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.

Water’s vibrations

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.

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, 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

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 10m 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

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.

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.

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 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.

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 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 ~ .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-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

Gamma Ray

The universe in different spectral regions…

X-Ray

Visible

Microwave

The universe in more spectral regions…

IR