# Heisenberg Principle in Context of Absorption/Emission Spectroscopy

• DDTea
In summary, the Heisenberg Uncertainty Principle states that some operators do not commute, so the order of measurements determines the results with spectroscopy. This is why we see discrete line spectra with atoms, as the energy of their electronic transitions cannot be measured with arbitrary precision over a finite period of time. Molecules, on the other hand, show much broader absorption and emission spectra because they have vibrational and rotational transitions as well. These broad spectra are not observed with atoms as they are symmetric and have no vibrational or rotational degrees of freedom.
DDTea
Why do we get line spectra from absorption/emission of atoms, but band spectra from absorption/emission of molecules?

As I understand the Heisenberg Uncertainty Principle mathematically, some operators do not commute and as such, the order of measurements determines the results. In regard to spectroscopy, then, the energy of electronic transitions cannot be measured with arbitrary precision over a finite time period. That makes sense with say, UV/Vis spectroscopy of organic molecules like benzene: we see a big band around ~250 nm corresponding to the pi-->pi* shift. We can determine the energy of that shift more precisely by taking multiple measurements and averaging them.

What about atoms, though? Why do we see discrete line spectra? Wouldn't that violate the Heisenberg uncertainty principle to know *exactly* the energy of their electronic transitions over a finite period? Or rather, how exactly *do* we know the energy of their transitions? Are they the results of theoretical calculations or actual instrumental measurements?

Molecules show much broader absorption and emission spectra because, in addition to electronic transitions, molecules have vibrational and rotational transitions as well. See the image here. The diagram shows two electronic states (S0 and S1). Within those states are shown different rotational/vibrational states. Now, at normal temperatures, nearly all of the molecules will be in the ground electronic and vibrational states. Upon absorption of a photon, the molecule will be excited to one of the vibrational states in S1. As you can see, the energy of the transition depends on which vibrational state the molecule occupies after excitation. If the molecule goes into the v=1 state, the transition will have used a higher energy photon than a transition to the v = 0 state. The vibrational state that the molecule ends up in after absorption of a photon is a random process with probabilities dictated by the Franck-Condon principle. Therefore, because the molecule can be excited into any number of vibrational states with different energies, the molecule can absorb photons with a fairly wide range of energies.

After excitation, the molecule relaxes quickly to the ground vibrational state of S1. This generally occurs through a non-radiative relaxation process called internal conversion. When the molecule emits a photon to return to the ground electronic state, the molecule can fall into any number of vibrational states in S0. So, if the molecule ends up in the v=0 state after emission it will have emitted a photon of higher energy than a molecule that ends up in the v=1 state. Therefore, because the molecule can end up in a number of different vibrational states after emission of a photon and these vibrational states have different energies, molecules can emit photons with a relatively broad range of energies.

These broad spectra are not observed with atoms because atoms are symmetric and have no vibrational or rotational degrees of freedom.

Although the emission and absorption spectra of atoms are described as line spectra, they do still have finite width (dependent on the time over which emission/absorption are observed) and obey the Heisenberg uncertainty principle. The term "line spectra" merely reflects that the absorption/emission spectra of atoms are much narrower than the broad absorption/emission spectra of molecules.

Ygggdrasil said:
Molecules show much broader absorption and emission spectra because, in addition to electronic transitions, molecules have vibrational and rotational transitions as well.

Yours is the most clear, efficient, convincingly knowledgeable explanation i have ever encountered here on physorg.
We are grateful for your interest and skills in our world of science.
Thank you.

## 1. What is the Heisenberg Principle in the context of absorption/emission spectroscopy?

The Heisenberg Principle states that it is impossible to know both the exact position and momentum of a particle at the same time. In the context of absorption/emission spectroscopy, this means that the more accurately we measure the energy of a particle, the less accurately we can determine its position.

## 2. How does the Heisenberg Principle affect absorption/emission spectroscopy measurements?

The Heisenberg Principle states that there is an inherent uncertainty in measuring the energy of a particle. This uncertainty translates to a broadening of spectral lines in absorption/emission spectroscopy, making it difficult to accurately determine the energy levels of a system.

## 3. Can the Heisenberg Principle be overcome in absorption/emission spectroscopy?

No, the Heisenberg Principle is a fundamental law of quantum mechanics and cannot be overcome. However, there are techniques such as time-resolved spectroscopy that can help minimize the effects of uncertainty in measurements.

## 4. How does the Heisenberg Principle relate to the uncertainty principle?

The Heisenberg Principle is a specific instance of the more general uncertainty principle, which states that there is a fundamental limit to the precision with which certain pairs of physical properties can be known simultaneously. The Heisenberg Principle specifically applies to the position and momentum of a particle.

## 5. What are the practical implications of the Heisenberg Principle in absorption/emission spectroscopy?

The Heisenberg Principle makes it challenging to accurately measure the energy levels of a system, particularly when the energy differences between levels are small. To overcome this, scientists must use advanced techniques and carefully consider the effects of uncertainty in their measurements. Additionally, the Heisenberg Principle highlights the importance of understanding the limitations of our measurements and the need for further research and development in the field of spectroscopy.

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