Slide for 2011

I am used to being able to answer many questions for you, becauseI 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 WEIRDNESSAs 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

A metal say magnesium

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Light Source

Light is shined on to a piece of metal under voltage.Electrons near the surface can be knocked off atoms by absorbing light

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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

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Predicted BUT NOT observed

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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 electronsI 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.

Photoelectric effect applet

4.) Electrons were ejected “instantly”

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.

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The electron needs a certain amount of energy to break free (ionization energy, Ie).

That energy comes in chunks / quanta

Energy meter

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A larger quantum delivers more energy.

Energy meter

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A larger quantum

Energy meter

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Even larger

Energy meter

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.

hotter

cooler

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

energy of a photon of light

Planck’s constant6.626 x 10-34 J/s

frequency of light (Hz)

max planck

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 Frequency and Energy of photon

Increasing wavelength

R O Y G B I V

high energy photonsI would probably know how photon energies change in Vis spectrum

Red- Radio low energyViolent- UV damages skin high energy

Back to the photoelectric effect

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What really happened a photon of red light has the least amount of energy.

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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.

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This is a slight simplification we will come back to later

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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

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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.

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Once the threshold energy of light is there.More light (chunks) intensity means the faster electrons are ejected (photoelectrons).

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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 asE=hf

Energy needed to break the electron freeCalled the work function.

Depends on the metal.Some metals hold on tighter than others…

Energy leftover from the photon. Becomes some other energy like KE or a lower

photon.Total

photon energy

hf = + KE

Total photon

energy (J)

Energy used to break the electron free (J)

Also called the work function

Energy left over as kinetic (J)

hf = + KE

0

hf0 =

the lowest frequency that will eject an electron

f0 = h

Remember energy of a photon of light

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.

a.) What is the work function?b.) What is the stopping potential of a photoelectron?

1.1x10-19 J

What is the definition of Voltage / Electric

Potential?

UEV = 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

UEV = q

Stopping potential (if you write this down, it will not be available.. understand it)

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?

UEV = q

1.3x10-19 JV =

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

• unique to each element like a fingerprint

We know what elements are in stars by looking at their light

emission 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?

Line spectra for different elements

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

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Nucleus

Energy Level 1 Energy Level 2Energy Level 3

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

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The further the orbit is from the nucleus, the more energy it has.

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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.

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DOES NOT HAPPEN

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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.

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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”.

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Also an electron can only emit a specific certain energies of light when they move down levels.(again the difference between energy levels)

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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

• May fall down in steps

• Each with a different energy

• Each jump emits a photon

Changing the energy

Changing the energy• The bigger the drop, the greater energy of the

photon

• The higher the energy the shorter the wavelength

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Emission spectra a hydrogen based on electron transitions.

Bohr correctly models the difference in energy levels for hydrogen based on this theory.

Niels Bohr

En = Z2

n2E1

# protons in nucleus

Energy level (1,2,3 etc..)(ground is 1)

Ground state energyUsually in eV

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….

Z2

n2E1En =

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)

So for hydrogen1 proton

-13.6 eV

1n2

(-13.6 eV)En =

1n2

(-13.6 eV)En =

n = 1 (ground state)

n = 2

n = 3

n = 4n = 5

1-13.6 eVE1 =

-13.6 eV

22

-13.6 eVE2 = -3.4 eV

-1.5 eV

-0.85 eV-0.54 eV

For hydrogen, the first 5 levels. Notice that the energies are negative so that as it goes up it gains energy.

n = 1 (ground state)

n = 2

n = 3

n = 4n = 5

-13.6 eV

-3.4 eV

-1.5 eV

-0.85 eV-0.54 eV

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

f = 2.92 x 1015 Hz

= 1.03 x 10-7 m

= 103 nm

103 nmWould put us in UV

n = 1 (ground state)

n = 2

n = 3

n = 4n = 5

-62 eV

-15 eV

-7 eV

-4 eV-3 eVAn electron drops from the n=3

state to the ground state.

What possible energy photons could be emitted?

The first 5 energy levels in a hypothetical atom.

55 eV

8 eV

47 eV

n = 1 (ground state)

n = 2

n = 3

n = 4n = 5

-62 eV

-15 eV

-7 eV

-4 eV-3 eVA photon with an energy of 15 eV

reaches the atom where the electron state is unknown. What

happens.

The first 5 energy levels in a hypothetical atom.

The difference between any two levels is not equal to 15 eV. It passes through (transparent)

n = 1 (ground state)

n = 2

n = 3

n = 4n = 5

-62 eV

-15 eV

-7 eV

-4 eV-3 eVIf the atom emitted a photon of

light equal to 3 eV. Where would the electron be briefly?

The first 5 energy levels in a hypothetical atom.

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

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 Scattering

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

p = h f c

Momentum of a photon

and E = h f

so we could rewrite as…

A photon of light

p = h f

p = h

c

Momentum of a photon

c = f

f = c

f – i =h

mec(1 - cos )

Mass of electron

Deflected angle of photon

Compton effect scattering

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

Can be explained in terms of particle

Reflection

Refraction

Interference

Diffraction

Polarization

Photoelectric effect

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…

=hp

de Brogliewavelength

momentummv

Hey, that looks like the equation for photon

momentum!

But does it have any real world testability?

=6.626x10-34

.15 kg

The wavelength of .15 kg baseball thrown at 40 m/s

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

2.) Accelerated through voltage

3.) Struck a crystal of nickel. The atomic spacing of which is close to the predicted

de Broglie wavelength

4.) a moveable detector could measure the location

of the peak intensity

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…

Energy comes as particles, that’s crazy

Matter comes as particles, that’s crazy

Charge comes as particles, that’s crazy

Space comes as particles, that’s crazy

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atoms

Electron / proton

photon

Time comes as particles, that’s crazy

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