Chapter 33 Early Quantum Theory and Models of Atom

1. Chapter 33 Early Quantum Theory and Models of Atom

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

3. Blackbody radiation All objects emit radiation → thermal radiation 1) Total intensity of radiation ∝ T4 2) Continuous spectrum of wavelength Blackbody: absorbs all the radiation falling on it Idealized model Blackbody radiation → easiest 3

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

5. Planck’s quantum hypothesis Planck’ formula (1900): Max Planck (Nobel1918) Completely fit the data! Planck’s constant: The energy of any molecular vibration could be only some whole number multiply of hf. 5

6. (a) (b) continuous discrete Concept of quantum 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 6

7. Photon theory of light Little attention to quantum idea Until Einstein’s theory of light Molecular vibration → radiation Albert Einstein (Nobel1921) → quantum of radiation The light ought to be emitted, transported, and absorbed as tiny particles, or photons. 7

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

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

10. Experimental results 1) Ekmaxis independent of the intensity of light 2) Ekmaxchanges over the frequency of light 3)If f < f0 (cutoff frequency), no photoelectrons 10

11. energy Explanation by photon theory 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 (be absorbed) electron Minimum energy to get out: work function W0 Photoelectric equation 11

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

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

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

15. Experimental results 1) Besides 0, another peak  > 0 ( f < f0 ) 2) Δ=-0 depends on the scatteringangle Ordinary scattering & Compton scattering Can not be explained by model of EM waves 15

16. Explanation by photon theory 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 16

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

18. X-ray scattering 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? 18

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

20. *Photon interaction 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 20

21. Wave-particle duality 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. 21

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

23. de Broglie wavelength 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) 23

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

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

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

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

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

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

30. Bohr’s three postulates Rutherford’s model + quantum idea 1) Stationary states: stable & discrete energy level Neils Bohr (Nobel1922) 2) Quantum transition: (“jump”) emit or absorb a photon: 3) Quantum condition: (for angular momentum) 30

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

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

33. Energy levels 1) Quantization of energy (energy levels) n = 1: ground state, E1=-13.6eV; n = 2: 1st exited state, E2=-3.4eV; n = 3: 2nd exited state, E3=-1.51eV; … Negative energy → bound state 2) Binding / ionization energy → E=13.6eV 33

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

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

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

37. Single-electron ions 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: 37

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 38

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

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