# 2. The Particle-like Properties Of Electromagnetic Radiation

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2. The Particle-like Properties Of Electromagnetic Radiation
2.1 Photoelectric effect and Einstein’s theory 2.2 Black body radiation 2.3 Compton effect 2.4 Bremsstrahlung and pair production 2.5 The photon

Photoelectric effect and Einstein’s theory
light collector emitter electron i V A

The voltage V is increased gradually until no current pass through the outer circuit. The voltage in this case called stopping potential VS . The energy used to stop this electron is eVS . This value is equal to Kmax the maximum energy required to overcome the electric potential energy acquired by an electron.

Classical Postulates Electrons are released from the metal surface if the energy of the incident light exceeds the binding energy of the electron to the metal surface. This value is called work function f. The maximum kinetic energy Kmax should be proportional to the intensity of the radiation I. (it is thought that as the intensity of the incident light increased more energy is delivered to the surface of the metal).

Classical Postulates (continued)
The photoelectric effect should occur for light of any frequency or wavelength. ( as long as light intensity is enough) The first electrons should be emitted in a time interval of the order of seconds after radiation first strikes the surface.

Experimental Results Comparison to the classical postulates
The maximum kinetic energy is totally independent of the intensity of the light source. The photoelectric effect does not occur at all if the frequency of the light source is below a certain value (the cutoff frequency nC ) any light source of frequency above this value may cause emission of photoelectrons. The first photoelectrons are emitted virtually instantaneously (within 10-9 s) after the light source is turned on.

Kmax (VS) and Intensity
Stopping potential is independent on the intensity

Einstein Theory The energy of light wave is not continuously distributed over the wave front , but instead is concentrated in localized bundles (photons). The energy of each photon is given by

Einstein Theory (continued)
Since photons travel with the electromagnetic waves at the speed of light, they must obey the relativistic relation Therefore, Like other particles, photons carry linear momentum as well as energy.

Einstein Theory (continued)
Despite the rest mass of photon, according to the theory of relativity, is zero and photon vanishes at speed lower than that of light, its energy is still given by

If the photon energy is greater than the work function of the metal surface, photoelectron is released, or photoelectric effect doesn’t occur. In this equation the intensity I of the light source doesn’t appear. if the photon energy is hardly equal to the work function, the photon frequency in this case is called cutoff frequency and is given by

Work function and Planck’s constant

Example 3.3 What are the energy and momentum of a red light photon of wavelength 650 nm? What is the wavelength of a photon of energy 2.4 eV?

Example 3.4 The work function for tungsten metal is 4.52 eV. What is the cutoff frequency and wavelength? What is the maximum kinetic energy of the electrons when radiation of wavelength 198 nm is used? What is the stopping potential in this case?

I is the total intensity of electromagnetic radiation emitted at all wavelengths
The intensity dI in the wavelength interval between l and l + Dl is given by dI = R(l) dl R(l) is the radiancy : which is the intensity per unit wavelength interval.

The total intensity I is given by the area under the radiancy curve.

Wein’s Displacement Law
It is noticed from the spectrum figure that the wavelength lmax at which the radiancy reaches it maximum value is inversely proportional to the temperature T. lmax a 1/T lmax T = X 10-3 m.K

Example 3.5 (a) At what wavelength does a room-temperature (T=20 OC) object emit the maximum thermal radiation? (b) To what temperature must we heat it until its peak thermal radiation is in the red region of the spectrum? (c) How many times as much thermal radiation does it emit at the higher temperature?

Rayleigh-Jeans Formula

Comparison between the experimental data and Rayleigh-Jeans formula: AT long wavelengths R(l) approaches the experimental data, but at short wavelengths, the classical theory fails. This failure is called ultraviolet catastrophe.

The relation between Stefan-Boltzmann constant and Planck’s constant

The Compton Effect Radiation scatter from nearly loosely bound electrons. The incident radiation gives part of its energy to the electron; which is released from the atom, and the remainder of this energy is reradiated as electromagnetic radiation.

Compton scattering formula

Example 3. 6 X-rays of wavelength 0
Example 3.6 X-rays of wavelength nm are Compton-scattered, and the scattered beam is observed at an angle of 60o relative to the incident beam. Find: (a) the wavelength of the scattered X-rays. (b) the energy of the scattered X-rays (c) the kinetic energy of the scattered electrons (d) the direction of travel of the scattered electrons.

Bremsstrahlung and X-Ray Production

Electron=electron(with less energy) +photon

Pair Production

Electron-Positron Annihilation