Major Concepts in Physics Lecture 18.

1. Major Concepts in Physics Lecture 18. Prof Simon Catterall Office 309 Physics, x 5978 smc@physics.syr.edu http://physics/courses/PHY102.08Spring PHY102

2. Recap • Discussed how crises in late 19th physics led to new ideas about light/matter • Sometimes light behaves not as a wave but as a particle – the photon with E=hf • Similarly Bohr model for H atom suggests that electron (a particle) sometimes behaves as a wave ! l=h/p, p=mv Wave-particle duality PHY102

3. Direct confirmation of wave nature of electron • If electron behaves as wave – we should be able to make it undergo diffraction and interference ! • Demo – electron diffraction • Wavelength ? Very small. • Application .. Electron microscope. Can resolve structures about size of wavelength PHY102

4. Electron pattern on L, X-ray on R PHY102

5. Example (text problem 28.4): What are the de Broglie wavelengths of electrons with the following values of kinetic energy? (a) 1.0 eV and (b) 1.0 keV. (a) The momentum of the electron is and PHY102

6. Example continued: (b) The momentum of the electron is and PHY102

7. Electron microscope • Use this smaller wavelength to ``see`` finer detail … PHY102

8. Example (text problem 28.15): An image of a biological sample is to have a resolution of 5 nm. (a) What is the kinetic energy of a beam of electrons with a de Broglie wavelength of 5.0 nm? (b) Through what potential difference should the electrons be accelerated to have this wavelength? PHY102

9. Double slit interference – light or electrons … PHY102

10. Pattern for laser light PHY102

11. Electron interference time PHY102

12. Interpretation • Electron beam interferes like a wave! • Dots on screen represent electrons hitting detector. Note when they land they act like particles … • Intensity of pattern interpreted as probability that any given electron will land there • Interference remains even when intensity of beam is so low that only 1 electron is present! • Single electron interferes with itself!! PHY102

13. Uncertainty principle PHY102

14. Electron diffraction PHY102

15. Analysis: At angle q y-component of momentum is psinq But sinq=l/a=h/(pa) (diffraction) Thus uncertainty in y-component of momentum =h/a Dpy Dy>=h Heisenberg’s Uncertainty relation Product of uncertainities in position and momentum always at least h PHY102

16. Consequences of quantum uncertainty • A quantum particle is never at rest • If I try and confine a quantum particle to smaller and smaller distances – its energy will increase – explains stability of atoms – quantum uncertainty prevents electron from spiraling into nucleus • To have an electron with well-defined momentum – will always be spread out and exhibit wave-like properties PHY102

17. Example (text problem 28.19): At a baseball game, a radar gun measures the speed of a 144 gram baseball to be 137.320.10 km/hr. (a) What is the minimum uncertainty of the position of the baseball? px = mvx and vx = 0.10 km/hr = 0.028 m/s. PHY102

18. Discrete energy levels • Imagine an electron confined to 1d box • Wavelength must fit into box • l=2L/n • Therefore p=h/l=nh/2L • E=1/2p2/m=n2h2/8mL2 • Energy is quantized ! PHY102

19. Summary • For small objects like electrons motion not governed by Newton’s laws – instead quantum mechanics • Particles have both particle/wave properties with p=h/l • Wave-like character ensured by Heisenberg uncertainty relation Dp Dx>h • Quantum particles can interfere, diffract • And can be confined with only certain energies PHY102