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 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

But the vast majority of light in the universe comes from molecular vibrations emitting light. Electrons vibrate in their motion around nuclei High frequency: ~ cycles per second. Nuclei in molecules vibrate with respect to each other Intermediate frequency: ~ cycles per second. Nuclei in molecules rotate Low frequency: ~ cycles per second.

Water’s vibrations

Atomic and molecular vibrations correspond to excited energy levels in quantum mechanics. Energy 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. Energy 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 of light 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 (~ Hz!). Quantum-mechanically speaking, the levels shift during the collision.

Molecules have many energy levels. A typical molecule’s energy levels: Ground electronic state 1 st excited electronic state 2 nd excited electronic state Energy 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 = E electonic + E vibrational + E rotational 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. Energy 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. Energy 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 methane nitrous 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 N i is the number density of molecules in state i (i.e., the number of molecules per cm 3 ). T is the temperature, and k B is Boltzmann’s constant. Energy Population density N1N1 N3N3 N2N2 E3E3 E1E1 E2E2

The Maxwell-Boltzman distribution In equilibrium, the ratio of the populations of two states is: N 2 / N 1 = exp (–  E/k B T ), where  E = E 2 – E 1 = h As a result, higher-energy states are always less populated than the ground state, and absorption is stronger than stimulated emission. 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 THigh T Energy Molecules Energy Molecules

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 N 2 Absorption rate = B 12 N 1 I Stimulated emission rate = B 21 N 2 I In equilibrium, the rate of upward transitions equals the rate of downward transitions: Recalling the Maxwell- Boltzmann Distribution (B 12 I ) / (A + B 21 I ) = N 2 / N 1 = exp[–  E/k B T ] B 12 N 1 I = A N 2 + B 21 N 2 I Solving for N 2 /N 1 :

Einstein A and B coefficients and Blackbody Radiation Now solve for the irradiance in: ( B 12 I ) / ( A + B 21 I ) = exp[-  E/k B T ] Multiply by A + B 21 I : B 12 I exp[  E/k B T] = A + B 21 I Solve for I : I = A / {B 12 exp[  E/k B T] – B 21 } or: I = [A/B 21 ] / { [B 12 /B 21 ] exp[  E/k B T] – 1 } Now, when T  I should also. As T , exp[  E/k B T ]  1. So: B 12 = B 21  B  Coeff up = coeff down! And: I = [A/B] / {exp[  E/k B T ] – 1} Eliminating A/B : using  E = h

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:

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 infraredX-rayUV visible wavelength (nm) microwave radio 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 < Gauss; the earth’s magnetic field is ~ 0.4 G.

The long- wavelength electro- magnetic spectrum Arecibo radio telescope

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 GHz (1.228 GHz is a reference to compensate for atmos- pheric water effects) 4 signals are required; one for time, three for position. 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

IR Lie- detection 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 10  m 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 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

Laser welding Near-IR wavelengths are commonly used.

Atmospheric penetration depth (from space) vs. wavelength

Visible light Wavelengths and frequencies of visible light

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 N 2 + : 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.

Dye lasers cover the entire visible spectrum.

The Ultraviolet The UV is usually broken up into three regions, UVA ( nm), UVB ( nm), and UVC ( nm). UVC is almost completely absorbed by the atmosphere. You can get skin cancer even from UVA.

UV from the sun The ozone layer absorbs wavelengths less than 320 nm (UVB and UVC), and clouds scatter what isn’t absorbed. But much UV (mostly UVA, but some UVB) penetrates the atmosphere anyway.

IR, Visible, and UV Light and Humans (Sunburn) We’re opaque in the UV and visible, but not necessarily in the IR. Skin surface

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 sun in the UV Image taken through a 171-nm filter by NASA’s SOHO satellite.

The very short-wavelength regions Soft x-rays 5 nm >  > 0.5 nm Strongly 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.

The sun also emits x-rays. The sun seen in the x-ray region.

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 7 th 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 ~.01 – 1 e.v. Ionization energy ~ 100 – 1000 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 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-rays Amplified 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 electron x-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- e+e+ An electron and positron self-annihilate, creating two gamma rays whose energy is equal to the electron mass energy, m e c 2. 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

Gamma Ray The universe in different spectral regions… X-Ray Visible

Microwave The universe in more spectral regions… IR