Download Stopping Potential

Slide for 2011
I am used to being able to answer many questions for you, because
I have been able to finally answer a lot of my own questions.
Some I didn’t get it because I was sleeping, the teacher did not know, or
another teacher gave me misinformation which had to be corrected.
When I started this unit, I hoped to finally quell a lot of confusion in this
area for myself. But what I have found so far, I now have more
questions than when I started. Like a Feynman question….
The truth is that a lot of this is still being debated. Much of it is based on
Math that you won’t see for another couple of years.
So a better basis for this unit would be to provide you with the evidence
and let you come up with the conclusions and more questions.
LAST
unit.
QUANTUM WEIRDNESS
As 1st discovered from light….
These are chapters that are not yet finalized
So I take you through them with more
questions than answers.
But we need to see the evidence that has
scientists very confused and still hotly
debating.
First off the idea of something being “quantized”
Why would it be weird to have the “average 2.3 people”
in your family
Because people come in chunks
By the late 1800’s scientists were feeling pretty smug
that everything was pretty much figured out using
Newtonian Physics (also called classical physics)
Newtonian physics very well explained
motion of objects on earth and in space.
It even was used to explain the behavior
of the tiny atoms in gases and led to
thermodynamics.
Studies of electricity and magnetism
had even led to a correctly predicted
speed of light.
But then they saw some things that blew their minds.
And they saw that when you start looking at VERY
small things ….
It gets a little weird and Newtonian Physics
The 1st real evidence that something “ain’t right”
came from experiments with the
PHOTOELECTRIC EFFECT
Light is shined on to a piece of metal under voltage.
Electrons near the surface can be knocked off atoms
by absorbing light
detector
Light Source
current
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e- e- e- e- e- e- e- eee- e- ee- e- e- eA metal say magnesium
Classical physics predicts that as the light flowed
like water in a continuous stream delivering energy
to the electrons after all light is a wave….
They would EVENTUALLY absorb enough
energy like sponges and fly off when they reached
the ionization energy (it would take some time to soak it up)
A KEY point is that an electron must have AT LEAST a certain
amount of energy to break free from the atom (ionization energy).
Like the escape velocity from the earth
Predicted BUT NOT observed
detector
full
current
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In classical mechanics this makes sense. As work
is done on the car its speed continually increases.
The electron just needs enough energy to finally
break loose of the atom…..
Classical physics prediction #2 NOT OBSERVED
If the light was brighter (more intense) the
electrons would leave with more energy.
(They would suck up the energy more quickly reaching the ionization energy
needed more quickly… makes sense right?)
Classical physics prediction #3 not observed
As long as the light was bright enough you would
shoot off electrons
I guess they were thinking as long as you pumped in energy faster than the electrons were losing it
they would reach the ionization energy. (makes enough sense in classical mechanics)
Classical physics prediction #4 not observed
There would be some time delay before the
electrons shot off as they continued to absorb
enough energy to shoot off
What was actually observed…
(and this is all pretty important because led to quantum mechanics)
1.) No electrons were ejected (called photoelectrons) below a
threshold frequency of light no matter how bright the light.
2.) If the frequency of light increased above the threshold the
left with more energy (faster).
3.) If the brightness (intensity) of the light was increased
more electrons were ejected each second.
4.) Electrons were ejected “instantly”
Photoelectric effect applet
CONCLUSIONS (from the photoelectric effect and a bunch of other evidence)
1st off -Energy does NOT flow like water.
It is transferred in discrete chunks like tiny hammer
blows, a chunk of energy is called a quantum.
(Or in plural, quanta)
While energy is quantized, there does not appear to
be steps in how large an individual quantum is.
The electron needs a certain amount of energy to break
free (ionization energy, Ie).
That energy comes in chunks / quanta
Energy meter
e+
A larger quantum delivers more energy.
