Tue. Nov. 25, 2008Physics 208, Lecture 251 Exam 3 covers Lecture, Readings, Discussion, HW, Lab Exam 3 is Tue. Nov. 25, 5:30-7 pm, 2103 Chamberlin (here) Biot-Savart Law - currents produce magnetic fields Ampere’s law - shortcut to determining mag. fields from currents. Magnetic flux, Faraday effect, Lenz’ law, inductance, inductors Electromagnetic waves: Wavelength, freq, speed E&B fields, intensity, power, rad. pressure, Poynting vec Polarization Modern Physics (quantum mechanics) Photons & photoelectric effect Bohr atom: Energy levels, absorbing & emitting photons

Last Time… Photons as particles Photon absorption and emission Bohr atom

Tue. Nov. 25, 2008Physics 208, Lecture 253 Photon properties of light Photon of frequency f has energy hf Red light made of ONLY red photons The intensity of the beam can be increased by increasing the number of photons/second. (#Photons/second)(Energy/photon) = energy/second = power

Tue. Nov. 25, 2008Physics 208, Lecture 254 ? Only one photon present here Do an interference experiment again. But turn down the intensity until only ONE photon at a time is between slits and screen Photon interference? Is there still interference? A. YesB. No C. I’m confused

Tue. Nov. 25, 2008Physics 208, Lecture 255 Single-photon interference 1/30 sec exposure 1 sec exposure 100 sec exposure

Tue. Nov. 25, 2008Physics 208, Lecture 256 Probabilities Quantum mechanic says: Cannot predict where on camera photon will arrive. Individual photon hits determined probabilistically. Photon has a probability amplitude through space. Square of this quantity gives probability that photon will hit particular position on detector. The photon is a probability wave.

Tue. Nov. 25, 2008Physics 208, Lecture 257 Matter waves If light waves have particle-like properties, maybe matter has wave properties? de Broglie postulated that the wavelength of matter is related to momentum as This is called the de Broglie wavelength. Nobel prize, 1929

Tue. Nov. 25, 2008Physics 208, Lecture 258 Why h / p ? Works for photons Wave interpretation of light: wavelength = (Speed of Light) / Frequency = c / f Particle interpretation of light (photons): Energy = (Planck’s constant) x Frequency E = hf, so f = E / h for a photon But photon momentum = p = E / c…

Tue. Nov. 25, 2008Physics 208, Lecture 259 We argue that applies to everything Photons and footballs both follow the same relation. Everything has both wave-like and particle-like properties

Tue. Nov. 25, 2008Physics 208, Lecture 2510 Wavelengths of massive objects deBroglie wavelength = p=mv

Tue. Nov. 25, 2008Physics 208, Lecture 2511 Matter Waves deBroglie postulated that matter has wavelike properties. deBroglie wavelength Example: Wavelength of electron with 10 eV of energy: Kinetic energy

Tue. Nov. 25, 2008Physics 208, Lecture 2512 Wavelength of a football Make the Right Call: The NFL's Own interpretations and guidelines plus 100s of official rulings on game situations. National FootBall League, Chicago. 1999: "... short circumference, 21 to 21 1/4 inches; weight, 14 to 15 ounces.” ( kg) “Sometimes I don’t know how they catch that ball, because Brett wings that thing 60, 70 mph,” Flanagan said. ( m/s) Momentum: Need m, v to find Aaron Wells

Tue. Nov. 25, 2008Physics 208, Lecture 2513 This is very small 1 nm = m Wavelength of red light = 700 nm Spacing between atoms in solid ~ 0.25 nm Wavelength of football = nm What makes football wavelength so small? Large mass, large momentum short wavelength

Tue. Nov. 25, 2008Physics 208, Lecture 2514 Suppose an electron is a wave… Here is a wave: …where is the electron? Wave extends infinitely far in +x and -x direction x

Tue. Nov. 25, 2008Physics 208, Lecture 2515 Analogy with sound Sound wave also has the same characteristics But we can often locate sound waves E.g. echoes bounce from walls. Can make a sound pulse Example: Hand clap: duration ~ 0.01 seconds Speed of sound = 340 m/s Spatial extent of sound pulse = 3.4 meters. 3.4 meter long hand clap travels past you at 340 m/s

Tue. Nov. 25, 2008Physics 208, Lecture 2516 Beat frequency: spatial localization What does a sound ‘particle’ look like? Example:‘beat frequency’ between two notes Two waves of almost same wavelength added. Constructive interference Large amplitude Constructive interference Large amplitude Destructive interference Small amplitude

