In the last part, we looked at how photons are emitted and how this creates an emission and
absorption spectrum. In this part, we will examine how light or more specifically electromagnetic
radiation can interact with matter and what fingerprint these interactions leave behind.
Collisional Broadening Collisional or Pressure Broadening
In the last part, we discussed the emission and
absorption spectra and saw how discrete lines are created. These all assumed a
largely stationary gas particle with no other particles to interact with.
When you examine the emission spectra of low-pressure gases
you see very characteristic line emissions but as the pressure and
temperature increase the spectrum changes to a more continuous one.
Perturbation by colliding atoms in a high-pressure
gas results in the broadening of emission and absorption lines.
The broadening in frequency width is dependent upon the separation of the perturbing particles.
The finite duration of the emission of a photon by
the transition of an electron leads to a finite width line.
For high-pressure gas, radiating times can be much greater compared to the time between collisions.
The collisions cause premature transitions and emission of a photon. The decreased lifetime of
the state creates an increased uncertainty in photon energy, broadening the emission line.
As the temperature of the gas increases, the rate of collisions
increases and the broadening becomes more pronounced. In a low-pressure gas,
the particles can be considered as isolated which leads to discrete line emission. As
the pressure increases the system can no longer be considered as an isolated system. Instead,
the presence of surrounding atoms cause perturbations meaning there is no longer a fixed
separation between any two energy levels. This also applies to the process of absorption lines.
This means that the spectrum will become more and more continuous as the lines are broadened.
Photoelectric effect The photoelectric
effect is the emission of electrons when electromagnetic radiation, like light,
hits the material. The electrons emitted in this manner are called photoelectrons.
The experimental results disagree with classical electromagnetism,
which predicts that continuous light waves transfer energy to electrons, which would then
be emitted when they accumulate enough energy. If there was a subsequent change in the intensity of
the light there should theoretically be a change in the kinetic energy of the emitted electrons.
If the light source was sufficiently dim it should cause a delay in emission.
Experiments show that electrons are dislodged only when the light exceeds a certain frequency,
regardless of the light's intensity or duration of exposure. This demonstrated that light could
not be treated as a simple wave but instead a swarm of discrete packets known as photons.
Emission of conduction electrons from typical metals requires a few eV which
requires blue-violet light and ultraviolet light.
Thomson scattering Thomson scattering is the
elastic scattering of electromagnetic radiation by a free-charged particle. The particle's kinetic
energy and the photon frequency do not change as a result of the scattering. This works as
long as the photon energy is much smaller than the mass-energy of the particle. As long as the
motion of the particle is non-relativistic the main cause of the acceleration of the particle
will be due to the electric field component of the incident photon wave. The particle will move in
the direction of the oscillating electric field, resulting in electromagnetic dipole radiation.
The moving particle radiates most strongly in a direction perpendicular to its acceleration
and that radiation will be polarized along the direction of its motion.
For an electron, this limit is hard x-rays above this Compton scattering will take place.
Compton scattering Compton scattering
is an example of inelastic scattering of light by a free charged particle,
where the wavelength of the scattered light is different from that of the incident radiation.
It is the mechanism of scattering high-frequency photons after an
interaction with a stationary charged particle, usually an electron.
This results in a decrease in energy of the photon, its wavelength will increase.
Part of the energy of the photon is transferred to the recoiling electron.
If a photon interacts with a moving charged particle,
the particle can transfer its kinetic energy to the photon, increasing the photon's energy,
thereby decreasing its wavelength. This is called inverse Compton scattering
In both cases, the photon is absorbed and then
re-emitted in a different direction in order to conserve the momentum
Double and Multiple Compton Scattering
Is an important process in high-temperature photon-dominated plasma. A seed photon is
required and occurs when one incident photon is scattered on one electron and results in
two or more outgoing photons. Both double and multiple scattering cross sections;
which is a measure of the probability that photons interact with matter by a particular process;
are quantum mechanical effects and can not be deduced in classical physics.
Raman scattering Raman scattering is an
inelastic scattering of photons by matter. This means there is both an exchange of energy and
hence a change of frequency in the emitted photon. Typically this effect involves vibrational energy
being gained by a molecule as incident photons from a visible laser are shifted to lower energy.
Rayleigh scattering Rayleigh scattering is predominantly an
elastic scattering of electromagnetic radiation by particles much smaller than the wavelength
of the radiation. It results from the electric polarizability of the particles. The oscillating
electric field of a light wave acts on the charges within a particle, causing them to move at the
same frequency. The particle, therefore, becomes a small radiating dipole whose radiation we see
as scattered light. This effect is the reason for the blue colour of the daytime sky as well
as the yellowish to reddish hue of the low Sun. Sunlight is also subject to Raman scattering,
which changes the rotational state of the molecules and gives rise to polarization effects.
Mie scattering Mie scattering is an elastic scattering
of light by a dielectric sphere. This means it does change the frequency of the incoming photon.
In principle, this could be larger, or around the same size as the wavelength of light.
