![Matter Waves
Compute the wavelength of a 10 [g] bullet moving at 1000 [m/s].
λ = h/mv = 6.6x10-34 [J s] / (0.01 [kg])(1000 [m/s])
= 6.6x10-35 [m]
This is immeasureably small
For ordinary “everyday objects,”
we don’t experience that
MATTER CAN BEHAVE AS A WAVE](https://image.slidesharecdn.com/mit6007s11lec37-240528075952-e18e7010/85/photon-moveent-engineering-syllabus-1-ppt-26-320.jpg)
![Gamma
Rays
X Rays
UV Rays
Infrared
Radiation
Microwaves
Radio
Waves
But, what about small particles ?
Compute the wavelength of an electron
(m = 9.1x10-31 [kg]) moving at 1x107 [m/s].
λ = h/mv
= 6.6x10-34 [J s]/(9.1x10-31 [kg])(1x107 [m/s])
= 7.3x10-11 [m].
= 0.073 [nm]
These electrons
have a wavelength in the region
of X-rays](https://image.slidesharecdn.com/mit6007s11lec37-240528075952-e18e7010/85/photon-moveent-engineering-syllabus-1-ppt-27-320.jpg)
![19_quantum [Autosaved].ppt](https://cdn.slidesharecdn.com/ss_thumbnails/19quantumautosaved-221112073228-8af4d814-thumbnail.jpg?width=560&fit=bounds)
photon moveent engineering syllabus 1.ppt
- 1. Photon Momentum and Uncertainty Principle Outline - Photons Have Momentum (Compton Scattering) - Wavepackets - Review - Resolution of an Optical Microscope - Heisenberg’s Uncertainty Principle
- 2. TRUE / FALSE 1. The photoelectric effect was used to show that light was composed of packets of energy proportional to its frequency. 2. The number of photons present in a beam of light is simply the intensity I divided by the photon energy hν. 3. Infrared light at a wavelength of 1.24 microns has photon energy of 1.5 eV.
- 3. So is Light a Wave or a Particle ? Light is always both Wave and Particle ! On macroscopic scales, large number of photons look like they exhibit only wave phenomena. A single photon is still a wave, but your act of trying to measure it makes it look like a localized particle.
- 4. Do Photons Have Momentum ? What is momentum ? Photons have energy and a finite velocity so there must be some momentum associated with photons ! Just like Energy, TOTAL MOMENTUM IS ALWAYS CONSERVED
- 5. Photon Momentum IN FREE SPACE: IN OPTICAL MATERIALS:
- 6. Compton found that if you treat the photons as if they were particles of zero mass, with energy and momentum . the collision behaves just as if it were two billiard balls colliding ! (with total momentum always conserved) In 1924, A. H. Compton performed an experiment where X-rays impinged on matter, and he measured the scattered radiation. It was found that the scattered X-ray did not have the same wavelength ! Compton Scattering incident photon target electron at rest recoil electron scattered photon Image by GFHund http://commons. wikimedia.org/wiki/File:Compton, Arthur_1929_Chicago.jpg Wikimedia Commons.
- 7. Manifestation of the Photon Momentum Conservation of linear momentum implies that an atom recoils when it undergoes spontaneous emission. The direction of photon emission (and atomic recoil) is not predictable. A well-collimated atomic beam of excited atoms will spread laterally because of the recoil associated with spontaneous emission. A source emitting a spherical wave cannot recoil, because the spherical symmetry of the wave prevents it from carrying any linear momentum from the source. SOURCE EMITTING A PHOTON SOURCE EMITTING AN EM WAVE excited atom de -excited atom photon source of excited atoms collimating diaphragms beam spreads laterally because of spontaneous emission
- 8. SOLAR SAIL at rest INCOMING PHOTONS 1000 W/m2 every second photons with momentum + (1000 J/m2)/c impact the sail SOLAR SAIL moves REFLECTED PHOTONS 1000 W/m2 every second photons with momentum - (1000 J/m2)/c leave the sail with momentum + (2000 J/m2)/c … and gets that much more momentum every second … Pressure acting on the sail = (2000 J/m2) /c /second = 6.7 Newtons/km2 Photon Momentum - Moves Solar Sails Photon Momentum - Moves Solar Sails Image by D. Kassing http://en.wikipedia.org/wiki/File:SolarSail- DLR-ESA.jpg on Wikipedia Image in the Public Domain
- 9. Optoelectric Tweezers Transforms optical energy to electrical energy through the use of a photoconductive surface. The idea is similar to that used in the ubiquitous office copier machine. In xerography, a document is scanned and transferred onto a photosensitive drum, which attracts dyes of carbon particles that are rolled onto a piece of paper to reproduce the image. In this case, the researchers use a photosensitive surface made of amorphous silicon, a common material used in solar cells and flat-panel displays. Microscopic polystyrene particles suspended in a liquid were sandwiched between a piece of glass and the photoconductive material. Wherever light would hit the photosensitive material, it would behave like a conducting electrode, while areas not exposed to light would behave like a non-conducting insulator. Once a light source is removed, the photosensitive material returns to normal. Depending upon the properties of the particles or cells being studied, they will either be attracted to or repelled by the electric field generated by the optoelectronic tweezer. Either way, the researchers can use that behavior to scoot particles where they want them to go. ITO Glass Projected Image Glass Substrate Nitride Undoped a-Si:H n+a-Si:H ITO 10x Light Emitting Diode DMD Microdisplay
- 10. Review of Wavepackets WHAT WOULD WE GET IF WE SUPERIMPOSED WAVES OF MANY DIFFERENT FREQUENCIES ? LET’S SET THE FREQUENCY DISTRIBUTION as GAUSSIAN
- 11. Reminder: Gaussian Distribution μ specifies the position of the bell curve’s central peak σ specifies the half-distance between inflection points FOURIER TRANSFORM OF A GAUSSIAN IS A GAUSSIAN 50% of data within
- 12. REMEMBER: Gaussian Wavepacket in Space SUM OF SINUSOIDS = WAVEPACKET WE SET THE FREQUENCY DISTRIBUTION as GAUSSIAN
- 13. Gaussian Wavepacket in Space Gaussian Wavepacket in Space GAUSSIAN ENVELOPE Gaussian Wavepacket in Space In free space … … this plot then shows the PROBABILITY OF WHICH k (or ENERGY) EM WAVES are MOST LIKELY TO BE IN THE WAVEPACKET WAVE PACKET
- 14. UNCERTAINTY RELATIONS Gaussian Wavepacket in Time WAVE PACKET
- 15. Crookes Radiometer Today’s Culture Moment The crookes radiometer spins because of thermal processes, but he initially guessed it was due to photon momentum… invented in 1873 by the chemist Sir William Crookes Image by Rob Ireton http://www.flickr.com /photos/aoisakana/ 3308350714/ from Flickr.
