1. Chapter 33 Early Quantum Theory and Models of Atom

2. Revolution of classical physics 2 World was well explained except a few puzzles? M-M experimenttheory of relativity Black body radiationquantum theory Revolution of Q-theory: (1900 – 1926) → now? Two foundations of modern physics “two dark clouds in the sky of physics”

3. Blackbody radiation 3 All objects emit radiation → thermal radiation 1) Total intensity of radiation ∝ T 4 2) Continuous spectrum of wavelength Blackbody: absorbs all the radiation falling on it Idealized model Blackbody radiation → easiest

4. Classical theories 4 Wien’s law: Experiment Intensity Wavelength Wien Rayleigh-Jeans Planck

5. Planck’s quantum hypothesis 5 Planck’ formula (1900): Max Planck (Nobel 1918) Completely fit the data! Planck’s constant: The energy of any molecular vibration could be only some whole number multiply of hf.

6. Concept of quantum 6 The energy of any molecular vibration could be only some whole number multiply of hf. f : frequency of oscillation Quantum → discrete amount / not continuous hf : quantum of energy n : quantum number continuous (a) discrete (b)

7. Photon theory of light 7 Little attention to quantum idea Albert Einstein (Nobel 1921) Until Einstein’s theory of light Molecular vibration The light ought to be emitted, transported, and absorbed as tiny particles, or photons. → radiation → quantum of radiation

8. Energy of photon 8 Solution: Example1: Calculate the energy of a photon with Example2: Estimate the number of visible light photons per sec in radiation of 50W light bulb. Solution: Average wavelength: invisible light photons?

9. Photoelectric effect 9 Photoelectric effect: electron emitted under light Stopping potential / voltage: If voltage V changes photocurrent I also changes Saturated photocurrent

10. Experimental results 10 1) E kmax is independent of the intensity of light 2) E kmax changes over the frequency of light 3) If f < f 0 (cutoff frequency), no photoelectrons

11. Explanation by photon theory 11 The result can’t be explained by classical theory An electron is ejected from the metal by a collision (inelastic) with a single photon. photon energy electron (be absorbed) Minimum energy to get out: work function W 0 Photoelectric equation

12. Compare with experiment 12 1) Intensity of light ↗ n ↗, f doesn’t change 2) linear relationship 3)

13. Energy of photon 13 Example3: The threshold wavelength for a metal surface is 350 nm. What is the E kmax when the wavelength changes to (a) 280 nm, (b) 380 nm? Solution: No ejected electrons!

14. Compton effect 14 Compton’s x-ray scattering experiment (Nobel 1927) Scattering: light propagate in different direction EM waves: forced vibration → same f ( = 0 )

15. Experimental results 15 1) Besides 0, another peak > 0 ( f < f 0 ) Can not be explained by model of EM waves 2) Δ = - 0 depends on the scattering angle  Ordinary scattering & Compton scattering

16. Explanation by photon theory 16 What happens in the view of photon theory? A single photon strikes an electron and knocks it out of the atom. (elastic collision) Conservation of energy: Energy loss → > 0

17. Compton shift 17 Conservation of momentum: Compton shiftCompton wavelength

18. X-ray scattering 18 Example4: X-rays with 0 = 0.2 nm are scattered from a material. Calculate the wavelength of the x-rays at scattering angle (a) 45°and (b) 90°. Solution: Maximum shift?

19. Some questions 19 An collision between photon and free electron 1) Why there is still a peak of 0 ? 3) Why not absorb the photon ? 4) Why not consider in photoelectric effect? 2) What is the difference from photoelectric effect?

20. *Photon interaction 20 Four important types of interaction for photons: 1) Scattered from an electron but still exist 2) Knock an electron out of atom (absorbed) 3) Absorbed by an atom → excited state 4) Pair production: such as electron and positron Inverse process → annihilation of a pair

21. Wave-particle duality 21 Sometimes light behaves like a wave sometimes it behaves like a stream of particles Wave-particle duality as a fact of life Bohr’s principle of complementarity: To understand any given experiment of light, we must use either the wave or the photon theory, but not both.

