The worksheet for the simulation is in the student’s booklets

The worksheet for the simulation is in the student’s booklets.

Quantum and Nuclear Physics (B)

Mr. KlapholzShaker Heights

High School

http://www.wellsphere.com/wellpage/mri-lupus-vasculitis-image-brain

Summary of the Photoelectric effect:

Light makes electrons shoot off of metal (data).This shows that light is a particle (theory).

And now a detailed look at the photoelectric effect…

Light

• In 1660 Newton thought light was a particle.• In 1801 Young showed (in the “Double slit

experiment”) that light exhibited wave phenomena (interference and diffraction). Also the polarization of light makes only makes sense if light is a wave.

• So in the first half of the 1800’s, everyone was comfortable that light was a wave.

• It wasn’t that simple…

The Photoelectric EffectFrom 1840 -1900 data trickled in about a particular experiment that would really get people thinking.It would start one of the great “paradigm shifts” in human knowledge.

The Electroscope is a simple charge indicator.

http://123iitjee.com/mod/forum/discuss.php?d=1884

http://www.school-for-champions.com/science/static_detection.htm

Under the right circumstances, if you shine light on metal, it will become positively charged.

http://withfriendship.com/images/c/12935/Photoelectric-effect-wallpaper.jpg

Light can neutralize a negatively charged piece of metal…

http://www.mc2quantum.com/?p=260

but if the low frequency light is sent in, then no electrons are emitted.

http://www.mc2quantum.com/?p=260

The photoelectric effect basic facts:• It is a big deal for electrons to be emitted by the metal

because the electrons are attracted to the protons in the metal (yet the electrons still leave).

• Brighter light produces more electrons, but not electrons with more kinetic energy. (!)

• Greater frequencies yield greater kinetic energy for electrons (as individuals, not as a groups). (!)

• Below a ‘threshold frequency’ absolutely no electrons are emitted. (!)

• There is no lag time: electrons are emitted as soon as the light is turned on. (!)

Farewell to the wave theory of light

• Every one of the (!) symbols on the previous slide made no sense if light was a wave.

• For example, if light was a wave, then many low-energy light waves would eventually cause an electron to be emitted, but in the lab, low-energy light never makes a photelectron.

• Also, waves of greater light intensity would have affected the kinetic energy of the electrons, but this never happened.

Einstein !

Einstein won the Nobel prize for his theory on the photoelectric effect (1905).

• Light is made of particles of light (“photons”).• For an electron to be emitted, exactly one photon

must be absorbed. • The greater the intensity of light, the greater the

number of photons (per second), and the greater the number of electrons emitted. It seems so simple now.

Time out for a moment of DualityLight behaves as a wave and as a particle.

http://www.google.com/imgres?imgurl=http://changming.org/images/Yin_Yang.gif&imgrefurl=http://changming.org/&usg=__LAqFCNZunrxWsuTDgWpiiaN3fUw=&h=900&w=900&sz=13&hl=en&start=0&zoom=1&tbnid=NS2fvikd4e5jYM:&tbnh=113&tbnw=113&prev=/images%3Fq%3Dyin%2Byang%26hl%3Den%26gbv%3D2%26biw%3D1280%26bih%3D638%26tbs%3Disch:1&itbs=1&iact=hc&vpx=886&vpy=324&dur=8705&hovh=225&hovw=225&tx=130&ty=218&ei=fkPrTNPzHYT7lweCyemFAg&oei=fkPrTNPzHYT7lweCyemFAg&esq=1&page=1&ndsp=24&ved=1t:429,r:22,s:0

• Planck had shown how energy and frequency were related: E = hf. High frequency light (like UV) has high energy. Red light has low energy.

• Violet light, even dim violet light, can make an electron leave the metal, with plenty of kinetic energy to spare.

• Red light, even bright red light, cannot make even one electron leave the metal. [Of course, the details depend on the type of metal, the temperature, and so on.]

Threshold

• It takes a particular amount of energy to get an electron to leave the metal, due to Coulomb attraction. In this context, this energy is called the ‘work function’ (f).

• If a photon does not have at least the energy of the work function, then there is no way it will make an electron leave the metal.

Our first photoelectric equation:

Energy going in = Energy used + Energy coming outhf = Energy used + Energy coming

outhf = f + Energy coming out

hf = f + KE of electron

What would happen if the work function was greater than the energy of the incoming photon?

