# Stokes Lines

## Introduction

The formation of stokes lines is an important part of the Raman spectrography. 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 stokes 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, and detailed explanation for stokes anti stokes lines and calculating stokes and antistokes.

## Stokes and Antistokes Lines

A typical Raman spectrum is centred 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 centre 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 stokes lines in Raman spectra in detail as follows.

When a beam of monochromatic light is passed through the transparent liquid or gases 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.

Two cases are noticed depending upon whether the collision between the molecules and the photons are elastic or inelastic.

### I. 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.

### II. 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 state 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.

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.

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 the year 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 v$_{R}$ 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.e., the 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.e., the 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.

### Anti Stokes Lines

Anti Stokes lines are those lines 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 honour every year on February 28th National science day is celebrated. The Raman scattering experiment was first demonstrated on February 28, 1928.