Photo-Electric/Planck’s Constant Lab
Photo-Electric Facts







Max Planck



1858 – 1947
Introduced a
“quantum of
action,” h
Awarded Nobel
Prize in 1918 for
discovering the
quantized nature
of energy
Compton Scattering



Compton assumed
the photons acted
like other particles
in collisions
Energy and
momentum were
conserved
The shift in
wavelength is
    o 
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
Arthur Holly Compton





1892 – 1962
Discovered the
Compton effect
Worked with
cosmic rays
Director of the lab
at U of Chicago
Shared Nobel
Prize in 1927
Louis de Broglie



1892 – 1987
Discovered the
wave nature of
electrons
Awarded Nobel
Prize in 1929
h
(1  cos  )
mec
1
de Broglie Wavelength and
Frequency
Quick Quiz
What is the value of Planck’s Constant?
A. 1.6 x 10 -19 Coulombs
B. 6.6 x 10 -34 Joule-sec
C. 340 m/sec
D. 3 x 10 8 m/s

The de Broglie wavelength of a
particle is


h
h

p mv
The frequency of matter waves is
ƒ
E
h
The Davisson-Germer Experiment





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
The Electron Microscope



Erwin Schrödinger




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!
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
Werner Heisenberg



1901 – 1976
Developed an abstract
mathematical model to
explain wavelengths of
spectral lines
 Called matrix
mechanics
Other contributions
 Uncertainty Principle
 Nobel Prize in 1932
 Atomic and nuclear
models
 Forms of molecular
hydrogen
2



Thought Experiment
The Uncertainty Principle
The Uncertainty Principle
h
Mathematically,
xp x 
4
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:
h
E t 
4




Uncertainty Principle
Applied to an Electron



Today’s Lab
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)
Using a Tuning Fork to
Produce a Sound Wave
Producing a Sound Wave


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
Sound waves are longitudinal waves
traveling through a medium
A tuning fork can be used as an
example of producing a sound wave




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

This is an area of compression
3
Using a Tuning Fork, cont.


Using a Tuning Fork, final
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


This area is called a
rarefaction

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

Crests correspond to compressions and troughs to
rarefactions
Standing Waves

Speed of Sound in Air
m
T

v   331 
s  273 K



331 m/s is the speed of sound at
0° C
T is the absolute temperature




Forced Vibrations


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
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
 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
 Net displacement is zero at that point
 The distance between two nodes is ½λ
An antinode occurs where the standing wave vibrates
at maximum amplitude
Other Examples of
Resonance




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
Tube Closed at One End


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
Resonance in an Air
Column Closed at One End


The closed end must be a node
The open end is an antinode
fn  n

v
 nƒ1
4L
n  1, 3, 5, 
There are no even multiples of the
fundamental harmonic
Quick Quiz
In the lab today, what is in resonance?
A. Water and air
B. Sound waves going in 1 direction
C. Tuning fork and air in room
D. Tuning fork and air in column
5