Energy meter
e+
A larger quantum
Energy meter
e+
Even larger
Energy meter
e+
Light does not come as a stream of energy but in a
stream of individual bundles of energy.
A quantum of light energy is called a PHOTON.
Another piece of the puzzle comes from a
phenomena called black body radiation
Basically when something is heated like a light
bulb filament it emits light.
The frequency/color and amount of light emitted
changes with the temperature of the object.
When the filament is “cold” (298 K) it still emits electromagnetic waves
but not enough in the visible spectrum for us to see.
You are emitting “light” right now mostly in frequencies we can’t see.
cooler
hotter
An ingot of silicon
If we think of a gas, some of the atoms will be
moving very quickly and some very slows but most
will be close to the average (like a bell curve).
The frequencies of electromagnetic waves emitted by
an object is similar (making a bell curve)
A object emits some of all frequencies of light.
What it emits most brightly, shifts from long to shorter
wavelengths as it gets warmer.
We will see shortly, that
short wavelengths are more
energetic.
Max Planck was investigating this curious effect as
others had before.
Planck was able to model mathematically the shape
of the spectrum and how it changed with
temperature.
There was an issue with this phenomena.
Since the object was emitting some of all of wavelengths.
And there are an infinite number of wavelengths,
the object seemed to be emitting an infinite amount of energy.
He could only get the math to work out was by
PRETENDING that electromagnetic energy (light) only
came in these discrete chunks. (stupid math!)
He made an empirical equation that just fit the data, but he
thought the idea was preposterous.
E = hf
max planck
energy of a
photon of light
frequency of light
(Hz)
Planck’s constant
6.626 x 10-34 J/s
What confused me forever… there are an infinite possible number of
frequencies of light, but any frequency of light is delivered in
chunks by PHOTONS.
What is the energy of a 340 nm photon wavelength of
light in J and in eV. Electron volts is a very common
way of expressing energy when it is very .
small
An eV = 1.60 x10-19 J
Increasing
wavelength
Increasing Frequency
and Energy of photon
high energy photons
I would probably know how photon energies change in Vis spectrum
Red- Radio low energy
Violent- UV damages skin high energy
R O Y
G
B
I
V
Back to the photoelectric effect
What really happened a photon of red light has
the least amount of energy.
detector
full
current
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If the photon does not have enough energy to break the
electron free in one photon it does not leave. Energy
is only absorbed in chunks.
If it move up energy levels but not enough to break free it will drop back down to the ground state expelling the energy.
detector
full
current
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This is a slight simplification we will come back to later
Increasing the intensity of the light has no effect
here. More photons hit the surface but none of
them have enough energy to break it free.
The energy from light comes in chunks not streams
detector
current
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By increasing the frequency of light.
A photon of light can deliver enough energy to
break it free with some extra as KE.
detector
current
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Once the threshold energy of light is there.
More light (chunks) intensity means the faster
electrons are ejected (photoelectrons).
detector
current
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Einstein reads Planck’s paper as well as work on
the photoelectric effect and interprets.
1.) light is quantized
2.) The energy of a photon is given as
E=hf
Energy leftover from the photon. Becomes
some other energy like KE or a lower
photon.
Total
photon
energy
Energy needed to break the electron free
Called the work function.
Depends on the metal.
Some metals hold on tighter than others…
hf = f + KE
Total
photon
energy (J)
Energy left over as
kinetic (J)
Energy used to break the
electron free (J)
Also called the work function
0
hf = f + KE
Remember energy of
a photon of light
hf0 = f
f
f0 =
h
the lowest frequency that will eject an electron
The work function for aluminum is 4.08 eV.
a.) What is the minimum frequency of light that
will produce photoelectrons.
b.)If light with a frequency of 4 x 10 15 Hz is
incident upon it, what is the KE(max) that
electrons will eject.
c.) if the intensity of light were to double by two
what would happen to the KE(max) of the
electrons ejected?
