Knight - Chapter 28
(Grasshopper Book)
Quantum Physics
Blackbody Radiation and Planck’s
Hypothesis of Quantized Energy
An ideal blackbody absorbs all the light that is
incident upon it.
Blackbody Radiation and Planck’s
Hypothesis of Quantized Energy
An ideal blackbody is also
an ideal radiator. If we
measure the intensity of the
electromagnetic radiation
emitted by an ideal
blackbody, we find:
Blackbody Radiation and Planck’s
Hypothesis of Quantized Energy
This illustrates a remarkable experimental
finding:
The distribution of energy in blackbody
radiation is independent of the material from
which the blackbody is constructed — it
depends only on the temperature, T.
The peak frequency is given by:
Blackbody Radiation and Planck’s
Hypothesis of Quantized Energy
The peak wavelength increases linearly with
the temperature. This means that the
temperature of a blackbody can be
determined by its color.
Classical physics calculations were
completely unable to produce this
temperature dependence, leading to
something called the “ultraviolet
catastrophe.”
Blackbody Radiation and Planck’s
Hypothesis of Quantized Energy
Classical predictions were that the intensity
increased rapidly with frequency, hence the
ultraviolet catastrophe.
http://www.astro.ubc.ca/~scharein/a311/Sim.html#Blackbody
Blackbody Radiation and Planck’s
Hypothesis of Quantized Energy
Planck discovered that he could reproduce the
experimental curve by assuming that the
radiation in a blackbody came in quantized
energy packets, depending on the frequency:
The constant h in this equation is known as
Planck’s constant:
Blackbody Radiation and Planck’s
Hypothesis of Quantized Energy
Planck’s constant is a very tiny number; this
means that the quantization of the energy of
blackbody radiation is imperceptible in most
macroscopic situations. It was, however, a
most unsatisfactory solution, as it appeared
to make no sense.
*Photons and the Photoelectric Effect
Einstein suggested that the quantization of
light was real; that light came in small packets,
now called photons, of energy:
When a person visits the local tanning salon,
they absorb photons of ultraviolet (UV) light to
get the desired tan. What is the frequency and
wavelength of a UV photon whose energy is
6.5x10-19 J?
 
c
8

f
f 
3.00  10 m /s
E
h
9.80  10

14
 310 nm  0.31  m
Hz
6.5  10
6.63  10
 19
 34
J
J s
 9.8  10
14
Hz
Photons and the Photoelectric Effect
Therefore, a more intense beam of light will
contain more photons, but the energy of each
photon does not change.
*Photons and the Photoelectric Effect
The photoelectric effect occurs when a beam
of light strikes a metal, and electrons are
ejected.
Each metal has a minimum amount of energy
required to eject an electron, called the work
function, W0. If the electron is given an energy
E by the beam of light, its maximum kinetic
energy is:
Equation sheet- Kmax = hf - Φ
Light of frequency 9.95x1014 Hz ejects electrons
from the surface of silver. If the maximum
kinetic energy of the ejected electrons is
0.180x10-19 what is the work function of silver?
K m ax  hf  W 0
W 0  hf  K m ax   6.63  10
= 6.42  10
 19
J
 34
J  s   9.95  10
14
H z   0.180  10
 19
J
Photons and the Photoelectric Effect
This diagram shows the basic layout of a
photoelectric effect experiment.
Photons and the Photoelectric Effect
Classical predictions:
1. Any beam of light of any color can eject
electrons if it is intense enough.
2. The maximum kinetic energy of an ejected
electron should increase as the intensity
increases.
Observations:
1. Light must have a certain minimum frequency
in order to eject electrons.
2. More intensity results in more electrons of the
same energy.
Photons and the Photoelectric Effect
Explanations:
1. Each photon’s energy is determined by its
frequency. If it is less than the work function,
electrons will not be ejected, no matter how
intense the beam.
Photons and the Photoelectric Effect
2. A more intense beam means more photons,
and therefore more ejected electrons.
The Mass and Momentum of a Photon
Photons always travel at the speed of light (of
course!). What does this tell us about their mass
and momentum?
The total energy can be written:
Since the left side of the equation must be
zero for a photon, it follows that the right side
must be zero as well.
The Mass and Momentum of a Photon
The momentum of a photon can be written:
Dividing the momentum by the energy and
substituting, we find:
*The Mass and Momentum of a Photon
Finally, we can write the momentum of a
photon in the following way:
What is the wavelength of a photon that has
the same momentum as an electron moving
with a speed of 1400 m/s?
p  m v   9.11  10
 
h
p

 31
kg  1400 m /s   1.275  10
6.63  10
1.275  10
 34
 27
J s
kg  m /s
 27
kg  m /s
 520 nm  0.52  m
Photon Scattering and the Compton Effect
The Compton effect occurs when a photon
scatters off an atomic electron.
Photon Scattering and the Compton Effect
In order for energy to be conserved, the energy
of the scattered photon plus the energy of the
electron must equal the energy of the incoming
photon. This means the wavelength of the
outgoing photon is longer than the wavelength
of the incoming one:
*The de Broglie Hypothesis and Wave-Particle
Duality
In 1923, de Broglie proposed that, as waves can
exhibit particle-like behavior, particles should
exhibit wave-like behavior as well.
He proposed that the same relationship between
wavelength and momentum should apply to
massive particles as well as photons:
What speed must a neutron have if its de Broglie
wavelength is to be equal to the interionic
spacing of table salt (0.282 nm)?
 
h

p
v
h
m
h
mv

6.63  10
 0.282  10
9
 34
J s
m  1.675  10
 27
kg 
 1.40 km /s
The de Broglie Hypothesis and Wave-Particle
Duality
The correctness of this assumption has been
verified many times over. One way is by
observing diffraction. We already know that Xrays can diffract from crystal planes:
The de Broglie Hypothesis and Wave-Particle
Duality
The same patterns can be observed using either
particles or X-rays.
The de Broglie Hypothesis and Wave-Particle
Duality
Indeed, we can even
perform Young’s twoslit experiment with
particles of the
appropriate
wavelength and find
the same diffraction
pattern.
The de Broglie Hypothesis and Wave-Particle
Duality
This is even true if we have a particle beam so
weak that only one particle is present at a time
– we still see the diffraction pattern produced
by constructive and destructive interference.
Also, as the diffraction pattern builds, we
cannot predict where any particular particle will
land, although we can predict the final
appearance of the pattern.
The de Broglie Hypothesis and Wave-Particle
Duality
These images show the gradual creation of an
electron diffraction pattern.