Of Photons and Electrons Compton Effect, Pair Production and X-Rays

What Is a Photon? Massless particle Travels with speed of light c = 3.0x10 8 m/s Has momentum p = E/c But E = hf p = E/c = hf/c = h/  h/p

Photon Interactions With Matter Photoelectric Effect – photon knocks electron out of atom and disappears Compton Effect – photon scatters off electron and loses energy (frequency) Atomic excitation – electron takes all of photon’s energy and goes to higher energy state Pair Production – photon disappears, electron and positron created

Compton Effect Used in astronomy to detect violent events in distant galaxies Used in nuclear medicine to treat cancer

Compton Effect is a Collision Between Photon and Electron Resulting in a Lower Energy Photon Courtesy OSHA slc.gov/SLTC/radiofrequencyradiation/rfpresentation/ionizinglectur/slidepresentation/mainpage.html

Question What happens to the wavelength of a photon after it Compton scatters? (a) increases (b) decreases (c) remains the same Don’t forget: Wavelength and frequency are inversely related

Wavelength Increases ’ = + (h/m o c)(1 - cos  )  is angle of scattered photon with incident  Incident photon e - after collision Scattered photon

Compton Effect in Astronomy The Imaging Compton Telescope (COMPTEL) utilizes the Compton Effect and two layers of gamma-ray detectors to reconstruct an image of a gamma-ray source in the energy range 1 to 30 million electron volts (MeV). Graphics courtesy NASA Goddard Spaceflight Center Lab for High Energy Astrophysics

What the Compton Telescope Sees – the Gamma Ray Universe

Cobalt 60 Gamma Ray Irradiation for Cancer Treatment Radiologists must understand how gamma rays interact with tissues in the body.

Pair Production Involves creation of antimatter Minimum energy photon is 2m e c 2 = photon e+e+ e-e- 2 x 9.11x kg x(3.0x10 8 m/s) 2 = 1.64x J = 1.02 MeV Rest Energy of one electron is 0.51 MeV

What Happens to the Positron? It annihilates electron at rest – positron and electron rest mass converts to photon energy Produces two photons of energy 0.51 MeV each Photons must be emitted “back to back” to conserve momentum

Find Wavelength of 1.02 Mev Photon  = h/p = hc/E = (6.6 x J-s)(3.0 x 10 8 m/s)/(1.64x J ) = 1.2 x m

X -Ray Production When high speed electrons (30 – 150kV)slam into a metal target (usually tungsten)x-rays are given off X-Rays are EM radiation with wavelength about nm

Wavelength of an X-Ray Find the wavelength of the maximum energy x-ray that can be produced by 100 kV electrons = c/f = hc/hf = hc/E = (6.63 x J-s)(3x10 8 m/s)/(100 keV)x(1.6 x J/keV) = nm h= 6.63 x J-s

X-Ray Emission by Atoms Atoms become excited – higher energy state Give off x-rays when they “decay” to ground state Inner electrons are involved- much higher energy than outer electrons

X-Rays Applied CAT scan of dinosaur egg

X-Ray Diffraction Like visible light x-rays diffracts when it hits small objects Produces circular rings Effect is pronounced for atomic spacings around m Used to study complex organic molecules such as DNA

X-Ray Diffraction Image Courtesy Nonius B.V.

Particle or Wave? Young 2 Slit - WAVE Photoelectric and Compton Effect – PARTICLE Light has DUAL nature Bohr principle of complementarity- to understand any given experiment use wave theory or photon theory not both Niels Bohr

What Equation Links the Wave and Particle Properties? E = hf E is energy of a particle f is frequency of a wave You cannot have a visual picture of light which is correct for all situations

Wave Nature of Matter De Broglie (1923) Deep symmetry of nature requires that if = h/p for photon, particles have a wavelength  h/p = h/mv Called De Broglie wavelength

Wavelength of a Baseball Find the wavelength of a 0.20 kg baseball traveling 15 m/s  h/mv = (6.6 x J-s)/(0.20 kg)(15 m/s)= 2.2 x m Too small to have observable effects H=6.6 x 10-34J-s

Wavelength of an Electron Find the wavelength of a 100 eV electron v = (2eV/m) 1/2 = (2 x 1.6 x J/eV x 100V / 9.1 x kg) 1/2 = = 5.9 x 10 6 m/s  h/mv = (6.6 x J-s)/(9.1 x kg)/(5.9 x 10 6 m/s) = 1.2 x m

What If Electron Wavelength is Comparable to Interatomic Spacings? Crystal spacings about m Could electrons diffract like x-rays? YES, according to Davisson Germer experiment (1927) Typical Electron Diffraction pattern from a crystal. Courtesy fraction.htm

Davisson- Germer Experiment

Set-up for Electron Diffraction by Back-Scattering(reflection) Courtesy

Transmission Electron Scattering of Germanium Courtesy Northwestern University Materials Science Dept.

What is an Electron? Particle or wave? Use wave model when it works Use particle model when it works Electron is merely its measurable properties, a “logical construction.” Cathode Ray Tube used by J.J. Thompson in his discovery of the Electron. Photos courtesy American Institute of Physics