Millikan’s experiment(notice the polarity) …

http://secure-zone.cx.cc/t/

A close look at the applied voltage

• For the moment, assume that the light is of great enough frequency to eject some electrons.

• The voltage stops the electrons from leaving the target.

• The smallest voltage that can turn around the electrons is called the “Stopping Potential” (V).


• Not all of the electrons that leave the target have the same value for kinetic energy.

• Let’s focus on the most energetic electrons, the ones with KEmax.

• Why can’t the electrons that leave the target with KEmax get to the detector? …

• There is an electrical force that turns the electrons around. It takes a lot of energy to still make it to the detector.


• The experimenter (Millikan) used many different frequencies of light (that is his independent variable) and for each one he measured the ‘Stopping Potential’ (the smallest voltage that prevented electrons from leaving the target)…

A close look at the applied voltageFrequency / × 1012 Hz Stopping Potential / V

300 0.5

400 1

500 3

600 5

700 7

800 9


electrical energy / charge = voltageelectrical energy = charge × voltage

energy = qVIf V is tuned just right, so that the voltage is as small as possible but still prevents every electron from making it to the detector, then it is removing an amount of energy equal to the maximum kinetic energy of the electrons.

eV = KEmax.


hf = f + Kinetic Energy of Electronhf = f + eV

• Remember that V is the smallest possible voltage that stops the photelectrons.


hf = f + eVWhat would you see if you graphed Stopping

Voltage vs. frequency ?V = (h/e) f – (f/e)

y = mx + bIt makes a line, the slope is h/e. The y-intercept (f/e) gives the work function. The threshold frequency is also easy to spot…

Stopping Voltage vs. Frequency

http://www.tutorvista.com/topic/e-photos

Different metals have different work functions (different y-intercepts) and different threshold frequencies.

A variation of our photoelectric equation:

Conservation of energy gave us:Energy in = Energy out

hf = f + KEhf = f + eV

Every term is an energy.f is the minimum energy required to remove one

electron; this corresponds to the threshold frequency (f0) the minimum frequency that will

liberate one electron: f = hf0…

A variation of our photoelectric equation:

hf = f + eVhf = hf0 + eV

Let’s revisit the graph with this equation in mind.hf = hf0 + eVV = (h/e)f - (h/e)f0

For what value of f is V = 0?V = 0 when f = f0.

See this on the graph…

Stopping Voltage vs. Frequency

http://www.tutorvista.com/topic/e-photos

Spotlight on the photon

• The energy of the photon is E = hf.• The speed of a photon in a vacuum is 3 x 108

m s-1.• The momentum of massive things is p = mv.• The mass of the photon is 0, yet experiments

show that it has momentum.• What is the momentum of a photon?• p = E / c.

If you bounce electrons off of a crystal, the result is the same as bouncing a wave off of

a crystal (Davisson-Germer experiment).

http://www.matter.org.uk/diffraction/electron/electron_diffraction.htm#

Matter Waves• Matter acts as a wave.• The de Broglie wavelength: l = h / p = h / mv • Which diffracts more, small wavelengths or large

wavelengths?• sin q = l / b. The amount of diffraction is greater

for large l and small openings.• So, looking at l = h / p, which diffracts more, an

electron or you?• An electron will seem more like a wave than you

will.

Another moment of DualityMatter behaves as a wave and as a particle.


Dual DualityMatter and Light…

both are waves and both are particles.


“Nobody understands quantum mechanics.”

Richard FeynmanNobel Laureate, Physics

“The more you see how strangely nature behaves, the harder it is to make a model that explains how even

the simplest phenomena actually work. So theoretical physics has given up on that.”

TOK

Theoretical physicists have the job of predicting the results of experiments.In part this means that the classic question of “Why does that happen?” is no longer the primary job of scientists to answer.The pressing issues are “What will happen?” and “How can we use this?”

Review of Atomic Spectra

Is this an emission spectrum or an absorption spectrum?

http://www.astro.psu.edu/astrofest/samplespectra.html

All ‘bright line’ spectra are emission spectra.

http://www.astro.psu.edu/astrofest/samplespectra.html

This ‘dark line’ spectrum is from sunlight. The dark parts were absorbed by the atmosphere of the sun or the earth.

http://www.saburchill.com/HOS/astronomy/028.html

Review of Atomic Spectra

• Atoms emit light at the same frequencies (energies) that they absorb light.

