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Lecture 21
Quantum Physics I
Chapter 27.1  27.5
Outline
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Blackbody Radiation
The Photoelectric Effect
X-Rays
The Compton Effect
Blackbody Radiation
Objects at any temperature emit EM radiation that
is often referred to as thermal radiation.
A good representation of a blackbody is a cavity,
which light enters through a small hole and which
absorbs the entire incident radiation.
The total amount of radiation, emitted by a
blackbody, is proportional to its temperature and
depends only on its temperature.
Blackbody Spectrum
Properties of Blackbody Radiation
The peak of the intensity distribution shifts to
shorter wavelengths as the temperature increases.
Wien’s displacement: max T = 0.2898 102 m K.
Classic theory predicts that the amount of energy
radiated by a BB should increase as  approaches 0
and go to infinity (ultraviolet catastrophe).
The issue was resolved by Max Planck in 1900.
Planck proposed a theory that individual particles in
a BB emit only certain discrete energies (quanta).
E = h f, h = 6.626 1034 J s  Planck’s constant
The Photoelectric Effect
Experiments showed that light directed onto a
metal surface causes the surface to emit electrons.
This phenomenon is called photoelectric effect.
3 features of photoelectric effect:
• The electron is always emitted at once even
under a faint light.
• A bright light causes more electrons to be
emitted than the faint light, but the average kinetic
energy of the electrons is the same.
• The higher the light frequency, the more kinetic
energy the electrons have.
Explanation of the
Photoelectric Effect
Einstein suggested that some minimum energy ()
is needed to pull an electron away from a metal.
 is called the work function of the metal.
If the quantum energy E < , no electron comes out.
cutoff frequency
E=hf
hf = KEmax + 
fc =  /h = c/c
Photons have properties of particles: localized in a
small region of space, have energy and momentum,
and interact with other particles (like billiard balls).
Electronvolt
Energy unit: evectronvolt (eV)
1 eV is the energy an electron gets after passing
through a potential difference of 1 V.
1 eV = 1.6 1019 J
Stopping potential for the photoelectric effect is
the potential difference required to reduce the
current from the photoelectrons to zero.
eV0 = KEmax
eV0 = h f   = ch/  
Sample Problem
A light beam is shining on a metal target that has
a work function of 2.2 eV. If a stopping potential
of 1.3 V is required, what is the wavelength of the
incoming monochromatic light?
 = 2.2 eV
e Vs = h f  
ch/ = e Vs + 
 = c/ f
Vs = 1.3 V
h = 6.63 1034 J s
c = 3 108 m/s
ch
mJs
1 eV = 1.6 1019 J  =   = 3.55 107 m
1 nm = 109 m
e Vs +  s J
355 nm
X-rays
The wave theory of light and the quantum theory
of light complement each other.
In 1895 Wilhelm Roentgen discovered the inverse
photoelectric effect by observing a glow of a
fluorescent screen under bombardment by electrons.
The discovered radiation was very penetrating and
was called X-rays.
X-rays are produced whenever fast electrons are
suddenly stopped.
They turned out to be electromagnetic waves of
extremely high frequency.
X-Rays
X-rays have very short wavelengths ( ~ 1010 m
or 0.1 nm), much shorter than those of the visible
light.
They can show diffraction only on very closely
spaced structures (for example, crystals).
Crystal lattice structure
The condition for constructive interference of
X-rays is known as Bragg’s law.
The Compton Effect
The Compton effect deals with scattering of X-rays
off a material and an accompanied change of their
wavelengths.
The photon may transfer some energy and
momentum to the electron that it collided with,
decrease its energy, and increase its wavelength.
0  wavelength of the
incident photon
  wavelength of the
scattered photon
  scattering angle
h
 = 0 =  (1  cos )
mec
Compton wavelength
0.00243 nm
Summary
• Blackbody (thermal) radiation is emitted by an
object at any temperature and can be explained
only under an assumption about energy
emission in discrete values (quanta).
• The photoelectric effect demonstrates the
particle nature of light.