What is Light?

1. What is Light?

2. Light is a Wave! • Interference • In phase = constructive • Out of phase (180 degrees) = destructive • Thin Film Interference

3. Light is a Wave! • Thin Film Interference

4. 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

5. 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.

6. 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

7. 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

8. 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

9. hf = KE + Wo • Photon Energy = hf • KE = max. ejected electron energy • Wo = work function - minimum work needed to eject e- (material specific) Fo(threshold frequency)

10. 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!!!)

11. 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)

12. 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

13. Into The Atom!! Up And Atom!!

14. 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

15. 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

16. Planetary Model • α particle: • 8000x mass of e- • Velocity = 2 x 107 m/s • The model itself • 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

17. AtomicSpectra(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?

18. 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

19. Energy Levels • Hydrogen Atom • 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

20. 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)

21. 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)

22. 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) λ = h/(mv) λ = 6.63 x 10-34 /(.05*40) λ = 3.3 x 10-34 m (no wave behavior can be seen) e.g. electron (9.11 x 10-31kg / 107m/s) λ = h/(mv) λ = 6.63 x 10-34 /(9.11 x 10-31 * 107) λ = 7.28 x 10-11 m (X-rays in EM spectrum) • Verified in 1927 by Davisson and Germer • Experimentally determined electron wavelength

23. 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.

24. 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)

25. Quantum Mechanics • “Reality” is affected by the observer • Multiple states seem to coexist until measurement or observation takes place • Schrödinger’s Cat

26. Quantum Mechanics • 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)

27. Philosophical Implications of Quantum Mechanics • 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.“ • Albert Einstein: • Rejected Heisenberg’s views on the implications of Quantum Theory but realized that they are a logical consequence • Quantum Theory therefore “incomplete”.

28. Goodbye to What We “Knew”?(It gets worse…) • 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. • 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. • Time is not constant • Space is curved • Length contraction • Mass increase

29. 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)