This "lesson" is the outline for a speech that I gave many years ago for some Middle School teachers who wanted some background on the dual nature of light and matter. An index for the outline is provided in the table below. Additional resources can be found in the Related Documents at the bottom of the page.
Particles
- have mass (inertia)
- respond to forces (acceleration)
- have momentum (mass x velocity)
Waves
- transfer energy from one place to another
- mechanical (require a medium) and non-mechanical
Particle Nature of Light Newton's Corpuscular Theory of Light (1670)
- light corpuscles have mass and travel at extremely high speeds in straight lines
- rectilinear propagation - blocked by large objects (well-defined shadows)
- obey the law of reflection when bounced off a surface
- speed up when they enter denser media (gravitational force of attraction, net F = ma)
- paths in denser media "bend towards the normal"
- prism dispersion - contradicted corpuscular theory
Wave Nature of Light
Huygens Principle (1680)
- wavelet envelop model (each point on a wavefront acts as a source for the next wavefront)
- plane waves generate plane waves, circular waves generate circular waves
- light was composed of longitudinal waves like sound
- obey the law of reflection when bounced off a surface
- waves slowed down when they entered a denser medium causing their paths to "bend towards the normal"
- light SHOULD produce interference patterns and diffraction patterns
Thomas Young's Double Slit Experiment (1807)
- bright (constructive) and dark (destructive) fringes seen on screen
- wave nature of light
Diffraction vs Interference Patterns
Thin Film Interference Patterns
Poisson/Arago Spot (1820)
- diffraction fringes seen within and around a small obstacle or through a narrow opening
- wave nature of light
Young and Fresnel argue that light was a transverse wave (1820)
- polarization (iceland spar; polaroid filters)
- wave nature of light
Speed of Light Armand Fizeau and Jean Foucaults' experiment (1850)
- light travels slower through water than air
- wave nature of light
Ole Romer (1676) determined that the speed of light was finite
- used the time delay from the eclipsed moons of Jupiter
-
Huygens (1680) used Romer's 22-minute time for light to cross the diameter of the earth's orbit to get a value of 2 x 108 m/sec for the speed of light
Faraday - empirically postulated the existence of electric and magnetic fields (1830)
- changing magnetic fields induce electricity
- electric currents produce magnetic fields
James Maxwell's equations for Electromagnetism (1860)
- mathematical theory - the speed he predicted for electromagnetic waves nearly matched the measured speed of light leading him to predict that light was an electromagnetic wave
-
Maxwell's predicted speed (c = squareroot (1/µoepsilono) was verified by Heinrich Hertz in 1888 by timing the sparks between two induction coils and calculating the ratio of distance/time
The Luminiferous Aether (ether) Was light a mechanical or non-mechanical wave?
- all previously known waves were mechanical and needed a medium
Maxwell postulated the existence of the aether
- rigid, stiff solid to allow for light's extremely high speed even though it was not required mathematically, but "action at a distance" seemed absurd
null result of Michelson and Morley (Case Institute in Ohio in 1887)
- steady interference fringes regardless of the rotation of the interferometer or the direction of the earth's travel through the "aether wind"
Albert Einstein AND Special Relativity (1905) - there was NO need for the aether
- (1) the laws of physics do not depend on relative constant motion (inertial frames of reference)
- (2) the speed of light moving through free space is independent of the motion of its source and of the motion of the observer
Albert Einstein AND General Relativity
- Gravity is the warping of space
- precession of Mercury's orbit - 43 seconds of arc every 100 years
- Gravity changes the direction that light travels - gravity bends light
- Air Arthur Eddington 1919 solar eclipse expedition
- gravity lenses - "multiple stars" or "ring (halo) of stars"
Spectral Lines As early as the 1750's scientists were observing and recording spectral properties of excited gases and solids
- solids - continuous spectra
-
excited gases - discrete spectra (some gases had simple spectra; others had very complex ones)
Fraunhofer (1815)
- well-defined, dark lines present in the continuous spectra of bright stars
Astronomer John Hershel (1823)
- proposed that elements could be identified through spectrum analysis
Kirchhoff (1859)
- demonstrated that the lines represented absorption lines which revealed the chemical composition of the gases surrounding the stars since the dark lines in a chemical absorption spectra exactly matched the bright lines in its emission spectra
- discovery of helium, Lockyer (1870)
J. J. Balmer (1885)
- secondary teacher (math/physics) developed an empirical mathematical equation to generate the wavelengths for the lines in hydrogen's visible spectrum
Atomic Models Beginning of the 20th century:
- (1) atoms were electrically neutral - equal amounts of + and - charge
- (2) the negative charge is associated with cathode rays (electrons) particles having very small mass
- (3) atoms are stable
J. J. Thomson (1900)
- discovered the electron - cathode rays
-
plum-pudding model - electrons and protons evenly spread throughout the atom (diameter = 10-10 meters)
Max Planck (1900)
- blackbody radiation
- ultraviolet catastrophe
- E = hf where f = c/λ
Brownian Motion (1827)
- discovered initially by Scottish botanist, Robert Brown, when he witnessed pollen grains "jiggling" when examined under a microscope - later he saw the same agitated behavior with dust particles and grains of soot
- "Brownian Motion" is now known to be the result of the collisions between neighboring atoms/molecules (Einstein - 1905)
Rutherford's gold foil experiment (1909) with Geiger and Marsden (repeated with carbon and aluminum)
- 1 out of every 8000 alpha particles scattered through an angle > 90°
-
discovered a small positively charged nucleus (diameter ≤ 10-14 meters)
- the value of the charge needed from the scattering data would equate to the magnitude of the charge held in the nucleus - which would dictate the number of electrons surrounding the nucleus which closely matched the atomic number in Mendeleev's periodic table (1869)
Bohr model (1913) how were these electrons arranged?
