Transcript The Electromagnetic Spectrum and 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.

The Electromagnetic Spectrum
and 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
Sources of light
Accelerating charges emit light
Linearly accelerating charge
Synchrotron radiation—
light emitted by charged
particles deflected by a
magnetic field
Bremsstrahlung (Braking radiation)—
light emitted when charged particles
collide with other charged particles
B
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.
Water’s vibrations
Atomic and molecular vibrations
correspond to excited energy levels in
quantum mechanics.
Energy levels are everything in quantum mechanics.

Energy
Excited level
DE = hn
Ground level
The atom is vibrating
at frequency, n.
The atom is at least partially in
an excited state.
Excited atoms emit photons
spontaneously.
When an atom in an excited state falls to a lower energy level, it
emits a photon of light.
Energy
Excited level
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.
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) .
Collisions broaden the frequency range of
light emission.
A collision abruptly changes the phase of the sine-wave light emission.
So atomic emissions can have a broader spectrum.
Quantum-mechanically
speaking, the levels
shift during the collision.
Gases at atmospheric pressure have emission widths of ~ 1 GHz.
Solids and liquids emit much broader ranges of frequencies (~ 1013 Hz!).
Molecules have many energy levels.
A typical molecule’s energy levels:
E = Eelectonic + Evibrational + Erotational
2nd
excited
electronic state
Energy
1st excited
electronic state
Lowest vibrational and
rotational level of this
electronic “manifold”
Excited vibrational and
rotational level
Transition
Ground
electronic state
There are many other
complications, such as
spin-orbit coupling,
nuclear spin, etc.,
which split levels.
As a result, molecules generally have very complex spectra.
Atoms and molecules can also absorb
photons, making a transition from a lower
level to a more excited one.
Excited level
Energy
This is, of
course,
absorption.
Ground level
Absorption lines in an
otherwise continuous
light spectrum due to
a cold atomic gas in
front of a hot source.
Energy
Decay from an excited state can occur in
many steps.
Ultraviolet
Infra-red
Visible
Microwave
The light that’s eventually re-emitted after absorption may occur
at other colors.
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.
Visible
Infra-red
Greenhouse gases:
carbon dioxide
water vapor
methane
nitrous oxide
Methane, emitted by
microbes called
methanogens, kept
the early earth warm.
In what energy levels do molecules reside?
Boltzmann population factors
Energy
E3
E2
N3
Ni  exp Ei / kBT 
N2
N1
E1
Population density
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
Boltzmann’s
constant.
The Maxwell-Boltzman distribution
In the absence of collisions,
molecules tend to remain
in the lowest energy state
available.
Collisions can knock a molecule into a higher-energy state.
The higher the temperature,
the more this happens.
3
2
High T
N2 exp   E2 / kBT 

