Determining Spectra in Quantum Theory

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The reason for this shape of the spectrum is that gaseous CO 2 molecules not only vibrate, they also rotate. However, the molecules cannot rotate at any given rotational speed. Due to quantum physical laws only discrete rotational levels occur and these create the discrete spectral lines.

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The absorption of a photon induces the asymmetric stretching vibration and also brings the molecule onto the next higher or lower rotational level. This happens because the photon also transfers a quantum of angular momentum. From the position and intervals of these peaks it is possible to determine the characteristics of the molecule, which we assumed to be known here.

The height distribution of the peaks is a result of the Boltzmann distribution of rotational energies and therefore depends on temperature.

Planck’s Quantum Theory

And what about the two other vibrational modes shown in Figure 1? The middle line depicts the symmetric stretching vibration.

Spectral Line | COSMOS

This is characterized by the fact that the positive and negative centers of charge do not move against each other because the vibration is symmetric to the center of the molecule. So no vibrating dipole occurs, no infrared energy can be absorbed or radiated off and therefore this vibration is not visible in the infrared spectrum. On the other hand, this vibration is Raman active — but that is a story for another day. The vibration shown at the bottom of Figure 1 is a deformation vibration with two-fold degeneration. Degeneration means that several vibrations with the same frequency occur, here both in the and out of the image plane.

This vibration is infrared active and shows a distribution of the peaks similar to that shown in Figure 3. However, in contrast to Figure 3 there is a very strong peak at the fundamental resonance of cm The reason for this peak to be present is that the vibrating dipole occurs in normal direction to the main axis of the molecule.

Then the transfer of vibrational energy is also possible without a change of the rotational level. Infrared spectroscopy is a frequently used method in chemical analysis. Its functioning is based on the laws of quantum physics and these are clearly expressed in the spectra. Unfortunately, I cannot see figure 1.

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Figure 1: The normal modes of vibration of a CO2 molecule. Top: Asymmetric stretching vibration. Middle: Symmetric stretching vibration. Bottom: Deformation vibration Determining the concentration The number of infrared photons of this wavelength which are taken up by the CO 2 molecules from the infrared light is indicative of the number and concentration of the molecules in the sample. Figure 2: Absorption coefficient over the wave number for water with dissolved carbon dioxide Figure 2 shows part of the measured spectrum of a water sample containing dissolved carbon dioxide.


Measuring in the gas phase As we have seen that the surrounding water has an influence on the spectrum of the dissolved CO 2 we now want to observe the infrared spectrum of pure CO 2 in gaseous form. Figure 3: Asymmetric stretching vibration in the spectrum of gaseous carbon dioxide. Summary Infrared spectroscopy is a frequently used method in chemical analysis. Many thanks to Dr.

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Roman Benes at Anton Paar for his contributions to this blog post. Show all comments 3 dear sir or Madam, Thanks for the useful explanation. Thank you for your comment, now you should be able to see Figure 1.

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While the Bohr model and the other models were amazingly successful at explaining a number of atomic properties, the observations these models could not explain hinted at the need for a better theory quantum mechanics. Belloni, W.

Christian, and A. Preface I. Introduction 1: Introduction to Physlets II. Chapter 4: From Blackbody to Bohr.

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Sections 4. Problems 4. Chapter 4: From Blackbody to Bohr The late s and early s saw physics move from the classical period described by Newton's laws and Maxwell's equations to what we now call modern physics explained by special relativity and quantum theory. Table of Contents Sections Section 4.