Lecture 7

Chapter 3

Electromagnetic Theory, Photons.and Light

Sources of light Emission of light by atoms The electromagnetic spectrum – see supplementary material Light in bulk matter and dispersion

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

Synchrotron radiation: Advanced Photon Source

Argonne National Lab, Chicago, IL

http://www.aps.anl.gov/

1104 m circumference storage ring

The vast majority of light in the universe comes from molecular vibrations emitting light.

Electrons vibrate in their motion around nucleiHigh 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 rotateLow frequency: ~109 - 1010 cycles per second.

Emission of light by (isolated) atoms

Quantum mechanics: electrons in atoms can only be in discreet states characterized with specific (quantized) energy

Transition of electron between discreet states with different energies causes emission or absorption of a single photon with energy matching the energy difference between the electron statesThe energy of this photon and frequency of EM wave are connected via Planck’s constant: E = h

Atomic and molecular vibrations correspond to excited energy levels in quantum mechanics.

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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.

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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.

Atoms and molecules can also absorbphotons, making a transition from a lower level to a more excited one.

This is, of course, absorption.

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Ground level

Excited level

Absorption lines in an otherwise continuous light spectrum due to a cold atomic gas in

front of a hot source.

Einstein showed that stimulated emission can also occur.

Before After

Absorption

Stimulated emission

Spontaneous emission

Molecules have many energy levels.A typical molecule’s energy levels:

Ground electronic state

1st excited electronic state

2nd excited electronic state

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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.

Water’s vibrations

Decay from an excited state can occur in many steps.

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The light that’s eventually re-emitted after absorption may occur at other colors.

Infra-red

Visible

Microwave

Ultraviolet

The Greenhouse effectThe 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

Blackbody radiationBlackbody 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.

Blackbody emission spectrumThe higher the temperature, the more the emission and the shorter the average wavelength.

Blue hot is hotter than red hot.

The sun’s surface is 6000 degrees K, so its blackbody spectrum peaks at ~ 500 nm--in the green. However, blackbody spectra are broad, so it contains red, yellow, and blue, too, and so looks white.

Electromagnetic spectrum

See supplementary lecture notes

Light in bulk matter

Maxwell eq-ns in free space EM wave speed is00

1

c

In medium, 0 and 0 in Maxwell equation must be replaced by and and phase speed of EM wave in medium becomes slower:

1

v

Absolute index of refraction:00

vcn

Relative permittivity:

0

0

B

E

KK

Relative permeability: BE KKn

EKn Maxwell’sRelationFor nonmagnetic transparent materials KB1:

However, n depends on frequency (dispersion) and Maxwell equation works only for simple gases.