spectral lines and broadening , lorentz, pressure, collisional broadening

1. Lecture No. 04
Course title:
Atomic Spectroscopy
Topic: Spectral lines and Broadening
Course instructor: Dr. Salma Amir
GFCW Peshawar

2. Spectral lines
 A spectral line is a dark or bright line in an otherwise uniform
and continuous spectrum, resulting
from emission or absorption of light in a narrow frequency range,
compared with the nearby frequencies. Spectral lines are often used
to identify atoms and molecules.
 These "fingerprints" can be compared to the previously collected
"fingerprints" of atoms and molecules, and are thus used to identify
the atomic and molecular components

3. Types of line spectra
 Spectral lines are the result of interaction between a quantum
system (usually atoms, but sometimes molecules or atomic nuclei) and a
single photon.
 When a photon has about the right amount of energy (which is connected to its
frequency) to allow a change in the energy state of the system, the photon is
absorbed.
 Then it will be spontaneously re-emitted, either in the same frequency as the
original or in a cascade, where the sum of the energies of the photons emitted will
be equal to the energy of the one absorbed (assuming the system returns to its
original state)

4. A spectral line may be observed either as an emission line or
an absorption line.

5. Absorption and emission lines
 An absorption line is produced when photons from a hot,
broad spectrum source pass through a cold material. The
intensity of light, over a narrow frequency range, is
reduced due to absorption by the material and re-
emission in random directions.
 By contrast, a bright emission line is produced when
photons from a hot material are detected in the presence
of a broad spectrum from a cold source. The intensity of
light, over a narrow frequency range, is increased due to
emission by the material.

6. Information derived from Spectra
 Chemical composition of the gas Spectral lines are highly atom-specific, has a characteristic
"fingerprint" pattern of emission/absorption lines corresponding to specific energy levels
possible for electrons in that species. and can be used to identify the chemical composition of
any medium capable of letting light pass through it. The presence of an element can often be
determined by seeing its characteristic lines in a spectrum.
 Physical states of the gas Spectral lines also depend on the physical conditions of the gas, so
they are widely used to determine the chemical composition of stars and other celestial bodies
that cannot be analyzed by other means, as well as their physical conditions.
 Degree of excitation or ionization Number of excited or ionized atoms is reflected in the
strengths of lines corresponding to these transitions or ionized species.
 Temperature of the gas
 Density/pressure of the gas Higher density/pressure -- greater degree of excitation

7. Broadening of lines
 The result of a radiative atomic transition from an upper to a lower energy level is
radiation at a particular wavelength, as defined by
𝜆 =
ℎ𝑐
𝐸2 − 𝐸1
where h is Planck's constant and c is the velocity of light in vacuo.
However, atomic lines are not infinitely thin as would be expected and their width is
discussed by talking about half-width (∆v cm-1), illustrated in Fig

8. Spectral line broadening
(Reasons)
 There are a number of effects which control spectral line shape. A
spectral line extends over a range of frequencies, not a single
frequency (i.e., it has a nonzero linewidth). In addition, its center
may be shifted from its nominal central wavelength.
 There are several reasons for this broadening and shift. These
reasons may be divided into following categories –
 Natural-width broadening
 Doppler broadening
 Lorentz broadening
 Broadening due to extended fields.

9. 1. Natural-width broadening
 The natural width of a spectral line is determined by the Heisenberg
uncertainty principle and the lifetime of the excited state. According to
Heisenberg’s uncertainly principle, the product of the uncertainty in the
measurement of energy, ΔE, and time Δt is:
ΔEΔt ≥ h/2π
 Most excited states have lifetimes of 10−8 –10−10 s, so the uncertainty in the
energy of the electron slightly broadens the spectral line. This is called the
natural linewidth and is on the order of 10−4 Å (1.0 Å = 1.0 × 10−10 m).

10. 2. Doppler broadening
 Doppler broadening, due to random kinetic motion toward and away from the
detector, results in broadening of the spectral line on the order of 0.01–0.05 Å.
The random atomic movement of the atoms is directly related to the temperature,
which is why this broadening mechanism is called thermal.
 As we know from the Maxwell-Boltzmann statistics the speed of gas atoms follow
a gaussian profile and the mean energy is on the order of kT, where k is the
Boltzmann constant and T is the temperature. Mathematically it can be shown
that the spectral line broadening profile is also Gaussian, with a value given by:
 The equation shows that broadening increases with temperature and is higher for
light atoms. By doing the calculations you see that for hydrogen at the
temperature of 6000°K, the width of the Hα line is 0.036 nm.

11. 3. Pressure (Lorentz) broadening
 Collisions with other atoms in the atomizer lead to pressure (Lorentz)
broadening, on the order of 0.05 Å. which can become predominant in
high-density gas plasma emissions (high pressures).
 In this case, the spectral line profile is not Gaussian but Lorentzian,
characterized by a narrower spike and longer wings.
 Different gases have different effects. Collisional theory offers the
best fit equations to describe these events at the line centre, and
statistical theory describes the events at the wings.
 Lorentz broadening increases with pressure (P) and temperature (T),
and is generally regarded as being proportional to P and T . Thus, ∆v
increases with increasing T and P. It is accepted that Lorentz
broadening affects the wings of the profile.

13. 4. External Fields Broadening
 Magnetic or Electrical external fields cause the Zeeman effect or the
Stark effect with the splitting of the spectral lines and the final result
of causing a broadening of the lines.
 Stark broadening occurs as a result of atoms encountering strong
local electrical fields.
 In the presence of a magnetic field,
Zeeman splitting of the electronic
energy levels also occurs.