- 16. Heisenberg realized that ... In the world of very small particles, one cannot measure any property of a particle without interacting with it in some way This introduces an unavoidable uncertainty into the result One can never measure all the properties exactly Werner Heisenberg (1901-1976) Image in the Public Domain
- 17. Measuring Position and Momentum of an Electron Shine light on electron and detect reflected light using a microscope Minimum uncertainty in position is given by the wavelength of the light So to determine the position accurately, it is necessary to use light with a short wavelength BEFORE ELECTRON-PHOTON COLLISION electron incident photon
- 18. By Planck’s law E = hc/λ, a photon with a short wavelength has a large energy Thus, it would impart a large ‘kick’ to the electron But to determine its momentum accurately, electron must only be given a small kick This means using light of long wavelength ! Measuring Position and Momentum of an Electron AFTER ELECTRON-PHOTON COLLISION recoiling electron scattered photon
- 19. Implications It is impossible to know both the position and momentum exactly, i.e., Δx=0 and Δp=0 These uncertainties are inherent in the physical world and have nothing to do with the skill of the observer Because h is so small, these uncertainties are not observable in normal everyday situations
- 20. Example of Baseball A pitcher throws a 0.1-kg baseball at 40 m/s So momentum is 0.1 x 40 = 4 kg m/s Suppose the momentum is measured to an accuracy of 1 percent , i.e., Δp = 0.01 p = 4 x 10-2 kg m/s
- 21. Example of Baseball (cont’d) The uncertainty in position is then No wonder one does not observe the effects of the uncertainty principle in everyday life!
- 22. Example of Electron Same situation, but baseball replaced by an electron which has mass 9.11 x 10-31 kg traveling at 40 m/s So momentum = 3.6 x 10-29 kg m/s and its uncertainty = 3.6 x 10-31 kg m/s The uncertainty in position is then
- 23. Classical World The observer is objective and passive Physical events happen independently of whether there is an observer or not This is known as objective reality
- 24. Role of an Observer in Quantum Mechanics The observer is not objective and passive The act of observation changes the physical system irrevocably This is known as subjective reality
- 25. One might ask: “If light can behave like a particle, might particles act like waves”? YES ! Particles, like photons, also have a wavelength given by: The wavelength of a particle depends on its momentum, just like a photon! The main difference is that matter particles have mass, and photons don’t!
- 26. Matter Waves Compute the wavelength of a 10 [g] bullet moving at 1000 [m/s]. λ = h/mv = 6.6x10-34 [J s] / (0.01 [kg])(1000 [m/s]) = 6.6x10-35 [m] This is immeasureably small For ordinary “everyday objects,” we don’t experience that MATTER CAN BEHAVE AS A WAVE
- 27. Gamma Rays X Rays UV Rays Infrared Radiation Microwaves Radio Waves But, what about small particles ? Compute the wavelength of an electron (m = 9.1x10-31 [kg]) moving at 1x107 [m/s]. λ = h/mv = 6.6x10-34 [J s]/(9.1x10-31 [kg])(1x107 [m/s]) = 7.3x10-11 [m]. = 0.073 [nm] These electrons have a wavelength in the region of X-rays
- 28. Wavelength versus Size With a visible light microscope, we are limited to being able to resolve objects which are at least about 0.5*10-6 m = 0.5 μm = 500 nm in size. This is because visible light, with a wavelength of ~500 nm cannot resolve objects whose size is smaller than it’s wavelength. Bacteria, as viewed using visible light Bacteria, as viewed using electrons! Image is in the public domain Image is in the public domain
- 29. Electron Microscope This image was taken with a Scanning Electron Microscope (SEM). SEM can resolve features as small as 5 nm. This is about 100 times better than can be done with visible light microscopes! The electron microscope is a device which uses the wave behavior of electrons to make images which are otherwise too small for visible light! IMPORTANT POINT: High energy particles can be used to reveal the structure of matter ! Image in the Public Domain
- 30. SEM of various types of pollen Image in the Public Domain
- 31. SEM of an ant head Image in the Public Domain
- 32. Summary Light is made up of photons, but in macroscopic situations it is often fine to treat it as a wave. Photons carry both energy & momentum. Matter also exhibits wave properties. For an object of mass m, and velocity, v, the object has a wavelength, λ = h / mv One can probe ‘see’ the fine details of matter by using high energy particles (they have a small wavelength !)
- 33. MIT OpenCourseWare http://ocw.mit.edu 6.007 Electromagnetic Energy: From Motors to Lasers Spring 2011 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.