How Do Stokes Lines Help Explain Atomic Spectra?
The formation of stokes lines is an important part of the Raman spectrograph. We know that Raman spectra incorporate many important aspects regarding the scattering of light. According to Raman scattering, when a light ray is allowed to p[ass through a transparent medium, the particles of the molecules will scatter a part of light in all possible directions. Raman scattering is based on inelastic scattering of the monochromatic light, usually a LASER light in the UV region, near the Infrared region, and near the UV range.
A few parts of the scattered light have lower frequencies (higher wavelengths) than incident light, giving rise to the origin of the Stokes lines in a Raman spectrum. This occurs when a photon transfers part of its total energy to the molecule and, since it encounters a loss of energy, its frequency will be shifted towards lower frequencies. The molecule absorbs energy to undergo the transition to higher vibrational states. Thus, the stroke lines are those lines whose wavelengths are longer than that of the incident light. In this article, we will look into the concept of stokes line with comparison to anti-stokes lines, detailed explanation for stokes & anti stokes lines, calculating stokes and antistokes, and Raman frequency. So, without any further ado, let us understand the stokes & anti-stokes lines.
Stokes and Antistokes Lines
A typical Raman spectrum is centered at the frequency of incident light (normally a laser light in the visible part of the electromagnetic spectrum), with very high intensity owing to Rayleigh scattering. Stokes lines can be observed towards the lower frequencies and anti-Stokes can be seen towards the higher frequencies, later they are mirrored at the center of the Raman spectrum. Nevertheless, Stokes lines are more intense in comparison with the anti-Stokes counterparts, because the vibrational ground state is more populated than excited states. Let us understand the anti-stokes line and stroke lines in Raman spectra in detail as follows.
When a beam of monochromatic light is passed through the transparent liquid or gasses known as the scatterer, a small fraction of it is scattered due to the collision between the molecules of the scatterer and the photons of the light. It is explained by assuming that an energy level is formed like a complex between the molecule and the photon during a very short (About ～10⁻15 s interval of collision.
The photons have energy hv, which is insufficient for molecules to make a transition from the ground electronic state with low vibrational and rotational states to the higher electronic state.
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Two cases are noticed depending upon whether the collision between the molecules and the photons are elastic or inelastic.
1. If the Collision is Elastic:
Suppose that the collision between the molecules and the photons is an elastic collision, then the total energy of the molecules and the photons will remain unchanged. This explains that the molecule will not get scattered completely without absorbing photon energy. In other words, the collision will merely induce forced oscillations in the molecule. This will result in unmodified lines and this kind of scattering of monochromatic light is known as the Rayleigh scattering.
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2. If the Collision is Inelastic:
If the collision between the molecule and the photon is inelastic in nature then, there will be the exchange or transfer of energy between the molecule and the photons. This case is further studied by subdividing into two special cases that will lead to the explanation of the formation of stokes and anti-stokes lines.
1. The molecule is in the lower vibrational and rotational level before the collision and is present in any one of higher rotational- vibrational states of the same level (as allowed by selection rules) after Excitation and emission of a photon. Thus, the molecule absorbs or gains energy equal to the difference in the two energy levels involved. Because the energy is supplied by a photon of the incident light, the frequency of the emitted photon is less. The above explanation can be understood by the following diagram given below.
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2. Before the collision, the molecule is present in one of the excited vibrational and rotational energy states but after the emission of a photon, it occupies one of the lower vibrational energy states of the same level according to the selected role. Since the molecule imparts some of its intrinsic energy to the incident, thus the incident photon has higher energy than the incident photon. The above explanation can be understood by the following diagram given below.
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These two special cases constitute the Raman scattering and hence gives an idea about Raman spectra. Such scattering was observed by Sir C V Raman in 1928.
Raman Frequency
The frequency of the scattered light or the emitted photon which either lower or higher than the frequency of the incident photon is known as the Raman Frequency, denoted by vR
and it is given by the formula:
⇒ v\[_{R}\] = v\[_{0}\] + \[\frac{\epsilon' - \epsilon'' }{h}\] ……….(1)
Where,
\[ v_{0}\] - The frequency of the incident photon
\[ v_{R} \] - The frequency of scattered photon or Raman frequency
\[ \epsilon’\] - The energy of the molecule before the collision or before impact
\[ \epsilon’’ \] - The energy of the molecule after a collision or after impact
Now, if:
\[ \epsilon’\] = \[ \epsilon’’ \] then we have \[v_R = v_0\], This explains the Rayleigh scattering and formation of unmodified lines.
\[ \epsilon’\] > \[ \epsilon’’ \], then we have \[v_R < v_0\], i.eThe frequency of scattered light is less than the frequency of the incident light, this results in the formation of Stokes lines in Raman spectra.
\[ \epsilon’\] > \[ \epsilon’’ \], then we have \[v_R > v_0\], i.eThe frequency of scattered light is more than the frequency of the incident light, this results in the formation of Anti Stokes lines in Raman spectra.
