Metal e-e- e-e- e-e- e-e- e-e- e+e+

Consider a nearly enclosed container at uniform temperature: Light gets produced in hot interior Bounces around randomly inside before escaping Should be completely random by the time it comes out Pringheim measures spectrum, 1899 u( ) = energy/ volume /nm Black Body Radiation: Light in a Box

Quantum effects almost always involve individual particles These particles typically have charges like +e or –e The only practical way to push on them is with electric and magnetic fields The Electron Volt Charge is e and voltage is measured in volts Define: This unit is commonly used in quantum mechanics

Statistical Mechanics was a relatively new branch of physics It explained some things, like the kinetic theory of gasses Physicists tried to explain black body radiation in terms of this theory Attempting to Explain the Result It said that the energy in black body could have any possible wavelength There are many, many ways to fit short wavelengths inside the box The amount of energy in any given wavelength could be any number from 0 to infinity Therefore, there should be a lot more energy at short wavelengths then at long Prediction #1: There will be much more energy at short wavelengths than long Prediction #2: The total amount of energy will be infinity The “ultraviolet catastrophe”

Comparison Theory vs. Experiment: Theory Experiment What went wrong? Not truly in thermal equilibrium? Possible state counting done wrong? The amount of energy in any given wavelength could be any number from 0 to infinity Max Planck’s strategy (1900): Assume energy E must always be an integer multiple of frequency f times a constant h E = nhf, where n = 0, 1, 2, … Perform all calculations with h finite Take limit h  0 at the end

Why this might help: Assume energy E must always be an integer multiple of frequency f times a constant h Theory Experiment Notice the problem is at short wavelength = high frequency Without this hypothesis, energy can be small without being zero Energy  0  Average Energy Average  Energy Now add levels It can no longer have a little bit of energy For high frequency, it has almost no energy

Planck’s Black Body Law Max Planck’s strategy (1900): Take limit h  0 at the end Except, it fit the curve with finite h! Planck Constant Looks like light comes in chunks with energy E = hf - PHOTONS

Photoelectric Effect: Hertz, 1887 Metal is hit by light Electrons pop off Must exceed minimum frequency Depends on the metal Brighter light, more electrons They start coming off immediately Even in low intensity Metal e-e- e-e- e-e- e-e- Einstein, 1905 It takes a minimum amount of energy  to free an electron Light really comes in chunks of energy hf If hf < , the light cannot release any electrons from the metal If hf > , the light can liberate electrons The energy of each electron released will be K = hf – 

Photoelectric Effect Will the electron pass through a charged plate that repels electrons? Must have enough energy Makes it if: Metal e-e- +––+ VV f V max slope = h/e Nobel Prize, 1921

Sample Problem When ultraviolet light of wavelength 227 nm strikes calcium metal, electrons are observed to come off with a kinetic energy of 2.57 eV. 1.What is the work function for calcium? 2.What is the longest wavelength that can free electrons from calcium? 3.If light of wavelength 312 nm were used instead, what would be the energy of the emitted electrons? We need the frequency: Continued...

Sample Problem continued 2.What is the longest wavelength that can free electrons from calcium? 3.If light of wavelength 312 nm were used instead, what would be the energy of the emitted electrons? The lowest frequency comes when K = 0 Now we get the wavelength: Need frequency for last part:

The de Broglie Relation We have a formula for the energy of a photon: Now, steal a formula from special relativity: Combine it with a formula from electromagnetic waves: And we get the de Broglie relation: Photons should have momentum too

Atom The Compton Effect By 1920’s X-rays were clearly light waves 1922 Arthur Compton showed they carried momentum e-e- e-e- e-e-  Photon in Photon out Conservation of momentum and energy implies a change in wavelength Photons carry energy and momentum, just like any other particle

Light is... Initially thought to be waves They do things waves do, like diffraction and interference Wavelength – frequency relationship Planck, Einstein, Compton showed us they behave like particles (photons) Energy and momentum comes in chunks Wave-particle duality: somehow, they behave like both Electrons are... They act like particles Energy, momentum, etc., come in chunks They also behave quantum mechanically Is it possible they have wave properties as well? Waves and Electrons

The de Broglie Hypothesis Two equations that relate the particle-like and wave-like properties of light 1924 – Louis de Broglie postulated that these relationships apply to electrons as well Implied that it applies to other particles as well de Broglie was able to explain the spectrum of hydrogen using this hypothesis

The Davisson-Germer Experiment Same experiment as scattering X-rays, except Reflection probability from each layer greater Interference effects are weaker Momentum/wavelength is shifted inside the material Equation for good scattering identical  dd e-e- Quantum effects are weird Electron must scatter off of all layers

What Objects are Waves? 1928: Electrons have both wave and particle properties 1900: Photons have both wave and particle properties 1930: Atoms have both wave and particle properties 1930: Molecules have both wave and particle properties Neutrons have both wave and particle properties Protons have both wave and particle properties Everything has both wave and particle properties Dr. Carlson has a mass of 82 kg and leaves this room at a velocity of about 1.3 m/s. What is his wavelength?

It’s a Particle, It’s a Wave, No It’s a... Consider the two slit experiment We can do it with photons or electrons, it doesn’t matter We can build a detector that counts individual photons or electrons We can put through particles one at a time We can count the number of photons on a screen Over time, we build up an interference pattern Interference only works with both slits open Every photon is going through both slits Sometimes, we say we have wave-particle duality It acts sometimes like a particle, sometimes like a wave It is a quantum object – something completely new

Diffraction And Uncertainty A plane wave approaches a small slit, width a Initially it is very spread out in space But it has a very definite direction and wavelength It therefore has a definite momentum The uncertainty in a quantity is how spread out the possible value is After it passes through the slit, it has a more definite position It now has a spread in angle This creates an uncertainty in its momentum in this direction

The Uncertainty Relation Waves, in general, are not concentrated at a point They have some uncertainty  x Unless they are infinitely spread out, they also typically contain more than one wavelength The have some uncertainty in wavelength The have some uncertainty in momentum Hard mathematical theorem: Make a precise definition of the uncertainty in position Make a precise definition of the uncertainty in momentum There is a theoretical limit on the product of these:

Sample Problem An experimenter determines the position of a proton to an accuracy of 10.0 nm. 1.What is the corresponding minimum uncertainty in the momentum? 2.As a consequence how far will the proton move (minimum) 1.00 ms later? This corresponds to an uncertainty in the velocity of This means the proton will move a minimum distance:

New Equations for Test 4 Images Quantum: Light in Materials Diffraction Grating Reflection/ Refraction Diffraction Limit End of material for Test 4