The Electromagnetic Spectrum and Blackbody Radiation

1
The Electromagnetic Spectrumand Blackbody
Radiation

• Sources of light gases, liquids, and solids
• Boltzmann's Law
• Blackbody radiation
• The electromagnetic spectrum
• Long-wavelength sources
• and applications
• Visible light and the eye
• Short-wavelength sources and applications

Prof. Rick Trebino Georgia Tech www.physics.gatech
.edu/frog/lectures
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Where does light come from?
Weve seen that Maxwells Equations (i.e., the
wave equation) describe the propagation of light.
But where does light come from in the first
place? Some matter must emit the light. It does
so through the matters polarization
Note that matters polarization is analogous to
the polarization of light. Indeed, it will cause
the emission of light with the same polarization
direction.
where N is the number density of charged
particles, q is the charge of each particle, and
is the position of the charge. Here,
weve assumed that each charge is identical and
has identical motion.
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Polarized and unpolarized media
Unpolarized medium
Polarized medium
On the right, the displacements of the charges
are correlated, so it is polarized at any given
time (and its polarization is oscillating).
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Maxwell's Equations in a Medium

• The induced polarization, , contains the
  effect of the medium and is included in Maxwells
  Equations

This extra term also adds to the wave equation,
which is known as the Inhomogeneous Wave Equation
The polarization is the source term and tells us
what light will be emitted.
Notice that the induced polarization, and hence
, gets differentiated twice. But
is just the charge acceleration!
So its accelerating charges that
emit light!
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Sources of light
Accelerating charges emit light!

• Linearly accelerating charge
• Synchrotron radiationlight emitted by charged
  particles deflected by a magnetic field
• Bremsstrahlung (Braking radiation)light emitted
  when charged particles collide with other
  charged particles

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But the vast majority of light in the universe
comes from molecular vibrations emitting light.

• Electrons vibrate in their motion around nuclei
• High frequency 1014 - 1017 cycles per
  second.
• Nuclei in molecules vibrate with respect to each
  other
• Intermediate frequency 1011 - 1013
  cycles per second.
• Nuclei in molecules rotate
• Low frequency 109 - 1010 cycles per second.

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Waters vibrations
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Atomic and molecular vibrations correspond to
excited energy levels in quantum mechanics.
Energy levels are everything in quantum mechanics.
Excited level
DE hn
Energy
Ground level
The atom is at least partially in an excited
state.
The atom is vibrating at frequency, n.
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Excited atoms emit photons spontaneously.
When an atom in an excited state falls to a lower
energy level, it emits a photon of light.
Excited level
Energy
Ground level
Molecules typically remain excited for no longer
than a few nanoseconds. This is often also called
fluorescence or, when it takes longer,
phosphorescence.
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Different atoms emit light at different widely
separated frequencies.
Each colored emission line corresponds to a
difference between two energy levels. These are
emission spectra from gases of hot atoms.

Frequency (energy)
Atoms have relatively simple energy level systems
(and hence simple spectra).
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Collisions broaden the frequency range oflight
emission.

• A collision abruptly changes the phase of the
  sine-wave light emission. So atomic emissions
  can have a broader spectrum.
• Gases at atmospheric pressure have emission
  widths of 1 GHz.
• Solids and liquids emit much broader ranges of
  frequencies ( 1013 Hz!).

Quantum-mechanically speaking, the levels shift
during the collision.
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Molecules have many energy levels.

