Physics 222

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Physics 222 Physics 222 D.S. Durfee D.S. Durfee

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Physics 222. D.S. Durfee. The Physics Revolution of the 20 th Century. Relativity – physics of the fast Quantum Mechanics – law of the small Atoms: clocks, discharge lamps, lasers Molecules: chemistry Nuclei: fission, fusion Solid State: semiconductors Degenerate Matter: superconductors - PowerPoint PPT Presentation

Transcript of Physics 222

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Physics 222Physics 222

D.S. DurfeeD.S. Durfee

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The Physics Revolution of the The Physics Revolution of the 2020thth Century Century

Relativity – physics of the fastRelativity – physics of the fast Quantum Mechanics – law of the smallQuantum Mechanics – law of the small

– Atoms: clocks, discharge lamps, lasersAtoms: clocks, discharge lamps, lasers– Molecules: chemistryMolecules: chemistry– Nuclei: fission, fusionNuclei: fission, fusion– Solid State: semiconductorsSolid State: semiconductors– Degenerate Matter: superconductorsDegenerate Matter: superconductors– Coherence & Superposition: quantum Coherence & Superposition: quantum

computingcomputing

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Puzzles at the Beginning of the Puzzles at the Beginning of the Twentieth CenturyTwentieth Century

Null result of the Michelson-Morley Null result of the Michelson-Morley ExperimentExperiment

Ultraviolet CatastropheUltraviolet Catastrophe Photoelectric EffectPhotoelectric Effect Maxwell’s Equations Spell the Demise of Maxwell’s Equations Spell the Demise of

Atoms!Atoms! Discrete atomic emission linesDiscrete atomic emission lines

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Quantum Uncertainty RelationsQuantum Uncertainty Relations

Position – Momentum

Energy – Time

Other Dimensions

Angular Momentum

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Thought QuestionThought Question

Imagine that I measure the location and momentum of an Imagine that I measure the location and momentum of an electron. I measure the location with a precision of electron. I measure the location with a precision of 1nm. If I make a second measurement one second 1nm. If I make a second measurement one second later, about how well will I be able to predict where I later, about how well will I be able to predict where I will find the electron with the second measurement? will find the electron with the second measurement? (me ~ 1e-30 kg, h/4(me ~ 1e-30 kg, h/4¼¼ ~ 0.5e-34 Js) ~ 0.5e-34 Js)

A : To better than 1 nmA : To better than 1 nm B : To within around 1nmB : To within around 1nmC : To within 1 C : To within 1 μμmm D : To within 1 mmD : To within 1 mmE : Not even to within 1 mmE : Not even to within 1 mm

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Wave-Particle DualityWave-Particle Duality Things act as wave when propagatingThings act as wave when propagating

– or, in other words, we use waves to make or, in other words, we use waves to make predictions as to what we will find when we predictions as to what we will find when we make our measurement.make our measurement.

Things act as waves when we measure Things act as waves when we measure wave-like properties.wave-like properties.

Things act as particles when we measure Things act as particles when we measure particle-like propertiesparticle-like properties

Example: BEC interference --- theorists Example: BEC interference --- theorists confused about “undefined phase”confused about “undefined phase”

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Postulates of Quantum Postulates of Quantum MechanicsMechanics

Every physically-realizable system is described Every physically-realizable system is described by a state function by a state function ψψ that contains all that contains all accessible physical information about the accessible physical information about the system in that statesystem in that state

The probability of finding a system within the The probability of finding a system within the volume volume dvdv at time at time tt is equal to | is equal to |ψψ||22dvdv

Every observable is represented by an Every observable is represented by an operator which is used to obtain information operator which is used to obtain information about the observable from the state functionabout the observable from the state function

The time evolution of a state function is The time evolution of a state function is determined by Schrödinger’s Equationdetermined by Schrödinger’s Equation

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4.1 The Nuclear Atom4.1 The Nuclear Atom 120120

An atom is largely empty space (NOT!)An atom is largely empty space (NOT!)

4.2 Electron Orbits4.2 Electron Orbits 124124

The planetary model of the atom and The planetary model of the atom and why it failswhy it fails

4.3 Atomic Spectra4.3 Atomic Spectra 127127

Each element has a characteristic line Each element has a characteristic line spectrumspectrum

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4.4 - 4.54.4 - 4.5

4.4 The Bohr Atom 4.4 The Bohr Atom 130130Electron waves in the atomElectron waves in the atom

4.5 Energy Levels and Spectra4.5 Energy Levels and Spectra

A photon is emitted when an electron A photon is emitted when an electron jumps from one energy level to a jumps from one energy level to a lower levellower level

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4.6 Correspondence Principle4.6 Correspondence Principle 138138

The greater the quantum number, the The greater the quantum number, the closer quantum physics approaches closer quantum physics approaches classical physicsclassical physics

4.7 Nuclear motion4.7 Nuclear motion140140

The nuclear mass affects the The nuclear mass affects the wavelengths of spectral lineswavelengths of spectral lines

4.8 Atomic Excitation4.8 Atomic Excitation 142142

How atoms absorb and emit energyHow atoms absorb and emit energy

4.9 The Laser4.9 The Laser 145145

How to produce light waves all in stepHow to produce light waves all in step

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Reading Quiz QuestionReading Quiz Question

Which Which spectral seriesspectral series resulted resulted from a study of the from a study of the visiblevisible partpart of the hydrogen of the hydrogen spectrum?spectrum?

