PhysicsLAB: An Outline: Dual Nature of Light and Matter

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.

Atomic Models	Dual Nature of Matter	Luminiferous Aether
Particle Nature of Light	Spectral Lines	Speed of Light
Standard Model	Wave Nature of Light	Wave Nature of Particles
	Famous Experiments

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

top

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

top

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/µ_oepsilon_o) was verified by Heinrich Hertz in 1888 by timing the sparks between two induction coils and calculating the ratio of distance/time

top

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"

top

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

top

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)

discovered the neutron

Werner Heisenburg (1935)

first proposed the neutron-proton theory of nuclear structure

top

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!

top

Wave Nature of Particles

deBroglie wavelength (1923)

λ_deBroglie = 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

top

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)

top

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 Z_o 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)