Discussion of Properties of Waves The particle-like properties of electromagnetic radiation Classical Postulates Einstein theory Black Body Radiation Stefan's radiation law Wein's displacement law Rayleigh-Jeans Formula Planck’s Theory and Radiation Law The Compton Effect Bremsstrahlung and X-Ray Production Pair production Electron-Positron Annihilation

1. 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

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

3. 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.
S
max eV
E 

4. 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).

5. 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.

6. Experimental Results
Comparison to the classical postulates
1. The maximum kinetic energy is totally
independent of the intensity of the light source.
2. 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.
3. The first photoelectrons are emitted virtually
instantaneously (within 10-9 s) after the light
source is turned on.

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

8. 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


n

hc
h
E

9. 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.
c
E
p 




h
c
hc
p

10. 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
2
mc
E 

11. • If the photon energy is greater than the work
function of the metal surface, photoelectron is
released, or photoelectric effect doesn’t occur.
f

n
 h
kmax
• 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
h
c
f

n

12. Work function and Planck’s constant
f

n
 h
kmax
f

14. 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?

15. 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?

16. Black Body Radiation

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

18. Stefan’s Radiation Law
The total intensity I is given by the area under the
radiancy curve.

19. Wein’s Displacement Law
• It is noticed from the spectrum figure that the
wavelength max at which the radiancy reaches
it maximum value is inversely proportional to
the temperature T.
• max a 1/T
• max T = 2.898 X 10-3 m.K

20. 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?

21. Rayleigh-Jeans Formula

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

23. Planck’s Theory and Radiation Law

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

26. 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.

27. Compton scattering formula

28. Example 3.6
X-rays of wavelength 0.2400 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.

30. Bremsstrahlung and X-Ray Production

31. Electron=electron(with less energy) +photon

32. Pair Production

33. Electron-Positron Annihilation