Transcript What is Light?

What is Light?
Light is a Wave!
• Interference
– In phase = constructive
– Out of phase (180 degrees) = destructive
• Thin Film Interference
Light is a Wave!
• Thin Film Interference
Light is a Wave!
• Young’s Double Slit Experiment (1801)
– Java Applet
– Important Formula: d*sin Θ = m λ ; m = 1,2,3…
• Electromagnetic (EM) Waves
– Discovered by James Clerk Maxwell (1864)
– Perpendicular E and B fields
Wait a minute…
• Blackbody Radiation
• The “Ultraviolet Catastrophe”
• Classical Mechanics predicts that a heated body should emit
an infinite amount of energy, but experiment tells us
otherwise
• Max Planck proposed a theory that was able to
mathematically reproduce the blackbody radiation graphs :
E=nhf ; n=1,2,3…
• Energy of vibration could only be some whole number
multiple of hf
• Energy is “quantized” – not all energies possible.
Light is a Particle!
• Photoelectric Effect
– Discovered by Heinrich Hertz (early 1900s)
• EM pulses produce spark between two metal knobs
• Spark increased when UV light present (electrons)
– Explained by Albert Einstein
• Explained in 1905
• Nobel Prize 1921
Light is a Particle!
• Photoelectric Effect – The Experiment
– Speed vs. Light
• Proposed: Brighter light = more energy per electron
• Found: Brighter light cased more electrons, but at the
same energy
– Color
• Proposed: color has no/limited effect
• Only the frequency (color) of light affects electron
energies
• Higher f = Higher E
• Even extremely dim light with a high frequency
immediately ejected electrons w/ a high energy
Light is a Particle!
• Photoelectric Effect Explanation (A.E. – 1905)
– Light is quantized… it travels in “packets” and is
absorbed in this form (think of 1 cent)
– Electrons in metal can only absorb light energy by
absorbing one of these “quanta” (photon)
– E=hf h = Planck’s Constant
– If light shines on a metal, a photon can give up its
energy to the electron
– If the energy of the photon is enough, the electron
can be ejected from the metal
– Important Formula: hf = KE + Wo
hf = KE + Wo
KE (max)
– Photon Energy = hf
– KE = max. ejected electron energy
– Wo = work function - minimum work needed to
eject e- (material specific)
fre qu e n cy (Hz )
Fo (threshold frequency)
Energy of a Photon
• Planck’s Constant
– 6.63 x 10-34 J*s
– 4.136 x 10-15 eV/Hz
• Red Light (f = 4.3 x 1014 Hz)
– E= (4.136 x 10-15) * (4.3 x 1014) = 1.78 eV
• Blue Light (f = 6.3 x 1014 Hz)
– E= (4.136 x 10-15) * (6.3 x 1014) = 2.61 eV
• UV Light (f = 5 x 1018 Hz)
– E= (4.136 x 10-15) * (5 x 1018) = 20700 eV (Ouch!!!)
Light is a Particle!
(Part II)
• Compton Scattering
– Arthur H. Compton (1922)
– X-rays fired at electron target
– Scattered X-rays have lower frequency (lower E)
• Greater scatter angle – greater the change in frequency
– X-rays lose energy as they pass through matter
– X-rays (and therefore light) behave like particles
– By equating Einstein’s two famous “E” equations:
• Photon “mass” = (hf/c2)
• Photon “momentum” = (hf/c)
So what is Light?
• Wave
– Refraction
– Interference
• Particle
– Photoelectric effect
– Compton scattering
• How can it be both?
– Different sets of clues for recognition of the same
person
Into The Atom!!
Up And Atom!!
Into The Atom!!