Mie scattering is much strong that Rayleigh scattering and therefore a potential source
of interference. It can also produce resonances in the scattered light.
The grey and white colour of the clouds is caused by Mie scattering by water droplets,
which are of comparable size to the wavelengths of visible light.
In principle, we can therefore say that where the state of the electron before
and after the absorption and re-emitting of the photon is unchanged the incoming photon
frequency is the same as the re-emitted one. When this is not the case and the electron
is scattered then we can see that the electron moves relative to the observer and therefore we
get a Doppler shift and a subsequent change in the frequency relative to the observer.
Refraction In all the cases we have discussed so
far the photon is absorbed by an atom or molecule and then re-emitted. So how does refraction work
then? What causes the photon to slow down inside an optical medium? There are a number of different
ways of looking at this problem but I will only cover the classical electrodynamical approach.
Here we will consider light as an electromagnetic wave, as described by Maxwell's equations. In the
vacuum of space, they are free to travel but when they travel through a more dense material we need
to consider the effect that the oscillating electric field of the light wave has on the
atoms and electrons that make up the material. The electrons will start to oscillate in sympathy and
cause each particle to radiate a small secondary wave in all directions, like a dipole antenna.
These waves will interfere with the photon wave and the resulting wave will travel slower.
The important difference is that the photon does not cause the electrons in the atoms
to jump to an excited state. It merely causes an oscillation of the current state. This is
why the photons can pass through a medium like glass in a straight line and will only be bent
at the boundary between two different types of media due to the change in speed of the waves.
Reflection Reflection is similar to refraction in that
it is once more the incoming em wave which causes oscillations in the electrons of the material and
the photon is not absorbed by the reflecting material. In a metal, the waves are radiated
by the oscillating free electrons. This creates an oscillating current in the surface of the metal,
this creates an oscillating electric field which is 180 deg out of phase with the incoming wave.
The free electrons in a metal have a natural frequency of oscillation called the plasma
frequency. Metals will reflect em waves below their plasma frequency. If we take sodium
as an example this has a plasma frequency that corresponds to a wavelength of 210nm.
When the incoming em wave has a frequency above the plasma frequency the electrons
in the material will not be able to respond quickly enough and the wave
will pass through. In the case of sodium, this would be anything above ultraviolet.
Pair production
Is the creation of a subatomic particle and its anti-particle from a neutral boson.
It often specifically refers to a photon creating an electron-positron pair near
a nucleus. As energy must be conserved, the incoming energy of the photon must be above
the threshold of at least the total rest mass energy of the two particles created.
This is the opposite process of beta plus decay.
Photodisintegration Sometimes also called phototransmutation
or photonuclear reaction is a nuclear process where an atomic nucleus absorbs a high-energy
gamma-ray. This causes it to enter an excited state and immediately release this energy by
emitting part of the particles within the nucleus. This could be a neutron, proton or alpha particle.
In some sense, this is the opposite of the emission of a gamma ray in some nuclear
reactions and is a topic we will return in connection with the Structured Atomic Model.
Photofission is the process in
which a nucleus absorbs a gamma ray and then undergoes nuclear fission splitting into two
or more fragments. Gamma radiation of around the low tens of MeV can induce
fission in traditionally fissile elements such as thorium, uranium, and plutonium.
Dispersion Measure This only applies to radio waves due to the
lower energy of the photons. In the presence of charged particles, the electrostatic interaction
between the light and the charged particles causes a delay in the propagation of the light.
More energetic and hence higher frequency photons are less affected than lower frequency.
This causes the delay to increase with lower frequency. Generally,
this effect is more significant for electrons compared to protons, meaning the dispersion
measure is a way to gauge the number of free electrons in the intervening space.
Whistler Mode A whistler is a very low-frequency electromagnetic
wave generated by a discharge like a lightning strike. In the case of a lightning strike,
the wave travels along the Earth's magnetic field lines from one hemisphere to the other. During
this journey, it will undergo dispersion due to the plasma of the ionosphere and magnetosphere.
Meaning that the frequency would be perceived as a descending tone which can last for a few seconds.
Cherenkov radiation Cherenkov radiation is
electromagnetic radiation emitted when a charged particle passes through a dielectric medium at a
speed greater than the phase velocity of light in that medium. This results in the blue radiation
seen in an underwater nuclear reactor. In some sense, it is similar to a sonic boom.
In water, light will travel at about 3/4 its speed in a vacuum.
Nuclear reactions can cause particles to be emitted and accelerated to speeds
that are higher than this but slower than the speed of light in a vacuum.
When a charged particle passes through a medium,
the particle of the medium will polarize around it in response. The charged particle
excites the molecules in the polarizable medium and on return to their ground state,
the molecules re-emit the energy given to them to achieve excitation as photons. The polarization
field is asymmetric along the direction of motion of the particle, as the particles of the medium
do not have enough time to recover their normal states. This results in overlapping wavefronts and
constructive interference leading to an observed cone-like light signal at a characteristic angle.