Of Photons and Electrons

Compton Effect, Pair Production and X-Rays

What Is a Photon?

Massless particleTravels with speed of light c = 3.0x108 m/sHas momentum p = E/cBut E = hfp = E/c = hf/c = h/h/p

Photon Interactions With Matter

Photoelectric Effect – photon knocks electron out of atom and disappearsCompton Effect – photon scatters off electron and loses energy (frequency)Atomic excitation – electron takes all of photon’s energy and goes to higher energy statePair Production – photon disappears, electron and positron created

Compton Effect

Used in astronomy to detect violent events in distant galaxiesUsed in nuclear medicine to treat cancer

Compton Effect is a Collision Between Photon and Electron Resulting in a Lower Energy Photon

Courtesy OSHA http://www.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/moc)(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 2mec2 =

photon e+

e-

2 x 9.11x 10-31 kg x(3.0x108 m/s)2 = 1.64x10-13 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 energyProduces two photons of energy 0.51 MeV eachPhotons must be emitted “back to back” to conserve momentum

Find Wavelength of 1.02 Mev Photon

= h/p = hc/E =

(6.6 x 10-34 J-s)(3.0 x 108 m/s)/(1.64x10-13 J )

= 1.2 x 10-12 m

X -Ray Production

When high speed electrons (30 –150kV)slam into a metal target (usually tungsten)x-rays are given offX-Rays are EM

radiation with wavelength about 10-2 - 1 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 10-34 J-s)(3x108 m/s)/(100 keV)x(1.6 x 10-16 J/keV) = 0.012 nm

h= 6.63 x 10-34 J-s

X-Ray Emission by Atoms

Atoms become excited – higher energy stateGive off x-rays when they “decay” to ground stateInner 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 objectsProduces circular ringsEffect is pronounced for atomic spacings around 10-10 mUsed to study complex organic molecules such as DNA

X-Ray Diffraction Image Courtesy Nonius B.V.

Particle or Wave?

Young 2 Slit - WAVEPhotoelectric and Compton Effect –PARTICLELight has DUAL natureBohr principle of complementarity- to understand any given experiment use wave theory or photon theory not both

Niels Bohr1885-1962

What Equation Links the Wave and Particle Properties?

E = hfE is energy of a particlef 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 10-34 J-s)/(0.20 kg)(15 m/s)=

2.2 x 10-34 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 10-19 J/eV x 100V / 9.1 x 10-31 kg)1/2 =

= 5.9 x 106 m/s

h/mv = (6.6 x 10-34 J-s)/(9.1 x 10-31 kg)/(5.9 x 106 m/s) = 1.2 x 10-10 m

What If Electron Wavelength is Comparable to Interatomic

Spacings?

Crystal spacings about 10-10 mCould electrons diffract like x-rays? YES, according to Davisson Germer experiment (1927)

Typical Electron Diffraction pattern from a crystal. Courtesyhttp://www.matter.org.uk/diffraction/electron/electron_diffraction.htm

Davisson- Germer Experiment

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

Courtesy http://www.chem.qmw.ac.uk/surfaces/scc/scat6_2.htm

Transmission Electron Scattering of Germanium

Courtesy Northwestern University Materials Science Dept.

What is an Electron?

Particle or wave?Use wave model when it worksUse particle model when it worksElectron 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