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Anti Stokes Lines
Anti Stokes lines are those modified lines obtained with wavelengths shorter than the incident line. It is possible for the molecule to transfer energy to the incident photon and shift the frequency of scattered light to higher values (lower wavelengths). When this occurs, the molecule that is in an excited vibrational state undergoes the transition to the lower state or even to the ground state. A set of lines occurs in a Raman spectrum called anti-Stokes lines, owing to this process.
When the molecule makes a transition with ΔJ = -2, the scattered photon emerges with increased energy. These transitions account for the anti-Stokes lines of the Raman spectrum. The anti Stokes lines appear at displacements of 6B, 10B, 14B...for J = 2,3,4…. And the high-frequency side of the incident radiation. Note that J = 2 is the lowest state that can contribute to the spectrum under the selection rule ΔJ = -2.
Did You Know?
Sir C V Raman won the Nobel prize for his extraordinary contribution to the theory of scattering and he won the Nobel prize for Raman scattering. Sir C V Raman was the first Indian scientist to win the Nobel prize in his honor every year on February 28th National science day is celebrated. The Raman scattering experiment was first demonstrated on February 28, 1928.
FAQs on Stokes Lines: Definition, Applications & FAQs
1. What are Stokes lines in the context of Physics and Raman Spectroscopy?
In Raman Spectroscopy, Stokes lines are spectral lines that appear at a lower frequency (or longer wavelength) than the incident light. This phenomenon occurs due to inelastic scattering, where a photon from the incident light interacts with a molecule, transfers some of its energy to excite the molecule to a higher vibrational energy level, and is then scattered with reduced energy.
2. What is the main difference between Stokes lines and anti-Stokes lines?
The primary difference lies in the energy exchange between the incident photon and the molecule:
- Stokes Lines: The molecule is initially in its ground state. It absorbs energy from the photon, causing the scattered photon to have less energy and a lower frequency.
- Anti-Stokes Lines: The molecule is already in an excited vibrational state. It transfers energy to the photon during the interaction, causing the scattered photon to have more energy and a higher frequency.
3. Why are Stokes lines almost always more intense than anti-Stokes lines?
The intensity of spectral lines is proportional to the population of the initial energy state. At normal temperatures, most molecules exist in the lowest energy ground state rather than in an excited vibrational state. Since Stokes scattering originates from molecules in the ground state, there is a much higher probability of it occurring, resulting in significantly more intense Stokes lines compared to the much weaker anti-Stokes lines.
4. How does increasing the temperature of a sample affect the intensity of Stokes and anti-Stokes lines?
As the temperature of a sample increases, more thermal energy becomes available, causing more molecules to populate higher vibrational energy levels. This has two effects:
- The intensity of anti-Stokes lines increases because there are more molecules in the initial excited state required for this type of scattering.
- The intensity of Stokes lines decreases slightly as the population of the ground state diminishes.
However, even at elevated temperatures, the ground state typically remains the most populated, so Stokes lines usually remain more intense overall.
5. How do Stokes and anti-Stokes lines differ from Rayleigh scattering?
The fundamental difference is whether the scattering is elastic or inelastic. Rayleigh scattering is an elastic process where the scattered photon has the exact same energy and frequency as the incident photon. It is the most dominant form of scattering. In contrast, both Stokes and anti-Stokes lines are a result of Raman scattering, which is an inelastic process where the scattered photon's energy is either decreased (Stokes) or increased (anti-Stokes).
6. What practical information about a substance can we learn from its Stokes lines?
Analysing Stokes lines provides a powerful tool for chemical analysis. The specific energy shift, known as the Raman shift, between the incident light and a Stokes line corresponds directly to a specific vibrational mode of the molecule. This acts as a unique 'molecular fingerprint', allowing scientists to:
- Identify unknown substances.
- Study the strength and nature of chemical bonds.
- Determine the molecular structure and composition of a sample.
- Analyse crystalline phases and material stress.
7. Is it possible for anti-Stokes lines to be more intense than Stokes lines?
Yes, although it is not common under normal conditions. For anti-Stokes lines to be more intense than Stokes lines, a state of population inversion must be achieved. This is a special condition where more molecules are in an excited energy state than in the ground state. Such a scenario can be created using techniques like optical pumping with another laser, which artificially populates the higher energy levels, thereby increasing the probability of anti-Stokes scattering dramatically.