• A typical molecules energy levels

E Eelectonic Evibrational Erotational
2nd excited electronic state
Lowest vibrational and rotational level of this
electronic manifold
Energy
1st excited electronic state
Excited vibrational and rotational level
Transition
There are many other complications, such as
spin-orbit coupling, nuclear spin, etc., which
split levels.
Ground electronic state
As a result, molecules generally have very
complex spectra.
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Atoms and molecules can also absorb photons,
making a transition from a lower level to a more
excited one.
Excited level
This is, of course, absorption.
Energy
Ground level
Absorption lines in an otherwise continuous light
spectrum due to a cold atomic gas in front of a
hot source.
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Decay from an excited state can occur in many
steps.
Infra-red
Energy
Visible
Ultraviolet
Microwave
The light thats eventually re-emitted after
absorption may occur at other colors.
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The Greenhouse Effect
The greenhouse effect occurs because windows are
transparent in the visible, but absorbing in the
mid-IR, where most materials re-emit. The same is
true of the atmosphere.
Greenhouse gases carbon dioxide water
vapormethanenitrous oxide Methane, emitted by
microbes called methanogens, kept the early earth
warm.
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Global warming
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2008 global temperatures compared with 1951-1980
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Global warming facts
The concentration of CO2 in the atmosphere rose
from 290 ppm in 1900 to 316 ppm in 1959 and to
387 ppm in 2009. The ten warmest years ever
have occurred in the period 1997-2008. About
75 of the annual increase in atmospheric carbon
dioxide is due to the burning of fossil fuels.
The remaining 25 is attributed to changes in
land use, reducing the net uptake of CO2.
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Historical temperature and CO2 levels
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Einstein showed that stimulated emission can also
occur.
Before After
Spontaneous emission
Absorption
Stimulated emission
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In what energy levels do molecules reside?
Boltzmann population factors
Ni is the number density of molecules in state i
(i.e., the number of molecules per cm3). T is
the temperature, and kB is Boltzmanns constant.
N3
E3
N2
E2
Energy
N1
E1
Population density
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The Maxwell-Boltzman distribution
In the absence of collisions, molecules tend to
remain in the lowest energy state available.
Collisions can knock a mole- cule into a
higher-energy state. The higher the temperature,
the more this happens.
Low T
High T
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3
Energy
Energy
2
2
1
1
Molecules
Molecules

• In equilibrium, the ratio of the populations of
  two states is
• N2 / N1 exp(DE/kBT ), where DE
  E2 E1 hn
• As a result, higher-energy states are always less
  populated than the ground state, and absorption
  is stronger than stimulated emission.

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Blackbody radiation

• Blackbody radiation is emitted from a hot body.
  It's anything but black!
• The name comes from the assumption that the body
  absorbs at every frequency and hence would look
  black at low temperature.
• It results from a combination of spontaneous
  emission, stimulated emission, and absorption
  occurring in a medium at a given temperature.

It assumes that the box is filled with many
different molecules that that, together, have
transitions (absorptions) at every wavelength.
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Einstein A and B coefficients

• In 1916, Einstein considered the various
  transition rates between molecular states (say, 1
  and 2) involving light of irradiance, I
• Spontaneous emission rate A N2
• Absorption rate
  B12 N1 I
• Stimulated emission rate B21 N2 I
• In equilibrium, the rate of upward transitions
  equals the rate of downward transitions

B12 N1 I A N2 B21 N2 I Solving
for N2/N1
Recalling the Maxwell- Boltzmann Distribution
(B12 I ) / (A B21 I ) N2 / N1
expDE/kBT
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Einstein A and B coefficients and Blackbody
Radiation

• Now solve for the irradiance in (B12 I ) / (A
  B21 I ) exp-DE/kBT
• Multiply by A B21 I B12 I
  expDE/kBT A B21 I
• Solve for I I A /
  B12 expDE/kBT B21
• or I A/B21 / B12 /B21
  expDE/kBT 1
• Now, when T , I should also. As T ,
  expDE/kBT 1.
• So B12 B21 º B Coeff up coeff
  down!
• And I A/B / expDE/kBT 1
• Eliminating A/B
  
• (based on other
  using DE hn
  
  
• information)

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Writing the blackbody spectrum vs. wavelength
Units of I(n) energy/volume/frequency
Change variables from n to l
Units of I(l) energy/volume/wavelength
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Blackbody emission spectrum

• The higher the temperature, the more the emission
  and the shorter the average wavelength.

The suns surface is 6000 degrees K, so its
blackbody spectrum peaks at 500 nmin the
green. However, blackbody spectra are broad, so
it contains red, yellow, and blue, too, and so
looks white.
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Wien's Law Blackbody peak wavelength scales as
1/Temperature.

• Writing the blackbody spectrum vs. wavelength

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Color temperature
Blackbodies are so pervasive that a light
spectrum is often characterized in terms of its
temperature even if its not exactly a
blackbody. Keep in mind that blackbody spectra
are broad, so they usually look white with a tint
of the peak color (wavelength).
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The electromagnetic spectrum
The transition wavelengths are a bit arbitrary.
Visible light used to be 400 to 700 nm, but now
its officially 380 to 780 nm.
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The electromagnetic spectrum
Now, well run through the entire electromagnetic
spectrum, starting at very low frequencies and
ending with the highest-frequency gamma rays.
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60-Hz radiation from power lines
Yes, this very-low-frequency current emits 60-Hz
electromagnetic waves. No, it is not harmful. A
very flawed epidemiological study in 1979
claimed otherwise, but no other study has ever
found such results. Also, electrical power
generation has increased exponentially since
1900 cancer incidence has remained essentially
constant. Also, the 60-Hz electrical fields
reaching the body are small theyre greatly
reduced inside the body because its conducting
and the bodys own electrical fields (nerve
impulses) are much greater. 60-Hz magnetic fields
inside the body are lt 0.002 Gauss the earths
magnetic field is 0.4 G.
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The long-wavelength electro-magnetic spectrum
Arecibo radio telescope
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Radio microwave regions (3 kHz 300 GHz)
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Global positioning system (GPS)

