From Last Time(s)… Tues. Nov. 24, 2009Phy208 Lect Light shows both particle and wave-like properties Photon: E=hf Stable orbit E initial E final Photon Atoms emit and absorb photons

Tues. Nov. 24, 2009Phy208 Lect Exam 3 is Thursday Dec. 3 (after Thanksgiving) Students w / scheduled academic conflict please stay after class Tues. Nov. 24 to arrange alternate time. 5:30-7 pm, Birge 145 Covers: all material since exam 2. Bring: Calculator One (double-sided) 8 1/2 x 11 note sheet Schedule: Week14HW: assigned Thur. Nov. 19, due Fri. Dec. 4 (two weeks) Exam 3 practice problems available at Mastering Physics Last material for exam: Lecture of Tues. Nov. 24 Exam review: Tuesday, Dec. 1, in class

Tues. Nov. 24, 2009Phy208 Lect. 243 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

Thurs. Nov. 19, 2009Phy208 Lect. 234 Emitting and absorbing light Photon is emitted when electron drops from one quantum state to another Zero energy n=1 n=2 n=3 n=4 n=1 n=2 n=3 n=4 Absorbing a photon of correct energy makes electron jump to higher quantum state. Photon absorbed hf=E 2 -E 1 Photon emitted hf=E 2 -E 1

Tues. Nov. 24, 2009Phy208 Lect. 245 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

Tues. Nov. 24, 2009Phy208 Lect. 246 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…

Tues. Nov. 24, 2009Phy208 Lect. 247 We argue that applies to everything Photons and footballs both follow the same relation. Everything has both wave-like and particle-like properties

Tues. Nov. 24, 2009Phy208 Lect. 248 Wavelengths of massive objects deBroglie wavelength = p=mv

Tues. Nov. 24, 2009Phy208 Lect. 249 Matter Waves deBroglie postulated that matter has wavelike properties. deBroglie wavelength Example: Wavelength of electron with 10 eV of energy: Kinetic energy

Tues. Nov. 24, 2009Phy208 Lect 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

Tues. Nov. 24, 2009Phy208 Lect 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

Tues. Nov. 24, 2009Phy208 Lect Suppose an electron is a wave… Here is a wave: …where is the electron? Wave extends infinitely far in +x and -x direction x

Tues. Nov. 24, 2009Phy208 Lect 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

Tues. Nov. 24, 2009Phy208 Lect 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

Tues. Nov. 24, 2009Phy208 Lect Making a particle out of waves 440 Hz Hz 440 Hz Hz Hz 440 Hz Hz Hz Hz Hz

Tues. Nov. 24, 2009Phy208 Lect 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

Tues. Nov. 24, 2009Phy208 Lect Spatial extent of ‘wave packet’  x = spatial spread of ‘wave packet’ Spatial extent decreases as the spread in included wavelengths increases. xx

Tues. Nov. 24, 2009Phy208 Lect 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).

Tues. Nov. 24, 2009Phy208 Lect 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

Tues. Nov. 24, 2009Phy208 Lect 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

Tues. Nov. 24, 2009Phy208 Lect 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!

Tues. Nov. 24, 2009Phy208 Lect Electron waves in an atom Electron is a wave. Its ‘propagation direction’ is around circumference of orbit. Wavelength = h / p Waves on a circle?

Tues. Nov. 24, 2009Phy208 Lect 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

Tues. Nov. 24, 2009Phy208 Lect 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)

Tues. Nov. 24, 2009Phy208 Lect 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.

Tues. Nov. 24, 2009Phy208 Lect 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

Tues. Nov. 24, 2009Phy208 Lect 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

Tues. Nov. 24, 2009Phy208 Lect Hydrogen atom music Here the electron is in the n=3 orbit. Three wavelengths fit along the circumference of the orbit. The hydrogen atom is playing its third highest note. Highest note (shortest wavelength) is n=1.

Tues. Nov. 24, 2009Phy208 Lect Hydrogen atom music Here the electron is in the n=4 orbit. Four wavelengths fit along the circumference of the orbit. The hydrogen atom is playing its fourth highest note (lower pitch than n=3 note).

Tues. Nov. 24, 2009Phy208 Lect Hydrogen atom music Here the electron is in the n=5 orbit. Five wavelengths fit along the circumference of the orbit. The hydrogen atom is playing its next lowest note. The sequence goes on and on, with longer and longer wavelengths, lower and lower notes. But Remember that these are higher and higher energies! (Coulomb (electrostatic) potential energy dominates).