Stopping Potential & the
Photoelectric Effect
Instead of measuring the KE of the electrons ejected
(this would be hard), they measured the minimum
voltage that would keep the electrons from being
ejected.
How would this work??
A photon of light with an energy of 2.4x10-19 J, hits a
metal and ejects electrons with a maximum kinetic
energy of 1.3x10-19 J.
-19 J
1.1x10
a.) What is the work function?
b.) What is the stopping potential of a photoelectron?
What is the definition
of Voltage / Electric
Potential?
UE
V= q
What is the energy we are trying to stop?
What charge is involved? (the charge of light?)
The energy is the leftover KE and the charge
is that of an electron
Stopping potential
(if you write this down, it will not be available.. understand it)
UE
V= q
Stopping
potential
KE of
electron
Charge of
electron
A photon of light with an energy of 2.4x10-19 J, hits a
metal and ejects electrons with a maximum kinetic
energy of 1.3x10-19 J.
b.) What is the stopping potential of a photoelectron?
UE
V= q
V=
1.3x10-19 J
1.6x10-19 C
= .81 V
Rutherford gave us the nucleus.
Thompson discovered the electron.
But at this point we have no idea what the
electrons are doing.
Light tells us a story in the Bohr model
of the atom.
Important side note here:
All of this is on a scale way too small to see, and even what
we can “see” ultimately happens at the sub-atomic level.
All models are an approximation to understand and predict
and grow our understanding.
Models are evaluated on their “usefulness” and not their
“truthfulness”. When I said we don’t “Know” anything
freshmen year, I think you will see that now more….
Other curious goings on
The light emitted from a hot gaseous
element.
Or the light absorbed by an elemental gas.
The light is refracted by a prism to separate
the colors.
But what did they look like?
WHY?
Emission and Absorption
Spectra of Hydrogen gas
emission spectra for different elements
• unique to each
element like a
fingerprint

We know what
elements are in
stars by looking at
their light
Line spectra for different elements
• The atoms only
give off very
specific colors.
• Meaning an atom
of an element only
gives off specific
energy light
• WHY?
The emission spectra of the simplest atom
was the first explained mathematically
The first step
Hydrogen.
It only has one electron
Niels Bohr’s Model
• “Planetary model”
• Electrons are in
defined circular orbits
around the nucleus
Nucleus
Bohr Model – An electron has a very specific amount
of energy depending on which orbit it is in.
the energy difference between levels decreases as
you go up
-
-
Energy Level 3
Energy Level 1
Energy Level 2
The further the orbit is from the nucleus, the
more energy it has.
-
-
Aufbau principle (from the ground up) an electron
always occupies the lowest energy level available.
When they absorb energy, they move up to an
excited state. An orbit above their ground state.
Because the orbits have only certain energies,
a specific amount of energy must be absorbed.
DOES NOT HAPPEN energy
e-
ee-
energy
An electron must absorb a specific amount energy to
jump steps.
(the difference in energy between the two levels)
It can never exist between two orbits.
e-
e-
energy
If the energy of a photon of light does not equal the
difference between two energy levels it is not
absorbed.
The “light” goes through aka it is transparent to that
“light”.
e-
energy
Also an electron can only emit a specific certain
energies of light when they move down levels.
(again the difference between energy levels)
e-
e-
energy
In order for an electron to jump to a higher energy level it
has to absorb a quantum of energy equal to the
difference between energy levels.
If the orbit is not full and the quantum is the right
energy, the electron can jump to any orbit.
When the electron moves back down, it releases a
photon of light equal to the difference in energy levels.
• Only certain energies/frequencies of light
can be absorbed by the electron.
• Thus the missing LINES in the absorption
spectra
Changing the energy
• As the electron falls back to ground state,
it emits a photon
Changing the energy
• May fall down in steps
• Each with a different energy
• Each jump emits a photon
Changing the energy
• The bigger the drop, the greater energy of the
photon
• The higher the energy the shorter the
wavelength
Emission spectra a hydrogen based on electron transitions.
