# Quantum Physics I ```Lecture 21
Quantum Physics I
Chapter 27.1  27.5
Outline
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The Photoelectric Effect
X-Rays
The Compton Effect
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
The total amount of radiation, emitted by a
blackbody, is proportional to its temperature and
depends only on its temperature.
Blackbody Spectrum
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 &lt; , 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.
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