Einstein Published 4 Papers in 1905 that laid the foundation for modern physics:

• 6/9/1905 Photoelectric Effect: On the Heuristic Viewpoint Concerning the Production and Transformation of Light
• 7/18/1905 Brownian Motion: On the Motion of Small Particles Suspended in a Stationary Liquid, as Required by the Molecular Kinetic Theory of Heat
• 9/26/1905 Special Relativity: On the Electrodynamics of Moving Bodies
• 11/21/1905 E = mc: Does the Inertia of a Body Depend Upon Its Energy Content?

Wave - Particle Duality

• Light behaves both like a wave and a particle!

Dual Nature of Light

Photons

• Smallest possible piece of E&M Light
  • No rest mass
  • No charge
  • Move with a velocity of m/s

Energy of a Photon

• Energy of a photon is quantized.
  • Can only come in certain amounts.
• Discovered by Max Karl Ernst Ludwig Planck to explain blackbody radiation.
• Discovered that
• Planck’s constant, h, h = 6.63 x 10 Js
• Energy of a photon can come in amounts proportional to Planck’s constant.

Quantized vs. Continuous

Energy of a Photon

Check Yourself

A photon with a wavelength of meters has how much energy?

The spectrum of visible light emitted during transitions in excited hydrogen atoms is composed of blue, green, red, and violet lines. What characteristic of light determines the amount of energy carried by the photon.

1. amplitude
2. frequency
3. phase
4. velocity

Photoelectric Problem

• EM radiation striking a metal may emit electrons (photoelectrons).
• Not all EM radiation creates electrons.
• Higher intensity (brighter) light doesn’t affect whether photoelectrons are created.
• Higher frequencies of light affect creation of photoelectrons.

Photoelectric Effect with Einstein

• Electrons in the metal are held by an “energy well.”
• Electrons must absorb at least enough energy to get out of the well in order to become free of the metal.
• Electrons had to absorb a single photon with that minimum amount of energy, known as the work function.
• Any excess energy absorbed becomes the free electron’s kinetic energy.

Work Function

So do particles have wave behavior?

Compton Effect

• Arthur Compton shot x-rays so that they collided with electrons in graphite.
  • Photoelectron is emitted
  • Original x-ray was reemitted with a lower wavelength
  • So the photon lost energy and momentum
• Conclusion: photons has momentum and obey the laws of conservation of momentum and energy.

Compton Effect

Compton Effect Equations

• Combine , , and the momentum of a photon can be expressed as:

de Broglie Wavelength

• EM waves behave as particles
• Moving particles can exhibit wave properties
• Confirmed by shooting electrons through a double slit and seeing a diffraction pattern.
• Smaller particles have more wavelike behavior

Moving electrons are found to exhibit properties of

1. Particles only
2. waves only
3. both particles and waves
4. neither particles or waves

Which phenomenon best supports the theory that matter has a wave nature?

1. electron momentum
2. electron diffraction
3. photon momentum
4. photon diffraction

Wave particle duality is most apparent in analyzing the motion of a

1. baseball
2. space shuttle
3. galaxy
4. electron

Calculate the wavelength for a tennis ball (57 grams) moving at a speed of 30 m/s.

Note:

All science is either physics
or stamp collecting.
-Ernest Rutherford

Rutherford’s Gold Foil Experiment

• Shot alpha particles (helium nuclei) at a thin sheet of gold foil
  • Most particles went through undeflected
  • Some particles were deflected by large amounts
• Conclusions:
  • Atoms have a small, massive, positive nucleus
  • Electrons must orbit the nucleus
  • Most of the atom is empty space

Rutherford

Rutherfords Foils

• The lack of emission radiation as electrons move about the nucleus
• The unique spectrum of each element
• The stability of the atom

Bohr

• Electrons can only exist at discrete energy levels
• Each atom allows only a limited number of specific orbits (electrons) per energy level
• Electrons can change energy levels
  • Absorbs a photon of exactly the energy needed to reach a higher level.
  • Emit a photon of exactly the energy difference as electron falls to a lower level.

Energy Level Diagram

• Allows us to visualize energy levels in an atom
• Lowest energy level is the ground state

Hydrogen Atom

• Negative energy levels indicate electron is bound to the atom.
• If the electron reaches 0 eV, it is no longer bound and can be emitted as a photoelectron.
  • Any excess energy becomes the electrons kinetic energy.

Hydrogen Atom

An electron in a hydrogen atom drops from the n = 3 level to n = 2 state. Determine the energy of the emitted radiation.

Hydrogen Atom

What is the frequency of a photon emitted when an electron in a hydrogen atom drops from the n = 2 to the n = 1 energy level?

Mercury Atom

• Energy Levels differ by atoms
• Levels named by letters instead of numbers

Mercury Atom

An electron in a mercury atom drops from energy level f to energy level c by emitting a photon of what energy?

Mercury Atom

A mercury atom in the ground state absorbs 20 electronvolts of energy and is ionized by losing an electron. How much kinetic energy does this electron have after the ionization?

Atomic Spectra

• Atoms can only emit and absorb photons of certain frequencies
• Photon frequencies correspond to transitions in electron energy levels.
• Result: unique atomic spectra

Incandescence

Objects heated until they glow emit a continuous spectrum, described as blackbody radiation.

Gas Discharge Lamp

• Gas discharge lamps excited electrons by application of high electrical potential.
  • Electrons jump to higher energy.
  • As they relax to lower energy levels, photons of specific frequencies are emitted.
  • Spectrum is not continuous and is unique to the element.
• Analysis of spectra allows determination of gas composition.

The Standard Model

• An atom is the smallest part of an element that has the characteristics of that element.
• 1930s - scientists begin to discover even smaller particles
• This launches the Particle Physics movement.

Antimatter

• Antimatter is made up of particles with the same mass as regular particles, but opposite charges and other characteristics
  • Antiproton - same mass a proton, negative charge
  • Antineutron - same mass as a neutron, opposite magnetic moment.
  • Positron - same mass as an electron, positive charge.

Annihilation

• Matter particle corresponding to antiparticle meet to annihilate each other.
  • Complete conversion of both particles into energy
  • Conservation laws still apply
    • Mass-energy
    • Charge
    • Momentum

Structure of the Standard Model

• All 4 fundamental forces act on Hadrons
• Strong nuclear force doesn’t act on Leptons (electron is a lepton)
• Baryons charge is always a whole number (protons and neutrons)
• Mesons: Pion, neutral pion, Kaon, J/psi, Upsilon, Charmed meson, Bottom meson.

Quarks

• Corresponding anti-quark with opposite charge also exists.
• Proton = uud
• Neutron = udd

What is the charge of the down anti-quark?

Compared to the mass and charge of a proton, an antiproton has

1. the same mass and the same charge
2. greater mass and the same charge
3. the same mass and the opposite charge
4. greater mass and the opposite charge

Leptons

Corresponding anti-lepton with opposite charge also exists.

A particle unaffected by an electric field could have a quark composition of

1. css
2. bbb
3. udc
4. uud

What is the charge of an antistrange quark in Coulombs?