Bohr correctly models the difference in energy levels for
hydrogen based on this theory.
# protons in nucleus
2
Z
En = 2 E1
n
Ground state energy
Usually in eV
Niels Bohr
Energy level (1,2,3 etc..)
(ground is 1)
By the way this bohr stuff only seems to work for one electron atoms, more complex atoms were solved by
the “new” quantum mechanics using wave functions, orbitals, and probability functions. Etc….
Remember energy is always a comparison between two states.
So the ground state energy of an electron is considered to be the
difference in energy of the electron when it is “free” of the nucleus
and when it is bound by the nucleus in the lowest orbit.
Similarly this would be the energy needed to take the electron in the
ground state and remove it from the atom. (Ionization Energy)
1 proton
So for hydrogen
2
Z
En = 2 E1
n
-13.6 eV
1
En = 2 (-13.6 eV)
n
1
En = 2 (-13.6 eV)
n
For hydrogen, the first 5 levels. Notice that the energies are
negative so that as it goes up it gains energy.
E2 = -13.6 eV
22
E1 = -13.6 eV
1
-0.54 eV
-0.85 eV
n=5
n=4
-1.5 eV
n=3
-3.4 eV
n=2
-13.6 eV
n = 1 (ground state)
What frequency and wavelength of light must be absorbed
for an electron to go from the ground state to the 3rd energy
level?
What type of EM wave? (see next page)
E = 1.94 x 10-18 J
-0.54 eV
-0.85 eV
n=5
n=4
f = 2.92 x 1015 Hz
-1.5 eV
n=3
l = 1.03 x 10-7 m
-3.4 eV
n=2
l = 103 nm
-13.6 eV
n = 1 (ground state)
103 nm
Would put
us in UV
The first 5 energy levels in a hypothetical atom.
An electron drops from the n=3
state to the ground state.
-3 eV
-4 eV
n=5
n=4
What possible energy photons
could be emitted?
-7 eV
n=3
-15 eV
n=2
-62 eV
n = 1 (ground state)
55 eV
8 eV
47 eV
The first 5 energy levels in a hypothetical atom.
A photon with an energy of 15 eV -3 eV
reaches the atom where the
-4 eV
electron state is unknown. What
-7 eV
happens.
n=5
n=4
-15 eV
n=2
-62 eV
n = 1 (ground state)
The difference between any two
levels is not equal to 15 eV. It
passes through (transparent)
n=3
The first 5 energy levels in a hypothetical atom.
If the atom emitted a photon of
-3 eV
light equal to 3 eV. Where would -4 eV
the electron be briefly?
-7 eV
n=5
n=4
-15 eV
n=2
-62 eV
n = 1 (ground state)
n=3
Compton Scattering
Photons of X-ray light are shined onto a
piece of carbon
The photons emerge at a different angle
and with longer wavelengths. Ejected
electrons are also dectected
Compton Scattering
This kind of reminds me of a collision between 2 objects! Light is
not an object it doesn’t have mass…. or does it?
Compton analyzes it like any other collision, applying
conservation of energy and momentum! (He does use Einstein’s
recently released paper on Relativity and apparently the photon has
relativistic mass)
General analysis (conservation of energy and momentum)
The photon gives (kinetic) energy to the electron
The photon can’t slow down so it becomes a lower energy photon
(longer wavelength)
There is no initial Y momentum only X, so afterwards the Y momenta
must cancel.
A photon of light has momentum even though it has no
“rest” mass / non-relativistic mass
hf
p= c
Momentum of
a photon
and
E=hf
so we could rewrite as…
A photon of light
c=lf
hf
p= c
Momentum of
a photon
c
f=l
h
p=
l
Compton effect scattering
h
lf – l i =
(1 - cos q)
mec
Mass of
electron
Deflected angle
of photon
Compton & Photoelectric
effect animation
In a Compton experiment, x-rays are
scattered at an angle of 45o are found to
have a wavelength of .22 nm. What is
the wavelength and momentum of the
incident photon?
