1. 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

2. 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

3. Experimental arrangement:
Compton effect
Experimental arrangement:

4. 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

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

6. Compton effect
Results:

7. 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

8. 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

9. 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.

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

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

12. 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?

13. 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?

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

15. 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

16. 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.