Lecture 9: Building Blocks

Review from last time… discovery of the electron discovery of the electron discovery of the atomic nucleus discovery of the atomic nucleus quantization of atomic energy levels quantization of atomic energy levels  the mystery of spectral lines  Bohr model for Hydrogen  particle nature of light

The photoelectric effect In 1887 Hertz discovered that shining light onto a sheet of metal could cause the metal to eject electrons – but only high frequency (UV) light would work In 1887 Hertz discovered that shining light onto a sheet of metal could cause the metal to eject electrons – but only high frequency (UV) light would work lower frequency light would not produce the same effect lower frequency light would not produce the same effect if no electrons were emitted, increasing the brightness of the light had no effect. if no electrons were emitted, increasing the brightness of the light had no effect.

Einstein’s explanation electrons need a minimum kinetic energy to escape from the metal electrons need a minimum kinetic energy to escape from the metal light carries energy in discrete packets (photons) light carries energy in discrete packets (photons) the energy of a photon is proportional to its frequency the energy of a photon is proportional to its frequency  E = h where h = x eV s (Planck’s constant) (Planck’s constant)

Wave-particle duality Sometimes light behaves like a wave (double-slit experiment) Sometimes light behaves like a wave (double-slit experiment) sometimes it behaves like a particle (photoelectric effect) sometimes it behaves like a particle (photoelectric effect)

Electron Diffraction

Electrons are waves too! the two-slit experiment was performed for electrons (1927) the two-slit experiment was performed for electrons (1927) a diffraction pattern was produced, just like for light! a diffraction pattern was produced, just like for light! the answer to “are you a wave or a particle” depends on the question… the answer to “are you a wave or a particle” depends on the question… the act of observation affects the outcome of the experiment the act of observation affects the outcome of the experiment

The Uncertainty Principle The more we know about a particle’s position, the less we can know about its velocity (momentum) The more we know about a particle’s position, the less we can know about its velocity (momentum) the more we know about the momentum (velocity) the less we know about the position the more we know about the momentum (velocity) the less we know about the position

The two forms of the uncertainty principle position-momentum position-momentum  uncertainty in position times uncertainty in momentum = Plank’s constant  x  p = h energy-time energy-time  uncertainty in energy times uncertainty in time = Plank’s constant   t = h

The uncertainty principle is a manifestation of wave-particle duality A wave has a well-defined velocity/momentum but does not have a well-defined position A particle has a well-defined position but may not have a well-defined velocity

Schrodinger’s Wave Equation

Quantum Tunneling

The Exclusion Principle every particle is defined by a few pieces of information (quantum state) every particle is defined by a few pieces of information (quantum state) two electrons with exactly the same quantum numbers cannot occupy the same state two electrons with exactly the same quantum numbers cannot occupy the same state

Degeneracy Pressure

Fundamental Particles protons and neutrons are not the most fundamental particles protons and neutrons are not the most fundamental particles they can be broken down into more basic units called quarks and leptons they can be broken down into more basic units called quarks and leptons

six kinds of quarks can explain the “zoo” of hundreds of new particles that were discovered in the 1960’s

Fundamental Fermions upelectron down electron neutrino strangemuon charm muon neutrino toptauon bottom tauon neutrino QuarksLeptons

The Exclusion Principle applies to all Fermions

Every particle has an anti-particle every particle has an anti-particle which is its opposite in every way every particle has an anti-particle which is its opposite in every way all quantum numbers are opposite all quantum numbers are opposite for example, electron  positron for example, electron  positron proton  anti-proton proton  anti-protonetc.

matter and anti-matter annihilates annihilation pair production

Virtual Particles

Hawking Radiation

Black Hole Evaporation anti-particles have ‘negative mass’, so as the BH swallows anti-particles, it loses mass! anti-particles have ‘negative mass’, so as the BH swallows anti-particles, it loses mass! the time it takes for a BH with mass M to evaporate completely is: the time it takes for a BH with mass M to evaporate completely is: t = x 10 4  2 G 2 M 2 /(hc 4 ) seconds t = x 10 4  2 G 2 M 2 /(hc 4 ) seconds

Four Fundamental ForcesForce strength (within nucleus) strength (outside nucleus) exchangeparticleRole Strong1000gluonbindsnucleus Electro- magnetic 11photon binds atoms Weak guage boson nuclear reactions Gravity graviton large-scale structure

Summary quantum mechanics quantum mechanics  wave-particle duality  uncertainty principle  exclusion principle fundamental particles fundamental particles  quarks and leptons the four fundamental forces the four fundamental forces  strong, electro-magnetic, weak, gravity