Student Responses
Improved Participation
1. Interactive PP presentation.
2. Contribute to discussion with group members or interact more with
group.
3. Ask more questions
4. Read material prior to class
5. Work on examples; problem solving
6. Face forward during lectures.
1.1 Introduction to Waves
1.1.1
Examples of Waves
1.1.2
Types of Waves
1.1.3
Wave-Particle Duality
1.1.1 Examples of Waves
1. Water waves – measuring wave height
2. Sound waves – measuring air pressure
♦
♦
3. Electromagnetic waves – measuring electric and magnetic
fields
4. Matter waves – model what will probably happen to
electrons*
1.1.1 Examples of Waves
♦
Electromagnetic waves – measuring electric and magnetic fields
• Wave oscillating through space with electric and magnetic
field components at 90 degrees to each other that transport
energy through space; propagate at the speed of light (c).
• Wave modeled by Maxwell’s equations
Picture - http://hyperphysics.phy-astr.gsu.edu/hbase/HFrame.html
1.1.1 Examples of Waves
♦
Matter waves – model what will probably happen to electrons*
* In the case of matter waves, there is a wave equation, however, the
equation is not modeling the movement of the electrons. The
wave equation tells us information about the electrons for special
cases.
We can model the interference results of free electrons traveling
through space, or the energy of electrons bound to a nucleus or
confined to a small space.
1.1.1 Examples of Waves
Electromagnetic waves
photons with quantized energy (E) and frequency (f)
corresponding to radio waves, microwaves, infrared waves, visible
light waves, ultraviolet waves, X-rays, and gamma rays.
All electromagnetic waves propagate at 3 x 108 m/s in vacuum.
E = hf
f = c/λ
E = hc/λ
h is Planck’s constant equal to 6.63 x 10-34 J s
c is the speed of light and is equal to 3 x 108 m/s in vacuum
(or 299,792,458 m/s)
λ is the wavelength
1.1.1 Examples of Waves
Electromagnetic waves
What are photons?
A photons is the same as saying electromagnetic wave, only it
also means that the photon has quantized energy values that
are not continuous. It also implies that the photon or electromagnetic wave also behaves like a particle.
What is “quantized”?
Something that is quantized, has values at specific intervals, and
cannot have values in between these values. The intervals do not
have to be whole numbers.
Ex. The number of eggs is 1, 2, 3, 4, … n
Ex. The number of pennies, you cannot have ½ a cent, but you can
have ½ a dime, which is a nickel.
Ex. The energy levels of electrons in a hydrogen atom are -13.6 eV,
3.4 eV, 1.5 eV, …
1.1.1 Examples of Waves
Electromagnetic waves
Table 1.1 Wavelength values for Electromagnetic
Spectrum*
Radio Waves
> 10 cm
Micro Waves
10 cm – 0.01 cm
Infrared Waves
700 nm – 0.01 cm
Visible Waves
400 – 700 nm
Ultraviolet Waves
400 nm – 1 nm
X-Rays
0.01 nm – 1 nm
Gamma Waves
* Approximate values
< 0.01 nm
1.1.1 Examples of Waves
Matter waves
charged particles traveling through space with velocity, v, and
corresponding kinetic energy ½ mv2.
The velocity of an electron can be related to its wavelength using
de Broglie’s relation...
λ = h/p
λ = h/mv.
This is useful, because it related particle properties (momentum)
to wave properties (wavelength). In de Broglie’s model, the
number of wavelengths are quantized.
Picture: http://www.clickandlearn.org/chemistry/DeBroglie.htm
1.1.1 Examples of Waves
EMW and Electron Interaction
Electrons in atoms have quantized energy levels.
In semiconductors, the energy levels interact in such a way
as to create a band gap of allowed energy levels. Quantum
mechanics is used to determine the number of possible
electrons at each energy level.
Photon
What does the term “quantized” mean?
1.1.1 Examples of Waves
Summary
Electromagnetic energy is quantized and equal to hf (or hc/λ).
All electromagnetic waves travel at speed equal to c (3 x 108
cm/s) in vacuum.
Electromagnetic waves behave as particles called photons.
Electrons exhibit particle and wave-like behavior.
1.1.2 Types of Waves
1. Longitudinal
2. Transverse
3. Standing
1.1.2 Types of Waves
Longitudinal waves
Longitudinal waves consist of particles moving back and forth in the
direction of wave propagation.
