Quantum Mysteries. Scott N. Walck. September 2, 2018

Transcription

1 Quantum Mysteries Scott N. Walck September 2, 2018

2 Key events in the development of Quantum Theory 1900 Planck proposes quanta of light 1905 Einstein explains photoelectric effect 1913 Bohr suggests special radii 1921 Stern and Gerlach demonstrate spatial quantization 1923 Compton sees frequency shift in scattered X-rays 1924 de Broglie suggests matter waves 1925 Heisenberg presents matrix mechanics 1926 Schrödinger presents wave mechanics 1927 Heisenberg presents uncertainty principle

3 Theories in Physics nonrelativistic quantum wave mechanics Schrödinger 1926 QED Feynman 1949 relativistic quantum Electroweak QCD Weinberg Wilczek quantum gravity? electricity Coulomb 1800 mechanics Newton 1687 nonrelativistic classical wave optics Young 1803 gravity Newton 1687 SR Einstein 1905 EM Theory Maxwell 1865 GR Einstein 1915 relativistic classical

4 Metric (SI) units Dimension Symbol Unit Abbreviation Length x meter m Mass m kilogram kg Time t second s Speed v m/s Energy E Joule J = kg m 2 /s 2 Momentum p kg m/s Angular Momentum L J s = kg m 2 /s Frequency f Hertz Hz = cycle/s

5 Metric prefixes Prefix Symbol Meaning Tera T Giga G 10 9 Mega M 10 6 kilo k 10 3 milli m 10 3 micro µ 10 6 nano n nm = m = m

6 Unit conversion 1 ev = J Example: Convert J into electron volts. Solution: J Example: Convert 1.7 ev into Joules. Solution: 1.7 ev J 1 ev 1 ev = 18.7 ev J = J

7 Classical waves There are many types of waves. sound waves water waves light waves waves on a string A basic wave (of any type) has 5 important properties. Wavelength is crest-to-crest distance at a snapshot in time Period is time between crest arrivals at a fixed point in space Frequency is the number of crests per second moving past a fixed point Wave speed is the speed of a crest Amplitude is the size or strength of a wave

8 Wavelength is crest-to-crest distance at a snapshot in time 1 λ wavelength 0.5 Position x (m) ,

9 Period is time between crest arrivals at a fixed point in space T = 360 s for this wave 1 T period 0.5 Time t (s) ,

10 Frequency is the number of crests per second moving past a fixed point 1 f = 4 Hz for this wave 0.5 Time t (s)

11 The 5 wave properties are not independent Period and frequency contain the same information in different form. f = 1 T Wavelength, period, and speed are related. The wave travels at one wavelength per period. v = λ T = λf

12 Classical wave summary Property Symbol Unit Wavelength λ m Period T s Frequency f Hz Speed v m/s Amplitude depends depends f = 1 T v = λ T = λf

13 A wave moves in space and time Position x (m) Time t (s) This wave moves in the positive x direction.

14 A sound wave is a pressure wave Speed of sound in air is about 343 m/s (depending on temperature and humidity) Air pressure oscillates in space and time 1 Pressure 0.5 Position x (m) ,

15 Exercise: Find the wavelength of a sound wave On the piano, the frequency of the A above middle C is 440 Hz. What is the wavelength of this sound wave as it travels through air?

16 A light wave is an electromagnetic wave Speed of light in vacuum is m/s. Electric field oscillates in space and time 1 Electric field 0.5 Position x (m) ,

17 Exercise: Find the frequency of a light wave Red light has a wavelength of 700 nm. What is its frequency?

18 The electromagnetic spectrum

19 Hot things radiate Fireplace at 600 K = 330 C = 620 F 6 Visible Light Intensity Frequency (10 14 Hz)

20 The ultraviolet catastrophe Sun at 6000 K = 5730 C = F 6 Planck theory Intensity Rayleigh-Jeans theory Visible Light Frequency (10 14 Hz)

21 The photoelectric effect shine light electrons fly off metal Light provides the energy needed to free electrons from the metal.

22 The photoelectric effect shine high frequency light electrons fly off shine low frequency light no electrons fly off metal metal violet has high frequency even if light is very bright

23 The photoelectric effect: Einstein s idea One photon must free one electron. Energy of one photon is E = hf. violet photon 3.1 ev electron 1.1 ev red photon 1.7 ev nothing metal costs 2.0 ev to free an electron metal costs 2.0 ev to free an electron

24 How to convert among photon wavelength, frequency, and energy Quantity Symbol Unit Wavelength λ m, nm Frequency f Hz, THz Energy E J, ev f = c λ E = hf c = m/s h = J s = ev s

25 Exercise: Find the wavelength and frequency of a 1.7-eV photon A red photon has an energy of 1.7 ev. What is its frequency? What is its wavelength?

26 Balmer: Hydrogen spectrum has sharp lines unlike a blackbody

27 Balmer (1885) looked at 5 lines from hydrogen λ 656 nm 486 nm 434 nm 397 nm 410 nm m = 5 m = 7 f 457 THz 617 THz 691 THz 755 THz m = 3 m = THz m = 6 He found a pattern: ( 365 nm 1 λ = 1 4 f = 3289 THz ) m 2 m 2

28 Bohr atom (1913) Wavelength, circumference (m) Circumference 10 9 must be a multiple of wavelength C = 3λ classical circular motion C = 2λ λ C 1 C = λ de Broglie wavelength Velocity (m/s) 10 6

29 Bohr model produces hydrogen energy levels Only certain radii are allowed Energy (ev) C = 2λ C = 3λ C = 4λ 15 C = λ Radius (m) 10 9

30 Hydrogen energy levels ev/ ev/ ev/ ev 2.55 ev 2.86 ev 3.02 ev 3.12 ev 457 THz 617 THz 691 THz 731 THz 755 THz 656 nm 486 nm 434 nm 410 nm 397 nm Differences in energy levels match the Balmer frequencies ev

31 Compton scattering red photon 1.7 ev violet photon 3.1 ev

32 Four theories of light Light is a ray Geometrical Optics Light is a wave (Young, 1803) Wave Optics Light is an electromagnetic wave (Maxwell, 1865) Classical Electromagnetic Theory (EM Theory) Light is a quantum field Photon Theory (starting with Planck and Einstein, ) QED (Quantum Electrodynamics, 1949)

33 Matrices Addition is commutative. [ [ ] + [ ] [ ] = ] = [ [ Multiplication is not commutative. [ ] [ ] [ = [ ] [ ] = [ ] ] ] = ] = [ [ ] ]

34 Exercise: Multiply matrices [ ] [ ] = [ ] [ ] = [ ] [ ] =