A: The Lyman seriesA: The Lyman seriesB: The Balmer seriesB: The Balmer seriesC: The Paschen seriesC: The Paschen seriesD: The Brackett seriesD: The Brackett seriesE: The Wurald seriesE: The Wurald series

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The Hydrogen SpectrumThe Hydrogen Spectrum

The Balmer SeriesThe Balmer Series

2

1

4

11

nR

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Rutherford’s ExperimentRutherford’s Experiment

θ

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What would happen if I shot What would happen if I shot a bullets through a piece of a bullets through a piece of

jello?jello?Thought QuestionThought Question

A: All of them would come nearly straight A: All of them would come nearly straight through, but with a slightly smaller through, but with a slightly smaller velocityvelocity

B: Some of them would be deflected B: Some of them would be deflected slightly, some would lose a little velocityslightly, some would lose a little velocity

C: Some would go nearly straight C: Some would go nearly straight through, some would deflect at large through, some would deflect at large angles, some would ricochet almost angles, some would ricochet almost straight back straight back

D: They would all reflect straight backD: They would all reflect straight back

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Thought QuestionThought Question

What would happen if I shot a bullets What would happen if I shot a bullets through a piece of jello containing through a piece of jello containing shredded carrots?shredded carrots?

A: All of them would come nearly straight A: All of them would come nearly straight through, but with a slightly smaller through, but with a slightly smaller velocityvelocity

B: Some of them would be deflected B: Some of them would be deflected slightly, some would lose a little velocityslightly, some would lose a little velocity

C: Some would go nearly straight C: Some would go nearly straight through, some would deflect at large through, some would deflect at large angles, some would ricochet almost angles, some would ricochet almost straight back straight back

D: They would all reflect straight backD: They would all reflect straight back

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What would happen if I shot a What would happen if I shot a bullets through a piece of jello bullets through a piece of jello

containing iron anvils?containing iron anvils?Thought QuestionThought Question

A: All of them would come nearly straight A: All of them would come nearly straight through, but with a slightly smaller velocitythrough, but with a slightly smaller velocity

B: Some of them would be deflected slightly, B: Some of them would be deflected slightly, some would lose a little velocitysome would lose a little velocity

C: Some would go nearly straight through, C: Some would go nearly straight through, some would deflect at large angles, some some would deflect at large angles, some would ricochet almost straight backwould ricochet almost straight back

D: They would all reflect straight backD: They would all reflect straight back

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Johann Jakob BalmerJohann Jakob Balmer ( (May 1May 1, , 18251825 – – March 12March 12, , 18981898) was a Swiss ) was a Swiss mathematicianmathematician and an honorary and an honorary physicistphysicist. .

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The Hydrogen SpectrumThe Hydrogen Spectrum

The Balmer SeriesThe Balmer Series

2

1

4

11

nR

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Quiz QuestionQuiz Question

In Bohr’s model of the hydrogen In Bohr’s model of the hydrogen atom, what determined the atom, what determined the frequency of emitted light?frequency of emitted light?

A: The total energy of the orbiting A: The total energy of the orbiting electronelectron

B: The energy difference between B: The energy difference between initial and final electron statesinitial and final electron states

C: The frequency of revolution of the C: The frequency of revolution of the orbiting electronorbiting electron

D: The difference in revolution D: The difference in revolution frequency between initial and final frequency between initial and final electron stateselectron states

E: The sum of the initial and final E: The sum of the initial and final electron revolution frequencieselectron revolution frequencies

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Bohr’s TheoryBohr’s Theory

He did not think in terms of wavesHe did not think in terms of waves He simply postulated thatHe simply postulated that

– There are orbits in which the electron There are orbits in which the electron doesn’t radiate.doesn’t radiate.

– The light released when an electron The light released when an electron changes orbits is a photon with an changes orbits is a photon with an energy equal to the difference in energy energy equal to the difference in energy of the two orbitsof the two orbits

He further postulated that the orbits He further postulated that the orbits were circular, withwere circular, withL = n~

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Results of Bohr TheoryResults of Bohr Theory

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Thought QuestionThought QuestionHow many energy levels are there How many energy levels are there

between the hydrogen ground between the hydrogen ground state (-13.6 eV) and the state (-13.6 eV) and the continuum (0 eV)?continuum (0 eV)?

