Lecture 7 Chapter 3 Electromagnetic Theory, Photons. and Light Sources of light Emission of light by atoms The electromagnetic spectrum see supplementary material posted on the course website
Electric dipole radiation Oscillating charges in dipole create sinusoidal E field and generate EM radiation
Electric dipole radiation Dipole moment: p qd d p d 0 p cos t 0 cos t Electric field of oscillating dipole: E p 0 Irradiance: I 2 k sin cos 4 0 2 4 2 p0 sin 2 3 2 32 c 0 r kr t r * EM wave is polarized along dipole * I ~ 4 - higher frequency, stronger radiation * No radiation emitted in direction of dipole
Dipole antenna Example: connect AC generator to dipole antenna/ Charges will run up and down - dipole moment will be oscillating and radiation will be emitted
Sources of light Accelerating charges emit light Linearly accelerating charge Synchrotron radiation light emitted by charged particles deflected by a magnetic field B Bremsstrahlung (Braking radiation) light emitted when charged particles collide with other charged particles
Synchrotron radiation: Advanced Photon Source Argonne National Lab, Chicago, IL 1104 m circumference storage ring http://www.aps.anl.gov/
The vast majority of light in the universe comes from molecular vibrations emitting light. Electrons vibrate in their motion around nuclei High frequency: ~10 14-10 17 cycles per second. Nuclei in molecules vibrate with respect to each other Intermediate frequency: ~10 11-10 13 cycles per second. Nuclei in molecules rotate Low frequency: ~10 9-10 10 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 states The 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. Energy levels are everything in quantum mechanics. Excited level Energy E = h Ground level The atom is vibrating at frequency,. The atom is at least partially in an excited state.
Excited atoms emit photons spontaneously. When an atom in an excited state falls to a lower energy level, it emits a photon of light. Excited level Energy Ground level Molecules typically remain excited for no longer than a few nanoseconds. This is often also called fluorescence or, when it takes longer, phosphorescence.
Different atoms emit light at different widely separated frequencies. Each colored emission line corresponds to a difference between two energy levels. Frequency (energy) These are emission spectra from gases of hot atoms. Atoms have relatively simple energy level systems (and hence simple spectra).
Atoms and molecules can also absorb photons, making a transition from a lower level to a more excited one. Energy Excited level Ground level This is, of course, absorption. Absorption lines in an otherwise continuous light spectrum due to a cold atomic gas in front of a hot source.
Before After Spontaneous emission Absorption Stimulated emission Einstein showed that stimulated emission can also occur.
Molecules have many energy levels. A typical molecule s energy levels: 2 nd excited electronic state 1 st excited electronic state Energy E = E electonic + E vibrational + E rotational Lowest vibrational and rotational level of this electronic manifold Excited vibrational and rotational level Ground electronic state Transition There are many other complications, such as spin-orbit coupling, nuclear spin, etc., which split levels. As a result, molecules generally have very complex spectra.
Water s vibrations
Decay from an excited state can occur in many steps. Energy Infra-red Ultraviolet Visible Microwave The light that s eventually re-emitted after absorption may occur at other colors.
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.
Blackbody emission spectrum The 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 1 Maxwell eq-ns in free space EM wave speed is c 00 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 c Absolute index of refraction: n v 0 0 Relative permittivity: KE 0 Relative permeability: K n K E KB For nonmagnetic transparent materials K B 1: B 0 n K E Maxwell s Relation However, n depends on frequency (dispersion) and Maxwell equation works only for simple gases.