Unit - 2 Compton effect Dual nature of EM radiation Photons and matter: X-rays production, electron-positron pairs Problems Dr. Ritesh S. Palaspagar Dept. of Engg. Physics PRMIT&R

Photons Photons: Electromagnetic energy is quantized into localized bundles moving with velocity c and having energy proportional to the frequency and momentum inversely proportional to the wavelength These particlelike bundles are called photons

Experimental arrangement: Compton effect Experimental arrangement:

Classical predictions: Compton effect Classical predictions: em waves incident on electrons should: Have radiation pressure that should cause the electrons to accelerate Set the electrons oscillating Oscillating electrons should emit in the same frequency

Compton effect Results: Compton’s experiments showed that, at any given angle, one additional frequency of radiation is observed

Compton effect Results:

Dual nature of EM radiation To explain all experiments with EM radiation (light), one must assume that light can be descried both as wave (Interference, Diffraction) and particles (Photoelectric Effect, Compton Effect) Experimentally, it can be concluded that the “shorter” the wavelength of light, the harder to observe its wave properties For instance, wave properties of X-rays were observed only when solids were used as diffraction grating Thus, as result of the observations, we have to accept both models as true

Wave and particle models of light compliment each other Dual nature of EM radiation Wave and particle models of light compliment each other Neither model can be used to exclusively explain all properties of the light The wave and particle models relate to each other via relationship between the wavelength/frequency of light and the momentum/energy of photon

Photons and matter X-rays production: Electrons are emitted thermally from a heated cathode and accelerated toward the target. After electrons hit target, x-rays are emitted.

X-rays production: Number of electrons Accelerating potential Material Photons and matter X-rays production: If K’ = 0, Number of electrons Accelerating potential Material

Electron-positron pairs: Photons and matter Electron-positron pairs:

Problems X-rays with a wavelength of 120 pm undergo Compton scattering. (a) Find the wavelength of the photons scattered at angles of 30°, 60°, 90°, 120°, 150°, and 180°. (b) Find the energy of scattered electron in each case. (c) Which of the scattering angles provides the electron with the greatest energy?

Problems After 0.8 nm x-ray photon scatters from a free electron, the electron recoils at 1.4·106 m/s. (a) What is the Compton shift in the photon wavelength? (b) Through what angle is the photon scattered?

Problems Determine the maximal wavelength shift in the Compton scattering of electrons and protons.

Problems Determine the Plank’s constant h from the fact that the minimum x-ray wavelength produced by 40 keV electrons is 3.11·1011 m

Problems A particular pair is produced such that the positron is at rest and the electron has a kinetic energy of 1 MeV. Find the energy of incident photon.