the electromagnetic spectrum and blackbody radiation sources of light: gases, liquids, and solids...
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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
Sources of 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
Accelerating charges emit light
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.
Atomic and molecular vibrations correspond to excited energy levels in quantum mechanics.
Ene
rgy
Ground level
Excited level
E = h
The atom is at least partially in an excited state.
The atom is vibrating at frequency, .
Energy levels are everything in quantum mechanics.
Excited atoms emit photons spontaneously.
When an atom in an excited state falls to a lower energy level, it emits a photon of light.
Molecules typically remain excited for no longer than a few nanoseconds. This is often also called fluorescence or, when it takes longer, phosphorescence.
Ene
rgy
Ground level
Excited level
Different atoms emit light at different widely separated frequencies.
Frequency (energy)
Atoms have relatively simple energy level systems (and hence simple spectra) .
Each colored emission line corresponds to a difference between two energy levels.
These are emission spectra from gases of hot atoms.
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.
Molecules have many energy levels.
A typical molecule’s energy levels:
Ground electronic state
1st excited electronic state
2nd excited electronic state
Ene
rgy
Transition
Lowest vibrational and rotational level of this electronic “manifold”
Excited vibrational and rotational level
There are many other complications, such as spin-orbit coupling, nuclear spin, etc., which split levels.
E = Eelectonic + Evibrational + Erotational
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.
This is, of course, absorption.
Ene
rgy
Ground level
Excited level
Absorption lines in an otherwise continuous light spectrum due to a cold atomic gas in
front of a hot source.
Decay from an excited state can occur in many steps.
Ene
rgy
The light that’s eventually re-emitted after absorption may occur at other colors.
Infra-red
Visible
Microwave
Ultraviolet
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 vapor
methanenitrous oxide
Methane, emitted by microbes called
methanogens, kept the early earth warm.
Visible Infra-red
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 Boltzmann’s constant.
exp /i i BN E k T
En
erg
y
Population density
N1
N3
N2
E3
E1
E2
The Maxwell-Boltzman distribution
In equilibrium, the ratio of the populations of two states is:
N2 / N1 = exp(–E/kBT ), where E = E2 – E1 = h
As a result, higher-energy states are always less populated than theground state, and absorption is stronger than stimulated emission.
In the absence of collisions,molecules tend to remainin the lowest energy stateavailable.
Collisions can knock a mole-cule into a higher-energy state.The higher the temperature, the more this happens.
22
1 1
exp /
exp /B
B
E k TN
N E k T
Low T High T
En
erg
y
Molecules
En
erg
y
Molecules
3
2
1
2
1
3
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 After
Absorption
Stimulated emission
Spontaneous emission
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:
Recalling the Maxwell-Boltzmann Distribution
(B12 I ) / (A + B21 I ) = N2 / N1 = exp[–E/kBT ]
B12 N1 I = A N2 + B21 N2 ISolving for N2/N1:
Einstein A and B coefficients and Blackbody RadiationNow solve for the irradiance in: (B12 I ) / (A + B21 I ) = exp[-E/kBT ]
Multiply by A + B21 I : B12 I exp[E/kBT] = A + B21 I
Solve for I: I = A / {B12 exp[E/kBT] – B21}
or: I = [A/B21] / { [B12 /B21] exp[E/kBT] – 1 }
Now, when T I should also. As T , exp[E/kBT ] 1.
So: B12 = B21 B Coeff up = coeff down!
And: I = [A/B] / {exp[E/kBT ] – 1}
Eliminating A/B: using E = h
32
exp / 1B
hvI
hv k T
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 52 /
exp / 1B
hcI
hc k T
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
infrared X-rayUVvisible
wavelength (nm)
microwave
radio
105106
gamma-ray
The transition wavelengths are a bit arbitrary…
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 epide-miological 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.
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 required;one for time, three forposition.
2-m accuracy(100 m for us).
Global positioning system (GPS)
Microwave ovens
Microwave ovens operate at 2.45 GHz, where water absorbs very well.
Percy LeBaron Spencer, Inventor of the microwave oven
22,300 miles above the earth’s surface
6 GHz uplink, 4 GHz downlink
Each satellite is actually two (one is a spare)
Geosynchronous communications satellites
Cosmic microwave background
Interestingly, blackbody radiation retains a blackbody spectrum despite the expansion the universe. It does get colder, however.
The 3° cosmic microwave background is blackbody radiation left over from the Big Bang!
Wavenumber (cm-1)
Peak frequency is ~ 150 GHz
Microwave background vs. angle. Note the
variations.
TeraHertz light (a region of microwaves)
TeraHertz light is light with a frequency of ~1 THz, that is, with a wavelength of ~300 m.
THz light is heavily absorbed by water, but clothes are transparent in this wavelength range.
CENSORED
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.
Old Faithful
Such studies help to confirm that Old Faithful is in fact faithful and whether human existence is interfering with it.
Hotter and hence brighter
in the IR
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 10m and is relatively weak in this range
Using mid-IR laser light to shoot down missiles
The Tactical High Energy Laser uses a high-energy, deuterium fluoride chemical laser to shoot down short range unguided (ballistic flying) rockets.
Wavelength = 3.6 to 4.2 m
Auroras
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
Solar wind particles spiral around the earth’s magnetic field lines and collide with atmos-pheric molecules, electronically exciting them.
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.
Visible UV (false color)
Arnica angustifolia Vahl
The very short-wavelength regions
Soft x-rays
5 nm > > 0.5 nmStrongly interacts with core
electrons in materials
Vacuum-ultraviolet (VUV)
180 nm > > 50 nm Absorbed by <<1 mm of air
Ionizing to many 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.
Matter falling into a black hole emits x-rays.
A black hole accelerates particles to very high speeds.
Black hole
Nearby star
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.
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.
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 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.
High-Harmonic Generation and x-rays
gas jet
x-raysAmplified femtosecond laser pulse
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.
Ion electronx-ray
The strong field smashes the electron into the nucleus—a highly non-harmonic motion!
How do we know this? Circularly polarized light (or even slightly elliptically polarized light) yields no harmonics!
Gamma rays result from matter-antimatter annihilation.
e-
e+
An electron and positron self-annihilate, creating two gamma
rays whose energy is equal to the electron mass energy, mec2.
h = 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.
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.
A new one appears almost every day, and it persists for ~1 second to ~1 minute.
No one knows what they are.
The gamma-ray sky