AP Physics
Chapter 28
Quantum Mechanics and Atomic
Physics
Chapter 28: Quantum Mechanics and
Atomic Physics
28.1
28.2-5
Quantization: Planck’s Hypothesis
Omitted
Homework for Chapter 28
• Read Chapter 28
• HW 28: p. 889: 3-6, 9, 12, 15.
28.1: Matter Waves: The De
Broglie Hypothesis
Photon Momentum
• A photon is a massless particle which carries energy.
• Photon energy can be written E = hf = hc/
• The momentum of a photon carries is related to its wavelength by
p = E = hf = h
c
c

On Gold Sheet
• The energy in electromagnetic waves of wavelength  can be thought of as being
carried by photon particles, each having a momentum of h/.
• Louis de Broglie (1892 – 1987) – French physicist and Nobel laureate
• De Broglie speculated that if light sometimes behaves like a particle, perhaps
material particles, such as electrons, also have wave properties.
• In 1924 de Broglie hypothesized that a moving particle has a wave associated
with it. The wavelength of the particle is related to the particle’s momentum
(p=mv).
 = h =_h_
p mv
On Gold Sheet
• These waves associated with moving particles were
called matter waves or, more commonly de Broglie waves.
Question: If particles really are associated with a wave,
why then have we never observed wave effects
such as diffraction or interference for them?
Example 28.1: What is the wavelength of the matter wave associated with
a) a ball of mass 0.50 kg moving with a speed of 25 m/s?
b) an electron moving with a speed of 2.5 x 107 m/s?
The wavelength of the ball is much shorter than that of the electron. That is why
matter waves are important for small particles like electrons since their
wavelengths are comparable to the sizes of the objects they interact with. It is
easier to observe interference and diffraction for electrons than the ball and all
other everyday objects.
Problem Solving Hint: Accelerating an Electron Through a Potential
Difference, V
• Since p = mv and KE = ½ mv2,
KE = p2
2m
• By energy conservation, KE = UE = qV = eV
• So, p2 = eV
2m
or
p =  2meV
• For these conditions, the de Broglie wavelength is  = h =
h
=
p  2meV
• Substitute in the numbers for h, e, and m:  =
=
1.50
V
nm
1.50
V
x 10-9 m
where V is in volts.
h2___
2meV
Example 28.2: An electron is accelerated by a potential difference of 120 V.
a) What is the wavelength of the matter wave associated with the electron?
b) What is the momentum of the electron?
c) What is the kinetic energy of the electron?
• In 1927, two physicists in the US, C.J. Davisson and L.H. Germer, used a crystal to
diffract a beam of electrons, thereby demonstrating a wavelike property of particles.
• In order to test de Broglie’s hypothesis that matter
behaved like waves, Davisson and Germer set up
an experiment very similar to what might be used to
look at the interference pattern from x-rays
scattering from a crystal surface. The basic idea is
that the planar nature of crystal structure provides
scattering surfaces at regular intervals, thus waves
that scatter from one surface can constructively or
destructively interfere from waves that scatter from
the next crystal plane deeper into the crystal.
Video:
http://www.tutorvista.com/content/physics/physics-iv/radiation-andmatter/davisson-and-germer-experiment.php
Simulation:
http://phet.colorado.edu/en/simulation/davisson-germer
•This simple apparatus send an electron
beam with an adjustable energy to a
crystal surface, and then measures the
current of electrons detected at a particular
scattering angle theta. The results of an
energy scan at a particular angle and an
angle scan at a fixed energy are shown
below. Both show a characteristic shape
indicative of an interference pattern and
consistent with the planar separation in the
crystal. This was dramatic proof of the
wave nature of matter.
Davisson-Germer Experiment
• A single crystal of nickel was cut to expose a spacing of d = 0.215 nm between the
lattice planes.
• When a beam of electrons of kinetic energy 54.0 eV was directed onto the crystal
face, the maximum in the intesity of the scattered electrons was observed at an angle
of 50°.
• According to wave theory, constructive interference due to waves reflected from two
lattice planes a distance of d apart should occur at certain angles of scattering .
• The theory predicts the first order maximum should be observed at an angle given
by
d sin  = 
(0.215 nm) sin 50° = 0.165 nm
• The de Broglie wavelength of the electrons is:
 = 1.50 nm
• The wavelengths agree!!
1.50 nm = 0.167 nm
• Another experiment carried out in the same year by G.P.Thomson in Great Britain
added further proof.
• Thomson passed a beam of energetic electrons through a thin metal foil.
• The diffraction pattern of the electrons was the same as that of X-rays.
• Particles exhibit wavelike properties…..confirmed.
electron diffraction pattern
X-ray diffraction pattern
Check for Understanding
1. The momentum of a photon is
a) zero
b) equal to c
c) proportional to its frequency
d) proportional to its wavelength
e) given by the de Broglie hypothesis
Answer: c
hf = pc
2. The Davisson-Germer experiment
a) dealt with X-ray spectra
b) confirmed blackbody radiation
c) supplied further evidence for Wien’s displacement law
d) demonstrated the wavelike properties of electrons
Answer: d
Check for Understanding
3.
Homework for Chapter 28
• HW 28: p. 889: 3-6, 9, 12, 15.
Formulas for Chapter 28