From Last Time(s)…

1. Einitial Photon Efinal Stable orbit Stable orbit From Last Time(s)… Light shows both particle and wave-like properties Atoms emit and absorb photons Photon: E=hf Phy208 Lect. 24

2. Exam 3 is Thursday Dec. 3 (after Thanksgiving) 5:30-7 pm, Birge 145 Students w / scheduled academic conflict please stay after class Tues. Nov. 24 to arrange alternate time. 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 Phy208 Lect. 24

3. 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 Phy208 Lect. 24

4. Emitting and absorbing light Zero energy Photon is emitted when electron drops from one quantum state to another n=4 n=4 n=3 n=3 n=2 n=2 Photon emittedhf=E2-E1 Photon absorbed hf=E2-E1 n=1 n=1 Absorbing a photon of correct energy makes electron jump to higher quantum state. Phy208 Lect. 23

5. 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 Phy208 Lect. 24

6. for a photon 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)xFrequency • E = hf, so f = E / h But photon momentum = p = E / c… Phy208 Lect. 24

7. We argue that applies to everything • Photons and footballs both follow the same relation. • Everything has both wave-like and particle-like properties Phy208 Lect. 24

8. Wavelengths of massive objects • deBroglie wavelength = • p=mv Phy208 Lect. 24

9. Matter Waves • deBroglie postulated that matter has wavelike properties. • deBroglie wavelength Example: Wavelength of electron with 10 eV of energy: Kinetic energy Phy208 Lect. 24

10. Momentum: 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.” (0.43 - 0.40 kg) • “Sometimes I don’t know how they catch that ball, because Brett wings that thing 60, 70 mph,” Flanagan said. (27 - 32 m/s) Need m, v to find  Aaron Wells Phy208 Lect. 24

11. This is very small • 1 nm = 10-9 m • Wavelength of red light = 700 nm • Spacing between atoms in solid ~ 0.25 nm • Wavelength of football = 10-26 nm • What makes football wavelength so small? Large mass, large momentumshort wavelength Phy208 Lect. 24

12. x Suppose an electron is a wave… • Here is a wave: …where is the electron? • Wave extends infinitely far in +x and -x direction l Phy208 Lect. 24

13. 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 Phy208 Lect. 24

14. Constructive interference Constructive interference Destructive interference Large amplitude Small amplitude Large amplitude Beat frequency: spatial localization • What does a sound ‘particle’ look like? • Example:‘beat frequency’ between two notes • Two waves of almost same wavelength added. Phy208 Lect. 24

15. Making a particle out of waves 440 Hz + 439 Hz 440 Hz + 439 Hz + 438 Hz 440 Hz + 439 Hz + 438 Hz + 437 Hz + 436 Hz Phy208 Lect. 24

16. x Adding many sound waves • Six sound waves with different wavelength added together1= 2= /1.05 3= /1.10 4= /1.15 5= /1.20 6= /1.25 • Wave now resembles a particle, but what is the wavelength? • Sound pulse is comprised of several wavelength • The exact wavelength is indeterminate Phy208 Lect. 24

17. Spatial extent of ‘wave packet’ • x = spatial spread of ‘wave packet’ • Spatial extent decreases as the spread in included wavelengths increases. x Phy208 Lect. 24

18. 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 ofincreasing the spread in wavelength (giving a spread in momentum). Phy208 Lect. 24

19. 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’sconstant Phy208 Lect. 24

20. 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 Phy208 Lect. 24

21. 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! Phy208 Lect. 24

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

23. Wavelength 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 Phy208 Lect. 24

24. 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) Phy208 Lect. 24

25. Wave representingelectron Wave representing electron Electron standing-waves on an atom • Electron wave extends around circumference of orbit. • Only integer number of wavelengths around orbit allowed. Phy208 Lect. 24

26. Zero energy n=4 n=3 n=2 Energy n=1 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 Phy208 Lect. 24

27. 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 Phy208 Lect. 24

28. 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. Phy208 Lect. 24

29. 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). Phy208 Lect. 24

30. 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). Phy208 Lect. 24