1. Introduction to Modern Physics A (mainly) historical perspective on - atomic physics  - nuclear physics - particle physics

2. Theories of Blackbody Radiation Classical disaster ! Quantum solution

3. Planck’s “Quantum Theory” The “oscillators” in the walls can only have certain energies – NOT continuous!

4. The Photoelectric Effect Light = tiny particles! Wave theory: takes too long to get enough energy to eject electrons Particle theory: energy is concentrated in packets -> efficiently ejects electrons!

6. The Photoelectric Effect Energy of molecular oscillator, E = nhf Emission: energy nhf -> (n-1)hf  Light emitted in packet of energy E = hf Einstein’s prediction: hf = KE + W (work function)

7. c = f Speed of light 3 x 10 8 meter/second or 30cm (1 foot) per nanosecond Wavelength (meter) Frequency #vibrations/ second

8. hf = KE + W (work function)

9. The Photoelectric Effect Wave Theory Photon Theory Increase light intensity -> more electrons with more KE Increase light intensity -> more photons -> more electrons but max-KE unchanged ! Frequency of light does not affect electron KE Max-KE = hf - W If f < f(minimum), where hf(minimum) = W, Then NO electrons are emitted! X X

10. How many photons from a lightbulb? 100W lightbulb, wavelength = 500nm Energy/sec = 100 Joules E = nhf -> n = E/hf = E /hc  n = 100J x 500 x 10 -9 = 2.5 x 10 20 !! 6.63 x 10 -34 J.s x 3 x 10 8 m/s

11. So matter contains electrons and light can be emitted in “chunks”… so what does this tell us about atoms?? Possible models of the atom Which one is correct?

12. Electric potential V(r) ~ 1/r The Rutherford Experiment

13. Distance of closest approach ~ size of nucleus At closest point KE -> PE, and PE = charge x potential KE = PE = 1/4  0 x 2Ze 2 /R R = 2Ze 2 / (4  0 x KE) = 2 x 9 x 10 9 x 1.6 x 10 -19 x Z 1.2 x 10 -12 J = 3.8 x 10 -16 Z meters = 3.0 x 10 -14 m for Z=79 (Gold)

14. The “correct” model of the atom …but beware of simple images!

15. Atomic “signatures” Rarefied gas Only discrete lines! An empirical formula! n = 3,4,…

16. The Origin of Line Spectra

17. Newton’s 2 nd Law and Uniform Circular Motion  F = ma Acceleration = v 2 /r Towards center of circle!

18. How do we get “discrete energies”? Linear momentum = mv Radius r Angular momentum L = mvr Bohr’s “quantum” condition – motivated by the Balmer formula

19. Electron “waves” and the Bohr condition De Broglie(1923): = h/mv Only waves with a whole number of wavelengths persist Quantized orbits! n = 2  r Same!!

20. Electrostatic force: Electron/Nucleus COULOMBS LAW

21. Combine Coulomb’s Law with the Bohr condition: Newton’s 2 nd Law Circular motion 

22. (for Z = 1, hydrogen)

23. Calculate the total energy for the electron: Total Energy = Kinetic + Potential Energy Electrostatic potential Electrostatic potential energy

24. Total energy Substitute

25. So the energy is quantized ! … now we can combine this with

26. …and this correctly predicts the line spectrum for hydrogen, …and it gets the Rydberg constant R right! …however, it does not work for more complex atoms…

28. Experimental results

29. Quantum Mechanics – or how the atomic world really works (apparently!) De Broglie(1923): = h/mv Take the wave description of matter for real: Describe e.g. an electron by a “wavefunction”  (x), then this obeys: Schroedinger’s famous equation

30. Now imagine we confine an electron in a “box” with infinitely hard/high walls:

31. Waves must end at the walls so:

32. and the energy levels for these states are: Discrete energies!

33. The probabilities for the electron to be at various places inside the box are: vs. Classical Mechanics Uniform probability!

34. Applying the same quantum mechanical approach to the hydrogen atom: Probability “cloud” Bohr radius

35. The “n = 2” state of hydrogen:

36. Atomic orbitals

37. Weird stuff!!

38. Ghosts!!??

39. Conclusions - Classical mechanics/electromagnetism does not describe atomic behavior - The Bohr model with a “quantum condition” does better…but only for hydrogen - Quantum mechanics gives a full description and agrees with experiment - …but QM is weird!!