N1 exp   E1 / kBT 
Energy
Energy
Low T
3
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.
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 molecules
that that, together,
have transitions
at every
wavelength.
Einstein showed that stimulated
emission can also occur.
Before
Spontaneous
emission
Absorption
Stimulated
emission
After
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 MaxwellBoltzmann Distribution
(B12 I ) / (A + B21 I ) = N2 / N1 = exp[–DE/kBT ]
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 :
I = A / {B12 exp[DE/kBT] – B21}
Solve for I:
or:
B12 I exp[DE/kBT] = A + B21 I
I = [A/B21] / { [B12 /B21] exp[DE/kBT] – 1 }
Now, when T  I should also. As T , exp[DE/kBT ]  1.
So:
B12 = B21  B
And:
I = [A/B] / {exp[DE/kBT ] – 1}
Eliminating A/B:
 Coeff up = coeff down!
 2 hv3 
I
exp  hv / kBT   1
using DE = hn
Blackbody emission spectrum
The higher the temperature, the more the emission and
the shorter the average wavelength.
Blue hot is hotter
than red hot.
Wien's Law: Blackbody peak wavelength
scales as 1/Temperature.
Writing the Blackbody spectrum vs.
wavelength:
 2 hc 2 /  5 
I 
exp  hc /  kBT   1
Color temperature
Blackbodies are so pervasive that a
light spectrum is often characterized
in terms of its temperature even if
it’s not exactly a blackbody.
The electromagnetic spectrum
gamma-ray
microwave
2
10
1
106
10
visible
radio
infrared
0
105
10
-1
4
10
10
3
10
UV
2
10
wavelength (nm)
The transition wavelengths are a bit arbitrary…
X-ray
1
10
0
10
-1
10
The electromagnetic spectrum
Now, we’ll run through the entire electromagnetic spectrum, starting at
very low frequencies and ending with the highest-frequency gamma rays.
60-Hz radiation from
power lines
Yes, this very-low-frequency current
emits 60-Hz electromagnetic waves.
No, it is not harmful. A 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;
they’re greatly reduced inside the body because it’s conducting;
and the body’s own electrical fields (nerve impulses) are much
greater.
60-Hz magnetic fields inside the body are < 0.002 Gauss; the
earth’s magnetic field is ~ 0.4 G.
The longwavelength
electromagnetic
spectrum
Arecibo radio
telescope
Global positioning system (GPS)
It consists of 24 orbiting satellites in “half-synchronous orbits” (two
revolutions per day).
Four satellites per orbit,
equally spaced, inclined
at 55 degrees to equator.
Operates at 1.575 GHz
(1.228 GHz is a reference
to compensate for atmospheric water effects)
4 signals are required;
one for time, three for
position.
2-m accuracy
(100 m for us).
Microwave ovens
Microwave ovens operate at 2.45 GHz,
where water absorbs very well.
Percy LeBaron
Spencer, Inventor
of the microwave
oven
Geosynchronous communications
satellites
22,300 miles above the earth’s surface
6 GHz uplink, 4 GHz downlink
Each satellite is actually two (one is a spare)
Cosmic
microwave
background
Peak frequency is ~ 150 GHz
The 3° cosmic microwave
background is blackbody
radiation left over from
the Big Bang!
Wavenumber (cm-1)
Microwave background
vs. angle. Note the
variations.
Interestingly,
blackbody radiation
retains a blackbody
spectrum despite
the expansion the
universe. It does
get colder, however.
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.
Fortunately, I couldn’t get permission to show you the movies I
have of people with THz-invisible invisible clothes.
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.
IR Liedetection
I don’t really buy
this, but I thought
you’d enjoy it…
He’s really sweating now…
The military uses IR to see objects it
considers relevant.
IR light penetrates fog and smoke better than visible light.
Jet engines emit infrared light from 3 to 5.5 µm
This light is easily distinguished from the ambient infrared, which peaks
near 10mm and is relatively weak in this range
The infrared space observatory
Stars that are just
forming emit light
mainly in the IR.
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.
Laser
welding
Near-IR
wavelengths
are commonly
used.
Atmospheric penetration depth (from
space) vs. wavelength
Visible light
Wavelengths and
frequencies of visible
light
Auroras
Solar wind particles spiral around the earth’s
magnetic field lines and collide with atmospheric 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
Dye lasers cover the entire visible spectrum.
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.
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)
The sun in the UV
Image taken
through a
171-nm filter
by NASA’s
SOHO
satellite.
The very short-wavelength regions
Vacuum-ultraviolet (VUV)
180 nm > > 50 nm
Soft x-rays
5 nm > > 0.5 nm
Absorbed by <<1 mm of air
Ionizing to many materials
Strongly interacts with core
electrons in materials
Extreme-ultraviolet (XUV or EUV)
50 nm > > 5 nm
Ionizing radiation to all materials
Synchrotron Radiation
Formerly considered a nuisance to accelerators, it’s now often the
desired product!
Synchrotron radiation in all
directions around the circle
Synchrotron radiation only
in eight preferred directions
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 earth’s atmosphere is
highly absorbing at these wavelengths.
The sun also emits x-rays.
The sun seen in the x-ray region.
Matter falling into a black hole emits x-rays.
Nearby star
Black hole
A black hole accelerates particles to very high speeds.
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.
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.
Atomic structure and x-rays
Ionization energy
~ 100 – 1000 e.v.
Ionization energy
~ .01 – 1 e.v.
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 xrays.
The faster the electrons, the
higher the x-ray frequency.
X-rays penetrate tissue and do not
scatter much.
Roentgen’s x-ray image
of his wife’s hand (and
wedding ring)
X-rays for photo-lithography
You can only focus light to
a spot size of the light
wavelength. So x-rays are
necessary for integratedcircuit 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.
High-Harmonic Generation and x-rays
Amplified
femtosecond laser
pulse
x-rays
gas jet
An ultrashort-pulse x-ray beam can be generated by focusing a
femtosecond laser in a gas jet
Harmonic orders > 300, photon energy > 500 eV, observed to date
HHG is a highly nonlinear process
resulting from highly nonharmonic
motion of an electron in an intense field.
The strong field smashes the electron into the nucleus—a highly
non-harmonic motion!
Ion
x-ray
electron
How do we know this? Circularly polarized light (or even slightly
elliptically polarized light) yields no harmonics!
Gamma rays result from matterantimatter annihilation.
An electron and positron self-annihilate, creating two gamma
rays whose energy is equal to the electron mass energy, mec2.
ee+
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.
Gamma-ray bursts emit massive
amounts of gamma rays.
The gamma-ray sky
A new one
appears almost
every day, and
it persists for
~1 second to
~1 minute.
No one knows
what they are.
In 10 seconds, they can emit more energy than our sun will in its
entire lifetime. Fortunately, there don’t seem to be any in our galaxy.
The universe in
different spectral
regions…
Gamma Ray
X-Ray
Visible
The universe in more spectral
regions…
IR
Microwave