# The Electromagnetic Spectrum and Blackbody Radiation

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

Where does light come from?
We’ve seen that Maxwell’s 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 matter’s “polarization”: Note that matter’s 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, we’ve assumed that each charge is identical has identical motion.

Maxwell's Equations in a Medium
The induced polarization, , contains the effect of the medium and is included in Maxwell’s 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 it’s accelerating charges that emit light!

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

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 Movies from

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 vibrating at frequency, n. The atom is in a “superposition” of the ground and excited state. This is true for all types of vibrations.

Molecules (and everything else) have many energy levels and can emit light only by making a transition from one level to another. A typical molecule’s 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

Different atoms emit light at different widely separated frequencies.
Each colored “emission” line corresponds to a difference between two energy levels. Frequency (energy) Atoms have simpler energy level systems (and hence simpler spectra) because they have no nuclear vibrations (i.e., only electronic levels).

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 (~ 1013 Hz!). Quantum-mechanically speaking, the levels shift during the collision.

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.

Absorption Spontaneous Emission Stimulated Emission
Before After Absorption Spontaneous Emission Stimulated Emission

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. E3 N3 E2 N2 Energy N1 E1 Population density

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 3 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.

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: Absorption rate = B12 N1 I Spontaneous emission rate = A N2 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 Rearranging: (B12 I ) / (A + B21 I ) = N2 / N1 = exp[–DE/kBT ] Recalling the Maxwell- Boltzmann Distribution

Einstein A and B coefficients and Blackbody Radiation
Now solve for the irradiance in: (B12 I ) / (A + B21 I ) = exp[-DE/kBT ] Rearrange to: B12 I exp[DE/kBT] = A + B21 I or: I = A / {B12 exp[DE/kBT] – B21} or: I = [A/B21] / { [B12 /B21] exp[DE/kBT] – 1 } Now, when T ® ¥, I should also. As T ® ¥, exp[DE/kBT ] ® 1. So: B12 = B21 º B ¬ Coeff up = coeff down! And: I = [A/B] / {exp[DE/kBT ] – 1} Eliminating A/B: 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:

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. Image from the magazine Digital PhotoPro, “White Balance,”, May/June 2004

The Electromagnetic Spectrum
radio gamma-ray visible microwave infrared UV X-ray 106 105 wavelength (nm) 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.

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 image used with permission from Gabriela González, Department of Physics and Astronomy, Louisiana State University Arecibo radio telescope

Radio & microwave regions (3 kHz – 300 GHz)

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 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).

Microwave ovens Microwave ovens operate at 2.45 GHz, where water absorbs very well. Percy LeBaron Spencer, Inventor of the microwave oven Picture of Spencer from

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
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)

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 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 Images borrowed from Linda Hermans-Killam, Such studies help to confirm that Old Faithful is in fact faithful and whether human existence is interfering with it.

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 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

Laser welding Near-IR wavelengths are commonly used.

Atmospheric Penetration depth (from space) vs. Wavelength

Visible Light Wavelengths and frequencies of visible light
Hecht and

Dye lasers cover the entire visible spectrum.

Fluorescent lights “Incandescent” lights (normal light bulbs) lack the emission lines.

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. Images and text courtesy of the NDT Resource Center

The eye’s response to light and color
The eye’s cones have three receptors, one for red, another for green, and a third for blue. Intermediate colors, such as yellow and orange, are perceived by comparing relative responses of two or more different receptors.

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!

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 sun burned by all three.

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) Tanning salons use UVA, but it can still cause a sunburn.

The very short-wavelength regions
Vacuum-ultraviolet (VUV) 180 nm > l > 50 nm Absorbed by <<1 mm of air Ionizing to many materials Soft x-rays 5 nm > l > 0.5 nm Strongly interacts with core electrons in materials Extreme-ultraviolet (XUV or EUV) 50 nm > l > 5 nm Ionizing radiation to all materials

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 x-rays (blue), visible light (green) and radio (red).

Some x-rays are created in auroras.

Atomic structure and x-rays
The Essential Physics of Medical Imaging 2nd Edition, pg. 21 by Jerrold T. Bushberg, J. Anthony Seibert, Edwin M. Leidholdt, Jr, and John M. Boone 2002 by Lippincott Williams & Wilkins in PA ISBN: 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 x-rays. The faster the electrons, the higher the x-ray frequency. Images from Medical Imaging Physics, Fourth Edition by William R. Hende and E. Russell Ritenour 2002 by Wiley-Liss, New York ISBN: Pages 71, 75

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
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 electron x-ray How do we know this? Circularly polarized light (or even slightly elliptically polarized light) yields no harmonics!

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.

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. No one knows what they are. The gamma-ray sky Image borrowed from 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 Gamma-ray, visible, and microwave images used with permission from Gabriela González, Department of Physics and Astronomy, Louisiana State University Gamma-ray view: includes all wavelengths less than about 1.2E-5nm (photon energies greater than 1E8eV) X-ray and IR images from Optics I student Yujiro Ito, 2004. X-ray view: from ROSAT shows wavelengths of 0.8nm (blue), 1.7nm (green), and 5.0nm (red) Infrared view: from IRAS shows emission at 0.1nm, 0.06nm, and 0.012nm Visible

The universe in more spectral regions…
IR Images used with permission from Gabriela González, Department of Physics and Astronomy, Louisiana State University Microwave

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