Recall the selection rules for purely rotational microwave spectra: ΔJ = ±1. This came from angular momentum conservation (a photon has spin angular momentum ħ). In Raman scattering, one photon comes in and one photon goes out. What are the selection rules for rotational Raman transitions?(A) ΔJ = ±1(B) ΔJ = 0, ±1, ±2(C) ΔJ = 0, ±2 *(D) ΔJ = 0This is because a photon comes in and transfers one unit of ħ to the molecule, and one photon comes out again, which again has one unit of ħ. If the incoming and outgoing photons have the same spin, ΔJ = 0. If they have opposite spins, ΔJ = ±2. ____.

Recall the selection rules for purely rotational microwave spectra: ΔJ = ±1. This came from angular momentum conservation (a photon has spin angular momentum ħ). In Raman scattering, one photon comes in and one photon goes out. What are the selection rules for rotational Raman transitions?(A) ΔJ = ±1(B) ΔJ = 0, ±1, ±2(C) ΔJ = 0, ±2 *(D) ΔJ = 0This is because a photon comes in and transfers one unit of ħ to the molecule, and one photon comes out again, which again has one unit of ħ. If the incoming and outgoing photons have the same spin, ΔJ = 0. If they have opposite spins, ΔJ = ±2. ____.

Principles of Instrumental Analysis

7th Edition

ISBN:9781305577213

Author:Douglas A. Skoog, F. James Holler, Stanley R. Crouch

Publisher:Douglas A. Skoog, F. James Holler, Stanley R. Crouch

Chapter15: Molecular Luminescence Spectrometry

Section: Chapter Questions

Problem 15.2QAP

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Rotational spectra are affected slightly by the fact that different isotopes have different masses. Suppose a sample of the common isotope 1H35Cl is changed to 1H37Cl. (a) By what fraction is the molecule’s rotational inertia different? (The bond length is 0.127 nm in each case.) (b) What is the change in energy of theℓ = 1 to theℓ = 0 transition if the isotope is changed?
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.
Q5) Which of the following transitions are electric-dipole allowed? (i) 'Πε Π, (ii) ἦΣ → 'Σ, (iii) Σ+ Δ, (iv) Σ΄ «Σ, (v)Σ → Σ.
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?
C) (A) Which molecule has a chemical formula of C₁0H17CIO OH (C) 4 OH -CI (D) ^ 67. Which bond in this molecule will have a vibrational stretching frequency located at 1,742 cm ¹2 (B) (D) HO H CI OH OH (B) (D)
A rotating diatomic molecule absorbs radiation and has moment of inertia, I, equal to 1.00 x 10-46 kg m², a. which is the frequency of radiation when the molecule undergoes a transition from J = 4 to J=3?
Calculate the value of ml for a proton constrained to rotate in a circle of radius 100 pm around a fixed point given that the rotational energy is equal to the classical average energy at 25 degrees C. (Mass of a proton = 1.6726 x 10^-27 kg, classical average energy=1/2kBT, where kBT is Boltzman constant = 1.30 x 10^ -23 J K^-1, and T is the temperature.)
P7E.5 In infrared spectroscopy it is common to observe a transition from the v = 0 to v = 1 vibrational level. If this transition is modelled as a harmonic oscillator, the energy of the photon involved is ħo, where o is the vibrational frequency. (a) Show that the wavenumber of the radiation corresponding to photons of this energy, v, is given by v=@/2nc, where c is the speed of light. (b) The vibrational frequency of 'H*Cl is w = 5.63 x 10“s"; calculate v. (c) Derive an expression for the force constant k, in terms of v. (d) For "C"O the v = 0 →1 transition is observed at 2170 cm. Calculate the force constant and estimate the wavenumber at which the corresponding absorption occurs for "C*O. Use integer relative atomic masses for this estimate.
2/ Please explain the answer in detail The J = 0 to j = 1 transition for carbon monoxide (12C160) occurs at 1.153 × 105 MHz. Calculate the value of the bond length in carbon monoxide.
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
(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
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.