The Electromagnetic Spectrum and Blackbody Radiation Sources of

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: ~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 = h n 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 2 nd excited electronic state Energy 1 st 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.

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. 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!).

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, together, have transitions at every wavelength.

Before Absorption Spontaneous Emission Stimulated Emission After

Boltzmann Population Factors Energy E 3 E 2 Ni is the number density of molecules in state i (i. e. , the number of molecules per cm 3). N 3 N 2 N 1 E 1 Population density T is the temperature, and k. B 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. High T Energy Low T 3 2 1 1 Molecules In equilibrium, the ratio of the populations of two states is: N 2 / N 1 = exp(–DE/k. BT ), where DE = E 2 – E 1 = 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 = B 12 N 1 I Spontaneous emission rate = A N 2 Stimulated emission rate = B 21 N 2 I In equilibrium, the rate of upward transitions equals the rate of downward transitions: B 12 N 1 I = A N 2 + B 21 N 2 I Rearranging: Recalling the Maxwell. Boltzmann Distribution (B 12 I ) / (A + B 21 I ) = N 2 / N 1 = exp[–DE/k. BT ]

Einstein A and B coefficients and Blackbody Radiation Now solve for the irradiance in: (B 12 I ) / (A + B 21 I ) = exp[-DE/k. BT ] Rearrange to: B 12 I exp[DE/k. BT] = A + B 21 I or: I = A / {B 12 exp[DE/k. BT] – B 21} or: I = [A/B 21] / { [B 12 /B 21] exp[DE/k. BT] – 1 } Now, when T ® ¥, I should also. As T ® ¥, exp[DE/k. BT ] ® 1. So: B 12 = B 21 º B And: I = [A/B] / {exp[DE/k. BT ] – 1} Eliminating A/B: ¬ Coeff up = coeff down! 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.

The Electromagnetic Spectrum gamma-ray microwave 106 infrared visible radio UV 105 wavelength (nm) The transition wavelengths are a bit arbitrary… X-ray

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 Long. Wavelength Electromagnetic Spectrum Arecibo radio telescope

Radio & microwave regions (3 k. Hz – 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 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 operate at 2. 45 GHz, where water absorbs very well. Percy Le. Baron 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.

Tera. Hertz light (a region of microwaves) Tera. Hertz 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. ED R O S EN C Fortunately, I couldn’t get permission to show you the movies I have of people with THz-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 10 mm 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

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 mm 2 there and the density decreases rapidly outside of the fovea to less than 5, 000 per mm 2. Note the blind spot caused by the optic nerve, which is void of any photoreceptors.

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 (320 -400 nm), UVB (290 -320 nm), and UVC (220 -290 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 Soft x-rays 5 nm > l > 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 > l > 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 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 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.

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 ke. V 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 e. V, 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, mec 2. 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