Photo-Electric/Planck’s Constant Lab
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Photo-Electric Facts
No electrons are emitted if the incident light frequency is below some cutoff frequency that is characteristic of the material being illuminated
The maximum kinetic energy of the photoelectrons is independent of the light intensity
The maximum kinetic energy of the photoelectrons increases with increasing light frequency
Electrons are emitted from the surface almost instantaneously, even at low intensities
Einstein’s Explanation
A tiny packet of light energy, called a photon , would be emitted when a quantized oscillator jumped from one energy level to the next lower one
The photon’s energy would be E = hƒ
Each photon can give all its energy to one electron in the metal
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1858 – 1947
Introduced a
“quantum of action,” h
Awarded Nobel
Prize in 1918 for discovering the quantized nature of energy
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1892 – 1962
Discovered the
Compton effect
Worked with cosmic rays
Director of the lab at U of Chicago
Shared Nobel
Prize in 1927
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Compton assumed the photons acted like other particles in collisions
Energy and momentum were conserved
The shift in wavelength is
   o
 h
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1892 – 1987
Discovered the wave nature of electrons
Awarded Nobel
Prize in 1929
1

What is the value of Planck’s Constant?
A.
B.
1.6 x 10 -19 Coulombs
6.6 x 10 -34 Joule-sec
C.
D.
340 m/sec
3 x 10 8 m/s
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The de Broglie wavelength of a particle is
   h
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The frequency of matter waves is
ƒ 
E h
The Davisson-Germer Experiment
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They scattered low-energy electrons from a nickel target
They followed this with extensive diffraction measurements from various materials
The wavelength of the electrons calculated from the diffraction data agreed with the expected de
Broglie wavelength
This confirmed the wave nature of electrons
Other experimenters have confirmed the wave nature of other particles
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The electron microscope depends on the wave characteristics of electrons
Microscopes can only resolve details that are slightly smaller than the wavelength of the radiation used to illuminate the object
The electrons can be accelerated to high energies and have small wavelengths
Erwin Schrödinger
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1887 – 1961
Best known as the creator of wave mechanics
Worked on problems in general relativity, cosmology, and the application of quantum mechanics to biology
“Wave Function” is what is!
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Werner Heisenberg
1901 – 1976
Developed an abstract mathematical model to explain wavelengths of spectral lines
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Called matrix mechanics
Other contributions
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Uncertainty Principle
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Nobel Prize in 1932
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Atomic and nuclear models
Forms of molecular hydrogen
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The Uncertainty Principle
Mathematically,
 x
 p x
 h
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It is physically impossible to measure simultaneously the exact position and the exact linear momentum of a particle
Another form of the principle deals with energy and time:
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E
 t

4 h
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Thought Experiment
The Uncertainty Principle
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A thought experiment for viewing an electron with a powerful microscope
In order to see the electron, at least one photon must bounce off it
During this interaction, momentum is transferred from the photon to the electron
Therefore, the light that allows you to accurately locate the electron changes the momentum of the electron
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View the electron as a particle
Its position and velocity cannot both be know precisely at the same time
Its energy can be uncertain for a period given by  t = h / (4  E)
Today’s Lab
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Sound waves are longitudinal waves traveling through a medium
A tuning fork can be used as an example of producing a sound wave
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A tuning fork will produce a pure musical note
As the tines vibrate, they disturb the air near them
As the tine swings to the right, it forces the air molecules near it closer together
This produces a high density area in the air
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This is an area of compression
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As the tine moves toward the left, the air molecules to the right of the tine spread out
This produces an area of low density
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This area is called a rarefaction
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As the tuning fork continues to vibrate, a succession of compressions and rarefactions spread out from the fork
A sinusoidal curve can be used to represent the longitudinal wave
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Crests correspond to compressions and troughs to rarefactions
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331 m s
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T
273 K
331 m/s is the speed of sound at
0° C
T is the absolute temperature
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Standing Waves
When a traveling wave reflects back on itself, it creates traveling waves in both directions
The wave and its reflection interfere according to the superposition principle
With exactly the right frequency, the wave will appear to stand still
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This is called a standing wave
A node occurs where the two traveling waves have the same magnitude of displacement, but the displacements are in opposite directions
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Net displacement is zero at that point
The distance between two nodes is ½ λ
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An antinode occurs where the standing wave vibrates at maximum amplitude
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A system with a driving force will force a vibration at its frequency
When the frequency of the driving force equals the natural frequency of the system, the system is said to be in resonance
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Child being pushed on a swing
Shattering glasses
Tacoma Narrows Bridge collapse due to oscillations by the wind
Upper deck of the Nimitz Freeway collapse due to the Loma Prieta earthquake
4

Standing Waves in Air Columns
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If one end of the air column is closed, a node must exist at this end since the movement of the air is restricted
If the end is open, the elements of the air have complete freedom of movement and an antinode exists
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The closed end must be a node
The open end is an antinode f n
 n v
4 L
 n ƒ
1 n  1, 3, 5,
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There are no even multiples of the fundamental harmonic
In the lab today, what is in resonance?
A.
Water and air
B.
Sound waves going in 1 direction
C.
D.
Tuning fork and air in room
Tuning fork and air in column
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