Blackbody radiation The photoelectric effect Compton effect Line spectra Nuclear physics/bohr model Lasers Quantum mechanics

Transcription

1 Blackbody radiation The photoelectric effect Compton effect Line spectra Nuclear physics/bohr model Lasers Quantum mechanics Phys 2435: Chap. 38, Pg 1

2 Blackbody radiation New Topic Phys 2435: Chap. 38, Pg 2

3 Planck radiation law for blackbody radiation Predicted: Actual: ultraviolet catastrophe Stefan-Boltzmann law: I =! T 4 Wien displacement law: Rayleigh-Jeans (correct at long wavelength):! m T = 2.90 "10 #3 m$ K I(!) = 2"ckT! 4 Boltzmann Const. Phys 2435: Chap. 38, Pg 3

4 Planck radiation law Planck, in order to explain these laws had to resort to an act of desperation. He assumed the energy of the atoms in the wall were quantized : E = nhf, n = 1,2,3,... Planck s constant : h = x J. s Intensity as a function of wavelength, I(λ): Contains Stefan-Boltzmann, Wien, and Rayleigh-Jeans laws as special cases. Phys 2435: Chap. 38, Pg 4

5 Photoelectric effect New Topic Phys 2435: Chap. 38, Pg 5

6 Photoelectric effect Photoelectric effect observed in 1887 Proportional to number of electrons. Notice: V 0 independent of intensity. Problem: Electron not discovered until 1897! Light Measures maximum kinetic energy of electrons; V 0 a linear function of f. Phys 2435: Chap. 38, Pg 6

7 Planck and Einstein to the rescue! Planck relation; reinterpreted by Einstein Max Planck, Nobel Prize, 1918) K max = 1 2 m v 2 e max = (!e)(!v 0 ) A purely classical relation φ is the work function, the minimum energy needed to remove an electron 1eV = 1.60 x J Phys 2435: Chap. 38, Pg 7

8 Compton effect New Topic Phys 2435: Chap. 38, Pg 8

9 Compton effect A.H. Compton, Nobel Prize, Production Compton s experiment Phys 2435: Chap. 38, Pg 9

10 Compton effect Putting E = pc and E = hf together yields => p = hf c = h! Photons The wavelength shift calculated holds for the scattering of free electrons, But of course the electrons in an atom are bound to the nucleus. However, X-ray energies are much larger than the atomic binding energy, this treatment is still very accurate. Phys 2435: Chap. 38, Pg 10

11 ConcepTest 38.3(Post) Compton scattering As a result of Compton scattering, the scattered photon (1) has the same wavelength as the incident photon (2) has a longer wavelength than the incident photon (3) has a shorter wavelength than the incident photon Phys 2435: Chap. 38, Pg 11

12 Line spectra New Topic Phys 2435: Chap. 38, Pg 12

13 Line Spectra Lamp (all frequencies) Specific gas (line) spectrum Phys 2435: Chap. 38, Pg 13

14 Hydrogen spectrum Purely numerology. 4 Balmer lines visible; Lyman in the ultraviolet, Pashen, etc. in the infrared. Phys 2435: Chap. 38, Pg 14

15 Hydrogen energy levels Possible model Phys 2435: Chap. 38, Pg 15

16 Nuclear physics/bohr model New Topic Phys 2435: Chap. 38, Pg 16

17 The first nuclear experiment Rutherford (Nobel Prize, Chemistry, 1908) fruitcake model experiment! Phys 2435: Chap. 38, Pg 17

18 It was almost as incredible as if you had fired A 15-inch shell at a,piece of tissue paper and It came back and hit you. Phys 2435: Chap. 38, Pg 18

19 The nucleus Z: Atomic number Number of protons A: Mass number Number of protons and neutrons Notation: A Z A = Z + N Isotopes consist of different nuclei with Same Z, different N. Phys 2435: Chap. 38, Pg 19

20 Bohr model Combine Newton s inverse square law F = 1 e 2 2 4!" 0 r n With Bohr s ad hoc assumption We obtain E n =! me4 8" 0 2 h 2 1 n 2 Reduced mass does even better! L n = mv n r n = n h 2! ; n = 1,2,3,...! R = me4 8" 0 2 h 3 c Phys 2435: Chap. 38, Pg 20

21 Energy levels are complex! (Sodium) Phys 2435: Chap. 38, Pg 21

22 Bohr model is wrong! N. Bohr, Nobel Prize Although the Bohr model was correct in predicting the energy levels of hydrogen, it is a patchwork classical/quantum beast. If one attempts to apply it to other atoms, there are persistent discrepancies. It also makes a wrong prediction about hydrogen: that it has a magnetic moment in the ground state, L 1 =h/2π. The angular momenta ARE quantized, but the ground state has L 1 = 0. The picture of orbiting electrons, essentially like planets around the sun, is simply wrong!! Phys 2435: Chap. 38, Pg 22

23 Lasers New Topic Phys 2435: Chap. 38, Pg 23

24 Lasers Relevant concepts: population inversion, metastable state, stimulated emission, optical cavity For types of lasers, click here Phys 2435: Chap. 38, Pg 24

25 Quantum mechanics New Topic Phys 2435: Chap. 38, Pg 25

26 On the road to Quantum Mechanics The relation (photons as particles) p = hf c = h! also applies to electrons (particles as waves) and all other particles. Due to L. DeBroglie (1925). => Wave-particle duality a n i!!"!t Ψ(x,y,z,t) is the particle.. wavefunction. Schrodinger equation: = -!2 2m # % $! 2 "!x +!2 " 2!y +!2 " 2!z 2 & ( ' => Principle of complimentarity Phys 2435: Chap. 38, Pg 26