22. Wave nature of matter 22 L. de Broglie extended the wave-particle duality Symmetry in nature: For a particle with momentum p, wavelength: Wave particle L. de Broglie ( Nobel 1929) It’s called de Broglie wave or matter-wave

23. de Broglie wavelength 23 Example5: Calculate the de Broglie wavelength of (a) a 70kg man moving with speed 5m/s; (b) an electron accelerated through 100V voltage. Solution: (a) Much too small to be measured (b)

24. Experiments of de Broglie wave 24 1) Davisson-Germer experiment 2) G. P. Thomson’s experiment (Nobel 1937) 3) Other experiments & other particles

25. What is an electron? 25 An electron is neither a wave nor a particle de Broglie wave → a wave of probability It is the set of its properties that we can measure “A logical construction” —— B. Russell

26. Early models of atom 26 1) J. J. Thomson’s plum-pudding model 2) Rutherford’s planetary model (nuclear model) α particle scattering experiment Stability of atom & discrete spectrum

27. Atomic spectra 27 Light spectrum of atom: line spectrum (discrete) Characteristic of the material → “fingerprint” Emission spectrum & Absorption spectrum

28. Spectrum of Hydrogen 28 Hydrogen: simplest atom → simplest spectrum Balmer’s formula for visible lines: Rydberg constant: Balmer series I R range Visible light U V range (Infrared Ray) (UltraViolet ray)

29. General formula 29 There are other series in the UV and I R regions k = 1 → Lyman series ( ultraviolet ) k = 2 → Balmer series ( visible ) k = 3 → Paschen series ( infrared ) … Lyman Balmer Paschen

30. Bohr’s three postulates 30 Rutherford’s model + quantum idea Neils Bohr (Nobel 1922) 1) Stationary states: stable & discrete energy level 2) Quantum transition: (“jump”) emit or absorb a photon: 3) Quantum condition: (for angular momentum)

31. Bohr model (1) 31 Rutherford’s model + quantum idea Bohr radius: The orbital radius of electron is quantized

32. Bohr model (2) 32 Kinetic energy: Total energy: Potential energy: Energy is also quantized

33. Energy levels 33 n = 1: ground state, E 1 = - 13.6eV; n = 2: 1 st exited state, E 2 = - 3.4eV; n = 3: 2 nd exited state, E 3 = - 1.51eV; … 1) Quantization of energy (energy levels) Negative energy → bound state 2) Binding / ionization energy → E = 13.6eV

34. Transition & radiation 34 Jumping from upper state n to lower state k : Theoretical value of R : In accord with the experimental value!

35. Energy level diagram 35 n=1(ground) n=2(1 st exited) n=3(2 nd exited) n=4(3 rd exited) … -13.6eV -3.4eV -1.51eV -0.85eV Lyman Balmer Paschen E = 0

36. Transition of atom 36 Example6: Hydrogen atom in 3 rd excited state, (a) how many types of photon can it emit? (b) What is the maximum wavelength? Solution: (a) n = 4 1 2 3 4 -13.6eV -3.4eV -1.51eV -0.85eV 6 types of photon

37. Single-electron ions 37 Example7: Calculate (a) the ionization energy of He + ; (b) radiation energy when jumping from n=6 to n=2. (c) Can that photon be absorbed by H? Solution: (a) For single-electron ions:

38. 38 (b) radiation energy if jumping from n=6 to n=2 (c) Can that photon be absorbed by H? So it can be absorbed by Hydrogen atom

39. Value of Bohr’s theory 39 Niels Bohr Institute & Copenhagen School 1) Precisely explained the discrete spectrum 2) Lyman series & Pickering series 3) Ensures the stability of atoms Semi-classical: other atoms, line intensity, … New theory → quantum mechanics

40. *de Broglie’s hypothesis applied to atoms 40 Stable orbit for electron → “standing wave” de Broglie wave: Circular standing wave: Combine two equations: It is just the quantum condition by Bohr!