• Background (or, what we knew early 1900s)
• Electrons discovered 1890s
• J.J. Thomson uses cathode ray tube (TV tube) to determine
q/m ratio of electron (1897)
• Robert Millikan’s oil drop experiment determines precise value
of electron charge (1909)
• “Atoms” widely accepted as building block of matter
• Actual makeup of the atom was still a matter of
speculation
• Problems…
• Max Planck’s quantized energy idea was in direct opposition
to the predictions of classical mechanics, although the fact
that it worked was irrefutable
• “Wave-Particle Duality” still a troubling idea
Models of the Atom
• J.J. Thomson – “Plum Pudding” (1900)
• Atom is neutral
• Negatively charged electrons
• Positively charged “pudding”
• Ernest Rutherford – Planetary (1909)
• Gold Foil scattering experiment (Geiger and Marsden)
• Fired newly discovered α particles (2n, 2p+) at thin gold foil
• Expected (based on “plum pudding” model):
– particles to spread out due to “weak” electrical force
– Most pass through un-deflected
• Found:
– Most particles have small deflection
– Some have large deflection, even reverse direction
Planetary Model
• α particle:
• 8000x mass of e• Velocity = 2 x 107 m/s
• The model itself
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Strong forces must be causing large deflections
Tiny nucleus with all of the positive charge and mass
Electrons outside
Atom mostly “empty space”
e.g. Gold Atom
• Nucleus = 1 ft radius then outermost e- is 3.3 mi away
Atomic Spectra
(Atomic Fingerprinting)
• Absorption Spectrum
• Josef Fraunhofer (1814)
• Optician testing high quality prisms
• Found dark lines in the spectrum produced by sunlight
• White (continuous spectrum) light directed through gas cloud
• Light is analyzed by spectroscope (prism)
• Most wavelengths pass through but a few are absorbed by gas
(dark lines)
• Pattern of dark lines is discrete
• Emission Spectrum - Bunsen and Kirchoff (1859)
• Gas is stimulated (by heating or high voltage) to emit light
• Spectroscopic pattern is opposite of absorption spectrum
• Matched spectra of earth’s elements to Fraunhofer lines (He)
• What is the makeup of distant objects?
Bohr Atomic Model (1912)
• Combined planetary model and quantum mechanics
• Electrons orbit nucleus, but only certain orbits allowed
• Angular momentum quantized: L = (mr)v = n(h/2π) n=1,2,3…
• Fit mathematical prediction of H spectra by Balmer (1885)
• Electrons in atoms cannot lose/gain energy continuously
(Planck/Einstein) but do so in “jumps”
• Light emitted when e- jumps from higher to lower state
• Eu – El = hf
• Problem: Orbiting electrons do not emit EM waves (energy)
• Normally charged particles do when accelerated (changing E field)
• Atoms shouldn’t exist!
• Hydrogen Atom
• En = -(13.6 eV)(Z2/n2)
• Z = # protons (Z = 1 for Hydrogen)
• n = principal quantum number of orbit
Energy Levels
• Hydrogen Atom
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E1 = -(13.6)(12/12) = -13.6 eV
E2 = -(13.6)(12/22) = -3.40 eV
E3 = -(13.6)(12/32) = -1.51 eV
E∞ = -(13.6)(12/∞) = 0 eV
Excited states (E2, E3, etc…) have less negative energy
• Orbit closest to the nucleus (E1) has the lowest total energy
• Energy must be added to raise the electron’s total energy
• Ionization (Binding) Energy
• Minimum energy required to remove and electron from the
ground state
• I.E. = 13.6 eV for Hydrogen
Jumping Energy Levels
• E2->E1
E2-E1 = -3.4 – (-13.6) = 10.2 eV
Ultraviolet (Lyman Series)
• E3->E2
E3-E2 = -1.51 – (-3.4) = 1.89 eV
Visible (Balmer Series)
• E4->E3
E4-E3 = -0.87 – (-1.51) = 0.64 eV
Infrared (Paschen Series)
Atomic Spectra Explained by Bohr
• Absorption
• In heated/charged atoms, electrons will jump up energy levels
• Absorb only those particular frequencies of light which give
jumps to allowed energy states
• Emission
• As atoms cool, electrons jump to a lower energy state
• Give off photons in process only in allowed frequencies
• Bohr Model – The Good
• Accurately predicts spectra photon wavelengths for Hydrogen
• Accurately predicts ionization energy of Hydrogen
• … and the Bad
• Assumes (but does not explain) stability of atoms
– Why quantization?
– Why is the ground state is the lowest state?
• Does not accurately predict line spectra for more complex atoms*
* - (The solution to this problem we will not concern ourselves with)
Bring on Quantum Mechanics!
