition of Cl 2 is 565 em·'. Calculate the force constant of thebond.
Calculate the energy of the J=0 to J=1 rotational transition of the O₂ molecule with a bond length of 121 pm.
Suppose that the internuclear distance may be written R = Re + x where Re is the equilibrium bond length. Also suppose that the potential well is symmetrical and confines the oscillator to small displacements. Deduce expressions for 1/⟨R⟩2, 1/⟨R2⟩, and ⟨1/R2⟩ to the lowest non-zero power of ⟨x2⟩/Re2 and confirm that the values are not the same.
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.
The pure rotational spectrum of1H131I consists of a series of linesseparated bu 13.10 cm−1. Calculate (a) the moment of interia, and (b) the internuclear distance.