Broadening of spectral line

It has been observed that no strictly sharp spectral lines have been observed. It has a fixed width that depends on the reserving power of the optical instrument by which it is observed.

Generally the half intensity width is considered as a width of a spectral line which is defined as the distance between two points at two sides from the centre at which the intensity is half of that at centre where the point of maximum intensity.

There are many causes of broadening of spectral lines. Out of which we consider the following types

1. Natural Broadening (Uncertainty Principle)

  • Cause: According to the uncertainty principle in quantum mechanics, there is an inherent uncertainty in the energy levels of atoms or molecules. This results in a natural broadening of spectral lines.

  • Significance: Natural broadening provides information about the lifetime of excited states in atoms or molecules. Shorter lifetimes correspond to broader lines. This can reveal details about the dynamics of atomic or molecular transitions and their interactions with the surrounding environment.

2. Doppler Broadening

  • Cause: This occurs due to the thermal motion of atoms or molecules. As particles move towards or away from an observer, the frequency of emitted or absorbed radiation shifts due to the Doppler effect.

  • Significance: Doppler broadening provides information about the temperature of the emitting or absorbing material. It allows us to determine the velocity distribution of particles and their thermal energy. In astrophysics, for instance, Doppler broadening helps in studying the temperature and motions within stars and galaxies.

3. Pressure Broadening (Collisional Broadening)

  • Cause: When atoms or molecules collide with each other, energy levels can temporarily shift, leading to a broadening of spectral lines.

  • Significance: Pressure broadening is sensitive to the density and pressure of the gas. It provides information about the physical conditions of the medium where the spectral lines originate, such as in stellar atmospheres or laboratory plasmas.

4. Stark Broadening

  • Cause: In the presence of an electric field (such as in strong electric discharges or in the atmosphere of stars), spectral lines can be broadened due to the Stark effect, where energy levels are perturbed by the electric field.

  • Significance: Stark broadening can indicate the presence and strength of electric fields in various environments. It is particularly useful in plasma physics and astrophysics for studying the conditions within stars and in laboratory plasma experiments.

5. Quenching Broadening

  • Cause: This occurs when the atoms or molecules are subjected to collisions or interactions that "quench" or deactivate excited states more rapidly than spontaneous emission would occur.

  • Significance: Quenching broadening provides insights into collisional processes and interactions within gases. It helps in understanding how energy is redistributed and lost in various environments.

1. Natural width

According to classical electromagnetic theory, a vibrating electric charge is continuously damped by radiating energy. The energy of such an oscillator decreases exponentially

And the amplitude is

where Eo is energy at t= 0 and Ao is corresponding amplitude, Γ is damping constant whose value is given by

𝛾_o is the natural frequency of oscillation. Using fourier analysis, the variation of intensity with frequency is given by

For 𝛾= 𝛾_o, the intensity is maximum as shown in figure.

From above equation, it implies that for half intensity the denominator in equation 4 must satisfy the condition

4𝜋² ( 𝛾_o - 𝛾)² = ( Γ/2)²

2𝜋 ( 𝛾_o - 𝛾) = ( Γ/2)

Δ𝛾 = Γ/4𝜋 .......5

Thus the half intensity width of spectral lines in terms of frequency is

And half intensity width in terms of wavelength will be

Therefore the natural width of the spectral line is nearly 10^-4 A° which is same for all wavelength.

Broadening of spectral lines is crucial because it allows scientists to infer physical properties such as temperature, density, pressure, and electric fields in celestial objects, laboratory plasmas, and other environments. By analyzing the shape and width of spectral lines, researchers can probe the conditions and dynamics of matter under extreme conditions that would otherwise be difficult to observe directly. This information is fundamental for advancing our understanding of stars, galaxies, interstellar gas clouds, and many other astrophysical and laboratory phenomena.

This note is a part of the Physics Repository.