A: oneA: one

B: 13B: 13

C: 14C: 14

D: 1324D: 1324

E: None of the aboveE: None of the above

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Wave Theory of HydrogenWave Theory of Hydrogen

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5th Solvay Conference, Brussels, 23-29 October 1927 Back row: A Piccard, E Henriot, P Ehrenfest, D Durfee, Ed Herzen, Th De Donder, E Schroedinger

E Verschaffelt, W Pauli, Waldo, W Heisenberg, R H Fowler, L Brillouin.Middle Row: P Debye, M Knudsen, W L Bragg, H A Kramers, P A M Dirac, A H Compton,

L de Broglie, M Born, N Bohr.Front Row: I Langmuir, M Planck, Mme Curie, H A Lorentz, A Einstein, P Langevin, Ch E Guye,

C T R Wilson, O W Richardson.

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Quiz QuestionQuiz Question

““When When nn gets large, quantum gets large, quantum physics should start to look like physics should start to look like classical physics” is a classical physics” is a somewhatsomewhat accurate statement of the...accurate statement of the...

A: Equivalence PrincipleA: Equivalence Principle

B: Limiting Value PrincipleB: Limiting Value Principle

C: Legacy PrincipleC: Legacy Principle

D: Completeness PrincipleD: Completeness Principle

E: Correspondence Principle.E: Correspondence Principle.

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Thought QuestionThought Question

What would happen to the What would happen to the hydrogen spectrum if I replace the hydrogen spectrum if I replace the electron with a muon (which is like electron with a muon (which is like an electron but heavier)? an electron but heavier)? AA: : No changeNo change

B: Almost no changeB: Almost no change

C: All of the lines will shift to C: All of the lines will shift to significantly longer wavelengthssignificantly longer wavelengths

D: All of the lines will shift to D: All of the lines will shift to significantly shorter wavelengthssignificantly shorter wavelengths

E: I have no idea --- hey, its an honest E: I have no idea --- hey, its an honest answer! answer!

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Thought QuestionThought QuestionWhat would happen to the What would happen to the

hydrogen spectrum if I replace hydrogen spectrum if I replace the nucleus (a proton) with an the nucleus (a proton) with an alpha particle (two protons plus alpha particle (two protons plus two neutrons… i.e. more charge, two neutrons… i.e. more charge, more mass)?more mass)?

A: No changeA: No change

B: Almost no changeB: Almost no change

C: All of the lines will shift to significantly C: All of the lines will shift to significantly longer wavelengthslonger wavelengths

D: All of the lines will shift to significantly D: All of the lines will shift to significantly shorter wavelengthsshorter wavelengths

E: I have no ideaE: I have no idea

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Thought QuestionThought QuestionWhat would happen to the What would happen to the

hydrogen spectrum if I replace hydrogen spectrum if I replace the nucleus (a proton) with a the nucleus (a proton) with a deuteron (a proton plus a deuteron (a proton plus a neutron… i.e. same charge, more neutron… i.e. same charge, more mass)? mass)? A:A: No change No change

B:B: Almost no change Almost no change

C:C: All of the lines will shift to All of the lines will shift to significantly longer wavelengthssignificantly longer wavelengths

D:D: All of the lines will shift to All of the lines will shift to significantly shorter wavelengthssignificantly shorter wavelengths

E:E: I have no idea I have no idea

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Frank-Hertz ExperimentFrank-Hertz Experiment

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The Correspondence The Correspondence PrinciplePrinciple

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Quick Writing AssignmentQuick Writing Assignment

In one minute, write a short, clear, In one minute, write a short, clear, and concise paragraph which and concise paragraph which explains the correspondence explains the correspondence principle.principle.

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Bohr Theory Bohr Theory Successes/FailuresSuccesses/Failures

☺ Predicts emission and absorption lines of hydrogen Predicts emission and absorption lines of hydrogen andand hydrogen-like ions hydrogen-like ions

☺ Predicts x-ray emissions (Moseley’s law)Predicts x-ray emissions (Moseley’s law)☺ Gives an intuitive picture of what goes on in an atomGives an intuitive picture of what goes on in an atom☺ The correspondence principle is obeyed... sort ofThe correspondence principle is obeyed... sort of

X It can’t easily be extended to more complicated It can’t easily be extended to more complicated atomsatoms

X No prediction of rates, linewidths, or line strengthsNo prediction of rates, linewidths, or line strengthsX Fine structure (and hyperfine structure) not Fine structure (and hyperfine structure) not

accounted foraccounted forX How do atoms form molecules/solids?How do atoms form molecules/solids?

X Where did it come from? There must be a more Where did it come from? There must be a more general underlying theory!general underlying theory!

☺ It gave hints of a new, underlying theoryIt gave hints of a new, underlying theory