Tue. Nov. 25, 2008Physics 208, Lecture 2517 Making a particle out of waves 440 Hz Hz 440 Hz Hz Hz 440 Hz Hz Hz Hz Hz

Tue. Nov. 25, 2008Physics 208, Lecture 2518 Adding many sound waves Six sound waves with different wavelength added together 1 = 2 = / = / = / = / = /1.25 xx Wave now resembles a particle, but what is the wavelength? – Sound pulse is comprised of several wavelength – The exact wavelength is indeterminate

Tue. Nov. 25, 2008Physics 208, Lecture 2519 Spatial extent of ‘wave packet’  x = spatial spread of ‘wave packet’ Spatial extent decreases as the spread in included wavelengths increases. xx

Tue. Nov. 25, 2008Physics 208, Lecture 2520 Same occurs for a matter wave Localized particle: sum of waves with slightly different wavelengths. = h /p, each wave has different momentum. There is some ‘uncertainty’ in the momentum Still don’t know exact location of the particle! Wave still is spread over  x (‘uncertainty’ in position) Can reduce  x, but at the cost of increasing the spread in wavelength (giving a spread in momentum).

Tue. Nov. 25, 2008Physics 208, Lecture 2521 Heisenberg Uncertainty Principle Using  x = position uncertainty  p = momentum uncertainty Heisenberg showed that the product (  x )  (  p ) is always greater than ( h / 4  ) Often write this as where is pronounced ‘h-bar’ Planck’s constant

Tue. Nov. 25, 2008Physics 208, Lecture 2522 Uncertainty principle question Suppose an electron is inside a box 1 nm in width. There is some uncertainty in the momentum of the electron. We then squeeze the box to make it 0.5 nm. What happens to the momentum uncertainty? A. Momentum becomes more uncertain B. Momentum becomes less uncertain C. Momentum uncertainty unchanged

Tue. Nov. 25, 2008Physics 208, Lecture 2523 The wavefunction Quantify this by giving a physical meaning to the wave that describing the particle. This wave is called the wavefunction. Cannot be experimentally measured! But the square of the wavefunction is a physical quantity. It’s value at some point in space is the probability of finding the particle there!

Tue. Nov. 25, 2008Physics 208, Lecture 2524 Electron waves in an atom Electron is a wave. Its ‘propagation direction’ is around circumference of orbit. Wavelength = h / p Waves on a circle?

Tue. Nov. 25, 2008Physics 208, Lecture 2525 Waves on a circle My ‘ToneNut’. Produces particular pitch. Sound wave inside has wavelength =v/f (red line). Integer number of wavelengths required around circumference Otherwise destructive interference wave travels around ring and interferes with itself Blow in here Wavelength

Tue. Nov. 25, 2008Physics 208, Lecture 2526 Electron Standing Waves Electron in circular orbit works same way Integer number of deBroglie wavelengths must fit on circumference of the orbit. Circumference = (2  )x(orbit radius) = 2  r So condition is This says This is quantization angular momentum (L=mvr)

Tue. Nov. 25, 2008Physics 208, Lecture 2527 Wave representing electron Electron standing-waves on an atom Wave representing electron Electron wave extends around circumference of orbit. Only integer number of wavelengths around orbit allowed.

Tue. Nov. 25, 2008Physics 208, Lecture 2528 Hydrogen atom energies Wavelength gets longer in higher n states, (electron moving slower) so kinetic energy goes down. But energy of Coulomb interaction between electron (-) and nucleus (+) goes up faster with bigger n. End result is Zero energy n=1 n=2 n=3 n=4 Energy

Tue. Nov. 25, 2008Physics 208, Lecture 2529 Hydrogen atom question Here is Peter Flanary’s sculpture ‘Wave’ outside Chamberlin Hall. What quantum state of the hydrogen atom could this represent? A. n=2 B. n=3 C. n=4

Tue. Nov. 25, 2008Physics 208, Lecture 2530 Another question Here is Donald Lipski’s sculpture ‘Nail’s Tail’ outside Camp Randall Stadium. What could it represent? A. A pile of footballs B. “I hear its made of plastic. For 200 grand, I’d think we’d get granite ” - Tim Stapleton (Stadium Barbers) C. “I’m just glad it’s not my money” - Ken Kopp (New Orlean’s Take-Out)