1. [10] Consider an adsorption band in the combined rotational-vibrational spectrum of a linearmolecule, where the fundamental vibrational frequency involved in the observed band is 2325 cm-¹and the rotational constant of the molecule is B=2.4 cm³. Say hypothetically, the specific selectionrules for the rotational states are AJ = ±2. At what wave numbers would the first three peaks thatoccur at both higher and lower wave numbers than fundamental vibrational frequency occur at? Whattransitions would each peak correspond to?

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Answered: 1. [10] Consider an adsorption band in…

Chemistry

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ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

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Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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The vibrational energy levels for XO molecule can be described by the following formula: E(n) in Joule = 1.88x10-20(n+1/2) – 2.68x10-22(n+1/2)² where n is the vibrational quantum number. What would be the equilibrium dissociation energy (De) of the XO molecule in a kJ mol-1?
Calculate the wavenumbers of the two highest energy vibrational transitions for the 1271³5 CI molecule. [Note: m(¹271) = 126.9045 u, and m(35CI) = 34.9688 u; the vibrational wavenumber (V) is 384.3 cm³¹; the first order anharmonicity constant (X₂) is 0.0039.] - Hint: For this anharmonic oscillator, the question asks for an estimate of the type G(v+1) – G(v) = AG+2 for AG1/2 and AG3/2-
A Morse oscillator, V(r) = D[1 − e−a(r—ro)]², has D = 164 kJ/mole and w→ ve 1250 cm-1. Compute the energy level (in cm-1) corresponding to the eigenstate shown below. = (Note that the energy units, 11.9627 J/mole = 1 cm-1. It might be helpful to convert the value of D to units of cm-1 before you evaluate the energy level.) www
Determine the CO and CS bond lengths in OCS from the rotational constants B (16O12C32S) = 6081.5 MHz, B (16O12C34S) = 5932.8 MHz.
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.
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.
1. Water shows the following vibrations: A₁ symmetrical stretch at 3657 cm ¹, B2 asymmetrical stretch at 3756 cm ¹, A₁ deformation at 1595 cm ¹¹. Determine which vibrations are active in IR absorption spectra and which are active in Raman spectra.
But molecules combine both vibrational and rotational states in such a way that both selection rules must be satisfied if we are only talking about absorption or emission of electromagnetic radiation (i.e. photons). 5 1 images from Krane Ch 9. Relative absorption : 0.330 L=3 to L=2 L=2 to L = 1 Electronic excited state. Electronic ground state L→ L-1 L = 1 to L = 0 Ť 0.340 0.350 SE Energy (eV) 2B 0.360 : hf L=0 L=1 L=2 to to to L = 1 L = 2 L = 3 Photo 4 1 3 1 2 1 1 0 1 1 5 0 4 0 30 20 1 0 0 0 LN L→ L+1 0.370 0.380 no emission here because AL # 0, AL = +1 AN = ±1, HCI spectra. In the middle of the gap is the energy hf that would correspond to a pure vibrational transition, which would violate the rotational selection rule. What is the value of hf for the HCI spectra?
The Morse potential energy is very useful as a simple representation of the actual molecular potential energy. When 85Rb1H was studied, it was found that ˜ν = 936.8 cm−1 and x_eν˜ = 14.15 cm−1. Plot the potential energy curve from 50 pm to 800 pm aroundRe = 236.7 pm. Then go on to explore how the rotation of a molecule may weaken its bond by allowing for the kinetic energy of rotation of a molecule and plotting V∗ = V + hcBJ˜ (J + 1) with B˜. Plot these curves on the same diagram for J = 40, 80, and 100, and observe how the dissociation energy is affected by the rotations. Hints: Taking B˜ = 3.020 cm−1 as the equilibrium bond length will greatly simplify the calculation. The mass of 85Rb is 84.9118mu
(b) The lowest frequency rotational transition of ²H³³C1 occurs at 10.92 cm1. Determine (i) The rotational constant, B, in Hz (ii) The bond length
hydrogen molecule absorbs ultraviolet radiation in a transition from its 1Σg+ ground electronic state to an excited state that is energetically close to a dissociative 1Σu+ state. The absorption band has a relatively large experimental linewidth. Account for this observation.
A molecule in a liqu id undergoes about 1.0 x 1013 collisions in each second. Suppose that every col lis ion is effective in deactivating the molecule vibrationally and that one coll ision in 200 is effective. Calculate the width (in cm-1) of vibrational transitions in the molecule.

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