• It consists of 24 orbiting satellites in
  half-synchronous orbits (two revolutions per
  day).
• Four satellites per orbit,equally spaced,
  inclinedat 55 degrees to equator.
• Operates at 1.575 GHz(1.228 GHz is a
  referenceto compensate for atmos-pheric water
  effects)
• 4 signals are requiredone for time, three
  forposition.
• 2-m accuracy(100 m for us).

Corrections must be made for General Relativity!
Otherwise accuracy would be 8 m.
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Microwave ovens
Microwave ovens operate at 2.45 GHz, where water
absorbs very well.
Percy LeBaron Spencer, Inventor of the microwave
oven
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Geosynchronous communications satellites
22,300 miles above the earths surface 6 GHz
uplink, 4 GHz downlink Each satellite is actually
two (one is a spare)
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Cosmic microwave background
Microwave background vs. angle. Note the
variations.
Peak frequency is 150 GHz
The 3 cosmic microwave background is
blackbody radiation left over from
the Big Bang!

• Interestingly, blackbody radiation retains a
  blackbody spectrum despite the expansion the
  universe. It does get colder, however.

Wavenumber (cm-1)
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TeraHertz light (a region of microwaves)
TeraHertz light is light with a frequency of 1
THz, that is, with a wavelength of 300 mm. THz
light is heavily absorbed by water, but clothes
are transparent in this wavelength range.
CENSORED
Fortunately, I couldnt get permission to show
you the movies I have of people with
THz-invisible clothes.
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IR is useful for measuring the temperature of
objects.
Hotter and hence brighter in the IR
Old Faithful
Such studies help to confirm that Old Faithful is
in fact faithful and whether human existence is
interfering with it.
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IR Lie-detection
I dont really buy this, but I thought youd
enjoy it
Hes really sweating now
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The military uses mid-IR to see various objects.
Mid-IR from heat is easily distinguished from
the ambient far infrared, which peaks near 10 mm
and is relatively weak in this range. Also IR
penetrates fog and smoke better than visible
light.
4
10
l (mm)
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The infrared space observatory
Stars that are just forming are cooler than
mature stars and so emit light mainly in the IR.
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Using mid-IR laser light to shoot down missiles
Wavelength 3.6 to 4.2 mm
The Tactical High Energy Laser uses a
high-energy, deuterium fluoride chemical laser to
shoot down short range unguided (ballistic
flying) rockets.
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Atmospheric penetration depth (from space) vs.
wavelength
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Laser welding
Near-IR wavelengths are commonly used.
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Visible light

• Wavelengths and frequencies of visible light

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Auroras
Solar wind particles spiral around the earths
magnetic field lines and collide with
atmos-pheric molecules, electronically exciting
them.
Auroras are due to fluorescence from molecules
excited by these charged particles. Different
colors are from different atoms and molecules. O
558, 630, 636 nm N2 391, 428 nm H 486, 656
nm
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Dye lasers cover the entire visible spectrum.
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Fluorescent lights
Incandescent lights (normal light bulbs) lack
the emission lines.
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The human retina
Rods
Cones
The retina is a mosaic of two basic types of
photoreceptors, rods, and cones. Cones are
highly concentrated in a region near the center
of the retina called the fovea. The maximum
concentration of cones is roughly 180,000 per mm2
there and the density decreases rapidly outside
of the fovea to less than 5,000 per mm2. Note the
blind spot caused by the optic nerve, which is
void of any photoreceptors.
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The eyes response to light and color

• The eyes cones have three receptors, one for
  red, another for green, and a third for blue.

