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Atoms

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Rutherford Scattering 1909• Scientists thought the positive nucleus

would be the size of the atom.• Rutherford showed it was 104 times smaller.• Classical physics had no way to explain the

size of atoms.o Electron should radiate EM waves and spiral

into nucleus.• Quantum Mechanics prevents this.• We have that the atomic size is set by the

wave properties of electrons.

Higher energy probes short distance.

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Tiny Nucleus• Rutherford showed the nucleus

was 104 times smaller than theatom.• Electrons are point particles.• The atomic size is determined by

wave equation for electrons.• Property of fermions that no two

can be in the same state meansatoms with more electrons arebigger.

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Question: Rutherford

• Rutherford’sscattering resultshowing thenucleus was smallwas hard tounderstand inclassical physicsbecause:

E) All of the above

D) A and B

C) The light emitted by atoms couldnot be explained.

B) The chemical properties ofelements could not be explained.

A) The size of atoms could not beexplained.

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Atoms• Electron probability distribution

shown.• Nucleus is 105 times smaller than

1s state.• Hydrogen-like states

o Solve Schrödinger equation• Two spin states for each spatial

state.

! n!m

"r ,t( ) state

n = 1,2,3,... principle quantum number

! < n orbital angular momentum s, p, d, f ...

"! # m # ! z component of L

all integers

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Hydrogen-like Energy Levels

n = 1 : ! = 0 1s m = 0 2 electrons

n = 2 : ! = 0 2s m = 0 2 electrons

! = 1 2p m = !1,0,1 6 electrons

n = 3 : ! = 0 3s m = 0 2 electrons

! = 1 3p m = !1,0,1 6 electrons

! = 2 3d m = !2,!1,0,1,2 10 electrons

n = 4 : ! = 0 4s m = 0 2 electrons

! = 1 4p m = !1,0,1 6 electrons

! = 2 4d m = !2,!1,0,1,2 10 electrons

! = 3 4f m = !3,!2,!1,0,1,2,3 14 electrons

PrincipleQuantum Number

TotalAngularmomentum

z angularmomentum

ElectronsIn shell

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Atomic Energy Levels• Use the Hydrogen-like states

to describe the basic states ofatoms.

• Screening of nuclear chargefavors low angular momentuml.

• We can put two electrons intoeach state (two spin states).

• Big energy gaps atZ=2,10,18,36,54,96

• Helium, Neon, Argon,Krypton,Xenon,Radon

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Atomic Shell Model• Closed shells are spherically symmetric.

o Implies closed shells are simple and we cantreat closed shells like a spherically symmetricpotential that a few additional electrons move in.

o One electron outside a closed shell is simplelike one electron…

o This is why the periodic table works• Screening favors low l.

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Filling Up the Atomic ShellsElectron configuration determineschemical properties of elements.

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Question: Periodic Table

• Theperiodicpropertiesof theelements:

E) All of the above

D)A and B

C) Can be calculated in QuantumMechanics.

B) Can only be found from Chemistryexperiments.

A) Can be calculated in classical physics.

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Cosmology

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We are alsointerested in

things wedon’t see

News from the Universe

Hubble deep field:By looking far away wecan look back in time.

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Hubble Expansion of Universe• Universe is expanding

uniformlyo New space being

createdo Farther away stars move

away from us at greatervelocity.

o Known for a long time

• Like raisin breadexpanding.o The raisins move aparto But remain the same

size.

redshift

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• Big bang created space and time about 13.6 billion years ago.• Inflation allowed causal disconnection.

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Composition of Universe

• Stars and galaxies are only ~0.5%• Neutrinos are ~0.3–10%• Rest of ordinary matter (electrons and protons) are

~5%• Dark Matter ~30%• Dark Energy ~65%• Anti-Matter 0%

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Question: Age of the Universe

• What is theage of theuniverse?

E) Less than 1 million years.

D) About 100 trillion years.