• E = hf.• When an atom absorbs light, an electron has

jumped to a higher energy level. For example from level n = 1 to level n = 3.

• Different types of atoms (“elements”) have levels at different energies, so different elements emit and absorb different frequencies.

An electron in the 3rd energy level.

• If an electron is in the 3rd energy level, why can we see 3 frequencies of light?

• n = 3 to n = 1.• n = 3 to n = 2, and n = 2 to n = 1.

The first few Electron Energy Levels of Hydrogen

http://sfhs.sbmc.org/~thiggins/APPhysicsB/Chapters%2027-30/chapter_28_Notes.htm

Electron Energy Levels

• Energy levels are measured in electron Volts (eV).• The values are negative (!). This is because 0 energy

is the value of a free electron with no motion. Positive energies describe electrons that are free of an atom, and moving.

• Negative energies describe anything that is bound. The earth is bound to the sun, and electrons can be bound to a nucleus. The more negative the energy, the less energy it has.

Electron in a Box

http://musr.physics.ubc.ca/~htb/trevor/e-in-box.html

Electron in a Box

• This is a theoretical idea that helps us understand quantum theory.

• The electron is bouncing back and forth in a one-dimensional box.

• The electron is considered to be like a standing wave, a probability wave.

• Since there is no probability of the electron being outside the box, the wave has nodes at the edges of the box.

Electron in a Box of length L.‘n’ identifies the energy level

http://wiki.chemeddl.org/index.php/5.2_The_Wave_Nature_of_the_Electron

n = 1 L = (1/2)l

n = 2 L = (2/2)l

n = 3 L = (3/2)l

L = (n/2)l

Electron in a Box

• L = (n/2)l

• ln = 2L / n• Now add in the deBroglie idea: l = h/p• p = h / l• The momentum of the electron depends on which

energy level the electron is in.• pn = h / ln

• pn = h / (2L / n) = nh/2L

Electron in a Box (use KE = p2/2m) pn = nh/2LEk = p2/2m

Ek = (nh/2L )2/2m Ek = n2h2/8mL2

• The energy of the electron is quantized.• Quote from the IB syllabus: “Students should be

able to show that the kinetic energy EK of the electron in the box is given by:

Ek = n2h2 / 8meL2

Erwin Schrödinger (1926)

Schrödinger• The big news is the nature of the wave that

describes matter. • Schrödinger figured out that the amplitude of the

wave, the intensity of the wave, was related to the likelihood that a particle was in a location.

• The wave is a probability wave.• The symbol for the probability wave is Ψ (upper

case), ψ (lower case). We spell it psi and pronounce it either as ‘see’ or ‘sigh.’

The wave function: Ψ (and its square)• Ψ2 is the probability of finding the particle in a

particular location at a particular time.• For a hydrogen atom, there is a specific radius

(about 0.5 x 10-10 m) that is the most likely distance from the nucleus for an electron to be. The function Ψ2 has a maximum at that location, but Ψ2 is not zero anywhere!

Where is a particle in a box most likely to be?

Werner Heisenberg

Heisenberg Uncertainty Principle• The HUP is regarded by many as the most

fundamental idea in all of quantum mechanics.• The HUP is about measurement and about

knowledge (TOK).• The HUP says that the more you know about one

thing, the less you know about something else…

Heisenberg Uncertainty PrincipleDx Dp ≥ h / 4p

The uncertainty we have in measuring position (Dx), times the uncertainty we have in measuring the momentum (Dp) of the object when it is at that position, will always be greater than the Planck

constant divided by 4p.

Heisenberg Uncertainty PrincipleDE Dt ≥ h / 4p

The uncertainty we have in measuring energy, times the uncertainty we have in measuring when the

object had that energy, will always be greater than the Planck constant divided by 4p.

Heisenberg Uncertainty Principle• Even with perfect equipment these uncertainties

will be present.• The act of measuring position will disturb the

momentum, and vice versa.• The act of measuring energy will always put limits

on when the object had that energy.

Documents

The worksheet for the simulation is in the student’s booklets