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The eye is poor at distinguishing spectra.
Because the eye perceives intermediate colors,
such as orange and yellow, by comparing relative
responses of two or more different receptors, the
eye cannot distinguish between many spectra. The
various yellow spectra below appear the same
(yellow), and the combination of red and green
also looks yellow!
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How film and digital cameras work
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Most digital cameras interleave different-color
filters
So four times the number of pixels are required.
Digital TVs can emit any color from each pixel,
so an 8-Mpixel camera only requires a 2-Mpixel TV
(which is the full-HDTV standard).
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Color wheels
Hue wavelength Saturation spectral
width Value brightness (intensity)
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The Ultraviolet
The UV is usually broken up into three regions,
UVA (320-400 nm), UVB (290-320 nm), and UVC
(220-290 nm). UVC is almost completely absorbed
by the atmosphere.
You can get skin cancer even from UVA.
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UV from the sun
The ozone layer absorbs wavelengths less than 320
nm (UVB and UVC), and clouds scatter what isnt
absorbed. But much UV (mostly UVA, but some
UVB) penetrates the atmosphere anyway.
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IR, Visible, and UV Light and Humans
(Sunburn)
Skin surface
Were opaque in the UV and visible, but not
necessarily in the IR.
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Flowers in the UV
Since bees see in the UV (they have a receptor
peaking at 345 nm), flowers often have UV
patterns that are invisible in the visible.
Arnica angustifolia Vahl
Visible
UV (false color)
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The sun in the UV
Image taken through a 171-nm filter by NASAs
SOHO satellite.
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The very short-wavelength regions
Soft x-rays 5 nm gt l gt 0.5 nm Strongly interacts
with core electrons in materials
Vacuum-ultraviolet (VUV) 180 nm gt l gt 50 nm
Absorbed by ltlt1 mm of air Ionizing to many
materials
Extreme-ultraviolet (XUV or EUV) 50 nm gt l gt 5
nm Ionizing radiation to all materials
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Synchrotron Radiation
Formerly considered a nuisance to accelerators,
its now often the desired product!
Synchrotron radiation in all directions around
the circle
Synchrotron radiation only in eight preferred
directions
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EUV Astronomy
The solar corona is very hot (30,000,000 degrees
K) and so emits light in the EUV region.
EUV astronomy requires satellites because the
earths atmosphere is highly absorbing at these
wavelengths.
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The sun also emits x-rays.
The sun seen in the x-ray region. Theyre mostly
from the corona, which is 30,000,000K.
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Matter falling into a black hole emits x-rays.
Nearby star
Black hole
A black hole accelerates particles to very high
speeds.
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Supernovas emit x-rays, even afterward.
A supernova remnant in a nearby galaxy (the Small
Magellanic Cloud). The false colors show what
this supernova remnant looks like in the x-ray
(blue), visible (green) and radio (red) regions.
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X-rays are occasionally seen in auroras.
On April 7th 1997, a massive solar storm ejected
a cloud of energetic particles toward planet
Earth.
The plasma cloud grazed the Earth, and its high
energy particles created a massive geomagnetic
storm.
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Atomic structure and x-rays
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Fast electrons impacting a metal generate x-rays.

• High voltage accelerates electrons to high
  velocity, which then impact a metal.

Electrons displace electrons in the metal, which
then emit x-rays. The faster the electrons, the
higher the x-ray frequency.
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X-rays penetrate tissue and do not scatter much.
Roentgens x-ray image of his wifes hand (and
wedding ring)
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X-rays for photo-lithography
You can only focus light to a spot size of the
light wavelength. So x-rays are necessary for
integrated-circuit applications with structure a
small fraction of a micron. 1 keV photons from
a synchrotron 2 micron lines over a base of 0.5
micron lines.
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High-Harmonic Generation and x-rays
Focusing a femtosecond laser pulse into a gas jet
yields photons of frequency nw generally in the
XUV and x-ray regions! Harmonic orders n gt 300,
photon energy gt 500 eV (a few Angstroms!) have
been observed.
The strong field smashes the electron into the
nucleusa highly non-harmonic motion!
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Gamma rays result from matter-antimatter
annihilation.
An electron and positron self-annihilate,
creating two gamma rays whose energy is equal to
the electron mass energy, mec2.
e-
e
hn 511 kev
More massive particles create even more energetic
gamma rays. Gamma rays are also created in
nuclear decay, nuclear reactions and explosions,
pulsars, black holes, and supernova explosions.
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Gamma-ray bursts emit massive amounts of gamma
rays.
A new one appears almost every day, and it
persists for 1 second to 1 minute. Theyre
probably supernovas.
The gamma-ray sky
In 10 seconds, they can emit more energy than our
sun will in its entire lifetime. Fortunately,
there dont seem to be any in our galaxy.
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The universe in different spectral regions
Gamma Ray
X-Ray
Visible
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The universe in more spectral regions
Microwave