Ex. Sound waves traveling in air (pressure disturbances traveling in
the direction of sound)
Ex. The motion of a slinky from one end to another initiated by a
force into the slinky.
http://www.surendranath.org/Applets/Waves/Lwave01/Lwave01Applet.html
1.1.2 Types of Waves
Transverse waves
Transverse waves consist of particles traveling in the direction
perpendicular to wave propagation.
Ex. Wave on a string
Ex. Water waves
Ex. Electromagnetic waves
http://surendranath.tripod.com/Applets/Waves/Twave01/Twave01Applet.html
1.1.2 Types of Waves
EMW and Electron Interaction
Note that changing the frequency is completely independent of
changes in amplitude.
When examining the transfer of energy between electromagnetic
waves and electrons, the transfer of energy is a function of the
frequency.
The amplitude is related to the number of photons in an
electromagnetic wave of a certain energy or frequency.
In quantum mechanics, electrons are modeled by a wave
function that is purely mathematical and not representative of
anything physical.
In this case, the amplitude represents the probability of finding
an electron at a given location at time t.
1.1.2 Types of Waves
Standing Waves
If we combine a transverse wave traveling in the + x direction
(incident wave) with a transverse wave traveling in the –x direction
(reflected wave), we observe a wave that appears to be immobile
(resultant wave), and this kind of wave is characterized as a
standing wave.
Notice that by increasing the frequency,
the wavelength decreases and the
number of nodes (fixed points)
increases. If we take a snap shot of the
wave at any time, we observe a static
standing wave.
The interesting observation is that at any
given time the number of cycles is a
whole number. This is an example of
quantized value. Because the ends are
fixed, there can only be a whole number of
wave envelopes.
http://www.physics.smu.edu/~olness/www/05fall1320/applet/pipe-waves.html
1.1.2 Types of Waves
Summary
Types of Waves: Longitudinal, Transverse and Standing
Electromagnetic Waves are Transverse Waves
No of photons in an electromagnetic wave is proportional to
the wave amplitude
Energy of electromagnetic wave is proportional to the wave
frequency
In quantum mechanics, the amplitude represents the
probability of finding an electron at a particular location.
1.1.3 Wave-Particle Duality
Examples
Photoelectric effect - A photon targeting a metal surface will result
in energy transfer to a single electron, ejecting that electron from the
surface of the metal (discovered in 1887 by Heinrich Hertz, modeled
in 1905 by Albert Einstein, model verified by Robert Millikan in 1916).
Compton Effect and X-ray diffraction - Electrons with sufficient
energy (kinetic energy) that are decelerated as they hit an atom result
in the production of electromagnetic radiation or X-rays (with energy
equal to kinetic energy of the electron). If the electron has sufficient
energy, this process will result in the production of an X-ray photon
and the ejection of an electron – Compton effect. (discovered in 1895
by Wilhelm Roentegen, characterized in 1912 by Max von Laue,
developed by W.L. and W.H. Bragg, modeled in 1923 by Arthur
Compton).
Electron diffraction (double slit experiment) – When electrons
pass through 2 parallel slits, and are aimed at photographic film
behind the slits, an interference pattern is observed.
http://nanohub.org/resources/4916/about
1.1.3 Wave-Particle Duality
Macro vs Nano or
Classical Physics vs Quantum Mechanics
The wavelength of a golf ball: Quantum mechanics calculations
for a 46 g (43 mm diameter) golf ball moving through the air at 30
m/s results in a wavelength of 4.8 x 10-34 m. The value of the
wavelength in this case is very small compared to the size of the
object and does not have an impact on its motion through the air.
Quantum Mechanics calculations do not provide additional information
about the energy of the ball as it moves through a specified volume.
The wavelength of an electron: Quantum mechanics calculations
for an electron with a mass of 9.11 x 10-31 kg and a velocity of 107
m/s results in a wavelength of 7.3 x 10-11 m. This value is
comparable to the size of a hydrogen atom of 5.3 x 10-11 m.
Consequently, it is understandable that the wavelength of the electron
is an important factor in modeling the motion and behavior of an
electron. In this case, we need to perform quantum mechanics
calculations in order to determine the most probable position of the
electron in a specified volume and the possible quantized (specific)
energy values the electron can acquire.
1.1.3 Wave-Particle Duality
Summary
Electromagnetic radiation exhibits both wave and particle-like
properties
Electrons and all other particles exhibit both particle- and
wave-like properties.
Wave-particle duality proven experimentally
Wave-particle duality of particles is only important at the
nano-scale.