C) About 14 billion years.

B) We don’t know.

A) The universe has existed forever.

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Type-1A Supernovae

• White Dwarf star held up by Fermi pressure ofelectrons.o Accreting matter with time.

• At 1.4 solar masses gravitational energy issufficient to drive the reaction e+p→n+νe• Sudden collapse to neutron star

o Shock wave blows off outer envelope with hugeenergy release.

• The size of the explosion is a “standard candle”.

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Expansion: Type-1A Supernovae

• Type-IA Supernovae“standard candles”

• Brightness not quitestandard, but correlatedwith the duration of thebrightness curve

• Apparent brightness⇒ how far (“time”)

• Know red-shift⇒ expansion since thenExpansion of Universe is

accelerating

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Accelerating Universe• Einstein’s equation:

• If the energy dilutes as Universeexpands, it must slow down

• Need something that gains inenergy as Universe stretches

i.e, negative pressure• The cosmological constant Λ

has the equation of state w=p/ρ=–1

• Generically called “DarkEnergy”

• Many experiments converge

!R

R( )2

= 8!

3G

N"

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Cosmic Microwave Background• Photons produced when

atoms were formed inearly universe, about380,000 years after bigbang.

• Red-shifted to 2.73degrees due to expansionof universe.

• As far back as we can“see”.

• Inflation gives correlationsover regions no longercausally connected.

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WMAP

• Dipole due to motion subtracted• Temperature fluctuations correspond to density fluctuations in early universe

o They grew to form galaxies…

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What is WMAP• Satellite orbits L2

earth-sun Lagrangepointo 1.5 million km from

earth• Microwave detectors

o 0.3 degree pixelso 5 frequencieso from 22 to 90 GHz

• Maps full sky

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Evolution

• Initial fluctuations at 380,000 years• Matter condenses• First stars at 200,000,000 years, earlier than

expected• More stars form• Today

o Age of universe 13.7 billion years to 1% accuracy

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Geometry of UniverseThe amount of dark matter and energy in theuniverse plays a crucial role in determining thegeometry of space. If the density of matter andenergy in the universe is less than the criticaldensity, then space is open and negativelycurved like the surface of a saddle. If thedensity exactly equals the critical density, thenspace is flat like a sheet of paper. If the densityis greater than critical density, then space isclosed and positively curved like the surface ofa sphere. In this latter case, light paths divergeand eventually converge back to a point. TheInflationary Theory, an extension of the BigBang theory, predicts that density is very closeto the critical density, producing a flat universe,like a sheet of paper. WMAP has determined,within the limits of instrument error, that theuniverse is flat.

Flat universe consistent withinflation

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Summary of WMAP Data• Universe is 13.7 billion years old with a margin of error of close to 1%.• First stars ignited 200 million years after the Big Bang.• Light in WMAP picture from 380,000 years after the Big Bang.• Content of the Universe:

o 4% Atoms, 23% Cold Dark Matter, 73% Dark energy.o The data places new constraints on the dark energy. It seems more like a "cosmological constant" than

a negative-pressure energy field called "quintessence". But quintessence is not ruled out.o Fast moving neutrinos do not play any major role in the evolution of structure in the universe. They

would have prevented the early clumping of gas in the universe, delaying the emergence of the firststars, in conflict with the new WMAP data.

• Expansion rate (Hubble constant) value: Ho= 71 km/sec/Mpc (with a margin of error of about5%)

• New evidence for Inflation (in polarized signal)• For the theory that fits our data, the Universe will expand forever. (The nature of the dark

energy is still a mystery. If it changes with time, or if other unknown and unexpected thingshappen in the universe, this conclusion could change.)

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Question: Understanding the Universe

• What majoraspect of theuniverse doweunderstand.

E) The ultimate fate of the universe.

D) The origin of the cosmic microwavebackground.

C) What the dark energy is.

B) What the dark matter is.

A) The cause of the big bang.

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End