- steady orbitals - deBroglie wavelengths
- energy levels - light emission, light absorption - excitation and de-excitation
- spectral lines
Franck/Hertz (1914) experimentally verified discrete energy levels
- bombarded room temperature mercury vapor with electrons of specific KE
- absorption peak at 4.9 eV which was then shown to represent the energy of the 254 nm wavelength in mercury's emission spectrum
James Chadwich (1932) Werner Heisenburg (1935)
- first proposed the neutron-proton theory of nuclear structure
Particle Nature of Light Photoelectric effect (1905)
- light is made of photons
- quantized packets of radiant energy
- one photon emits one photo-electron
- current is proportional to the intensity of the light
- KE of the emitted photo-electrons is proportional to the frequency of the light
Compton Effect (1923) - bombarded graphite crystals with x-rays
- electrons were released - the momentum of the electrons revealed their KE which matched the energy lost by the x-rays - a classic collision had occured in which momentum was conserved
- x-rays have momentum
from special relativity E = mc2
momentum (p) = mv = (E/c2)(v)
for light, v = c
therefore p = E/c
since E = hf = h(c/λ),
p = (hc/λ)/c
p = h/λ
- photons (quantized bundles of radiant energy) which have no mass do have momentum!
Wave Nature of Particles deBroglie wavelength (1923)
-
λdeBroglie = h/mv
- an integer multiple of an electron's deBroglie wavelength produced a steady state orbital
Davisson-Germer Experiment (1927)
- diffraction of electrons through a crystal revealed the same pattern as x-rays diffracted through the crystal
- high energy electrons have wavelengths
- electron microscopes
Dual Nature of Matter Schrodinger's Wave Mechanics (1926)
- quantum mechanical (mathematical) model
- clouds of electrons - probabilities
Max Born (1933)
- electron diffraction - interference pattern of electrons through double slits
- statistical interpretation of many electrons not the exact behavior of each individual electron
non-collapsing matter
- deBroglie wavelengths
- fermions must obey the Pauli Exclusion Principle (1925)
Heisenburg's Uncertainty Principle (1927)
- photons interact with one electron not all of them
- interference of localized wave disturbances creates a wave packet which has appreciable amplitude in only a small region of space - acting like the motion of a particle
Δx Δp ≥ h/(2π)
ΔE Δt ≥ h/(2π)
Standard Model (1960's) Fundamental Particles
- up, charm, top (+2/3)
- down, strange, bottom (-1/3)
- electron, muon, tau (-1)
- electron neutrino, muon neutrino, tau neutrino
proton composition (uud) yields a charge of +1
neutron composition (ddu) yields a charge of 0
Bosons vs Fermions
- gauge bosons (force carriers) can march in step (photons, W and Z bosons, gluons)
- fermions (leptons: electron, muon, tau; and quarks) must obey the Pauli Exclusion Principle (1925)
Four Fundamental Forces
-
weak nuclear (W-, W+ and Zo producing natural radioactivity)
- strong nuclear (gluons and quarks confinement)
- electromagnetic (photons)
- gravitation (gravitons)
What causes mass?
- Higgs boson (postulated in 1960 but still not experimentally verified)
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