• Based on probabilities, not certainties
• Louis DeBroglie (1924)
– If waves behave like particles, can particles
behave like waves?
– Why should there be two sets of rules – one for
small objects and one for large objects?
– Proposed DeBroglie Wavelength: λ = h/(mv)
e.g. rock (50 g / 40 m/s)
e.g. electron (9.11 x 10-31 kg / 107 m/s)
λ = h/(mv)
λ = h/(mv)
λ = 6.63 x 10-34 /(.05*40)
λ = 6.63 x 10-34 /(9.11 x 10-31 * 107)
λ = 3.3 x 10-34 m
λ = 7.28 x 10-11 m
(no wave behavior can be seen)
(X-rays in EM spectrum)
– Verified in 1927 by Davisson and Germer
• Experimentally determined electron wavelength
Quantum Mechanics to the Rescue!
(well, kind of…)
• deBroglie and the wave nature of
particles (λ=h/mv)
• Each electron in orbit is a circular
standing wave
• Any wavelength is possible, but only
resonant (constructive interference)
modes are sustained
• Other wavelengths destructively interfere
with themselves and die out
• Smallest radius is when circumference = 1 λ
• Explains ground state as lowest state.
• If 2πr = nλ n = 1,2,3… then mvr = nh/2π
• Angular Momentum is quantized.
Quantum Mechanics Gets Weird
• Weird: Young’s Double Slit Experiment Mark II…
now with electrons which are particles? …or
waves?...both? (video)
• Really Weird: Quantum Eraser
• Try Not to Think Too Hard Or You’ll Spontaneously
Combust Weird: Delayed Choice Quantum Eraser
• I’m Outta Here Weird: Entanglement (video)
Quantum Mechanics
• “Reality” is affected by the observer
• Multiple states seem to coexist until
measurement or observation takes place
• Schrödinger’s Cat
Quantum Mechanics
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Uncertainty Principle – Werner Heisenberg (1927 – N.P. 1932)
Try to measure the position and velocity of a particle at any instant…
•Classical Mechanics
•The world is a clock
•There are no fundamental barriers to an ultimate refinement of the apparatus to
make such measurements
•I.e. We possess the ability of achieving infinite accuracy
•Quantum Mechanics
•The world is a roulette wheel
•If is fundamentally impossible to make simultaneous measurements of position
and velocity with infinite accuracy
•I.e. The measurement procedure itself limits the accuracy to which we can
determine the position and velocity simultaneously
Uncertainty Principle: Δx * Δp ≥ h/(2π)
Philosophical Implications of Quantum Mechanics
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Werner Heisenberg: Knowledge is fundamentally limited. The future is
indeterminable.
– “I believe that the existence of the classical ‘path’ can be pregnantly
formulated as follows: The ‘path’ comes into existence only when we observe
it. “
– “In the sharp formulation of the law of causality-- "if we know the present
exactly, we can calculate the future"- it is not the conclusion that is wrong but
the premise.“
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Albert Einstein:
– Rejected Heisenberg’s views on the implications of Quantum Theory but
realized that they are a logical consequence
– Quantum Theory therefore “incomplete”.
Goodbye to What We “Knew”?
(It gets worse…)
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Quantum Physics
– Offers explanations for why the physics of the “very small” is different than
what is predicted by “classical” (Newtonian) physics.
– Newtonian physics works well for baseballs and buildings, but not so well for
electrons and light.
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Special/General Relativity
– Einstein’s “greatest idea” - perfected in 1915.
– Offers explanation (and empirical evidence) on why the physics of the “very
large” (both in size and velocity) is different than what is predicted by
“classical” physics.
– Newtonian physics works well for normal speeds and masses, but not for
incredibly large masses and the speed of light.
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Time is not constant
Space is curved
Length contraction
Mass increase
Einstein’s Legacy
Nature and Nature's laws lay hid in night
God said “Let Newton be!”
And all was light.
- Epitaph on Newton by Alexander Pope (1727)
But the devil shouting ‘Ho!’
Said “Let Einstein be!”
And restored the status quo.
-Sir John Collings Squire (1941)