How much kinetic energy was delivered
to the electron?
A LED light source emits
So we know that light acts like a wave.
refraction, diffraction, interference
And also like a particle.
it exchanges energy like a particle in discreet blows.
SCIENCE ENTERS A GREY AREA
Wave-Particle Duality
Can be explained in
terms of waves
Reflection
Refraction
Interference
Diffraction
Polarization
Photoelectric
effect
Can be explained in
terms of particle
If waves can act like particles….
can particles act like waves?
Louis de Broglie began to wonder this very same
thing in this very tumultuous time in physics.
(early 1900’s)
duh BRO lee
He predicts mathematically that a particle
will have a wavelength according to…
h
l= p
de Broglie
wavelength
Hey, that looks like the
equation for photon
momentum!
momentum
mv
But does it have any real world testability?
The wavelength of .15 kg baseball thrown at 40 m/s
l=
6.626x10-34
.15 kg 40 m/s
= 1.1 x 10-34 m
Gamma rays are 10-12 m, about the diameter of a nucleus
The simple explanation is that “normal” objects have wavelengths way too small to be noticed.
But there are all sorts of funkiness with this from a practical perspective. Like wouldn’t it look
like a blurred? Or what is the amplitude of the oscillation?
The truth is as far as I get it, is that this doesn’t necessarily mean that the baseball is travelling in
transverse wave as it moves. A lot of quantum mechanics doesn’t make sense from a practical
perspective. There is a lot of probability / Wave math that doesn’t easily translate to something.
But, the WEIRD thing is that moving particles do exhibit wave properties modeled by the
equations.
Remember DIFFRACTION, the waves constructively and
destructively interfere whenever “obstacles” are reached.
Like a slit, multiple slits, a fine wire…. Any obstruction as
long as the obstacles are on the order of the wave length
Remember multi-slit interference of light.
Like a diffraction grating…
The interference causes a given wavelength of light
to be reinforced in certain locations.
The diffraction pattern on the left looks clean but the
diffraction pattern on the right looks kind of grainy?
Could something grainy interfere with itself like a wave?
The first experiment which verified the wave-particle
duality is dubbed the Davison-Germer experiment.
1.) Electrons were generated from a hot filament
4.) a moveable detector
could measure the location
of the peak intensity
2.) Accelerated
through voltage
3.) Struck a crystal of nickel. The atomic
spacing of which is close to the predicted
de Broglie wavelength
Results fit cleanly, with predictions made from de Broglie’s
wavelength even as the speed was changed which affected
wavelength etc…
What would happen to the wavelength if the speed were
increased?
Dr. Quantum revisits the double slit experiment
with WAVE-PARTICLE DUALITY video
(we are going down the rabbit hole)
The comments to this video on you tube were hilarious such as
Scr!* you dr. quantum, quit !*#*ing with my world.
General fodder below
quantum unit ends
Nuclear Chemistry last topic!
Just when you start to get comfortable thinking of
light as an electromagnetic wave. New evidence is
found.
Each portion of the electromagnetic spectrum has quantum energies appropriate for the excitation
of certain types of physical processes. The energy levels for all physical processes at the atomic
and molecular levels are quantized, and if there are no available quantized energy levels with
spacings which match the quantum energy of the incident radiation, then the material will be
transparent to that radiation, and it will pass through.
Back to a car accelerating
Does it really accelerate smoothly?
What is really accelerating the car?
Molecules slamming into the piston each one
delivering a blow causing it to move…
Animation here later…
Matter comes as particles, that’s crazy
Charge comes as particles, that’s crazy
atoms
Electron / proton
Energy comes as particles, that’s crazy
photon
Time comes as particles, that’s crazy
?????
Space comes as particles, that’s crazy
?????