Modern Physics

20th Century Discoveries

Historical Developments

• 1895: Roentgen discovers X-rays
• 1896: Becquerel discovers radioactivity
• 1897: Thomson discovers electron
• 1900: Planck �energy is quantized�
• 1905: Einstein�s theory of relativity
• 1911: Rutherford discovers the nucleus
• 1913: Millikan measures electron charge
• 1925: Pauli�s exclusion principle
• 1927: Heisenberg�s uncertainty principle
• 1928: Dirac predicts existence of antimatter
• 1932: Chadwick discovers neutron
• 1942: Fermi first controlled fusion reaction
• 1964: Gell-Mann proposes quarks

The Nucleus

• Mass number (A) is number of nucleons (protons + neutrons)
• Atomic number (Z) is number of protons
• Neutron number (N) number of neutrons
• Often, mass number and atomic number are combined with chemical symbol
• Example: aluminum, Z = 13, A = 27

Isotopes

• Atoms of the same element have same atomic number but can have different mass numbers
• These are called isotopes: atoms of the same element with different number of neutrons
• Chemical properties are the same but nuclear properties are different

Nuclear Mass

• Nuclei are extremely dense, about 2.3 x 1014 g/cm³
• Nuclear mass usually measured with atomic mass unit (u)
• Based on mass of carbon-12 atom whose mass is defined as 12 u
• 1 u = 1.6605402 x 10^-27 kg

Mass-Energy

• Nuclear mass can also be expressed in terms of rest energy by using Einstein�s famous equation E = mc²
• Mass is often converted to energy in nuclear interactions
• Substituting values for mass of 1u and converting to eV, we find 1u =931.50 MeV

Nuclear Stability

• Since protons have positive charge, they will repel each other with electric force
• Must be a stronger, attractive force holding them together in nucleus
• This force usually called the strong force
• Strong force acts only over extremely small distances
• All nucleons contribute to strong force
• Neutrons add to strong force without adding to repelling electrical force, so they help stabilize nucleus
• For Z > 83, repulsive forces can�t be overcome by more neutrons and these nuclei are unstable

Binding Energy

• Binding energy is difference between energy of free, unbound nucleons and nucleons in nucleus
• Mass of nucleus is less than mass of component parts
• Difference in mass is mass defect and makes up binding energy (E = mc²)

Nuclear Decay

• Unstable nuclei spontaneously break apart and emit radiation in the form of particles, photons, or both
• Process is called radioactivity
• Can be induced artificially
• Parent nucleus decays into daughter nucleus

Types of Radiation

Alpha radiation

• Least penetrating, can be stopped by sheet of paper
• Decreases atomic number by 2, mass number by 4
• Is actually a He nucleus, will quickly attract 2 electrons and become helium

Beta radiation

• Usually a neutron decays into a proton and an electron
• Missing mass becomes kinetic energy of electron
• Atomic number increases by 1, neutron number decreases by 1, mass number is the same
• Inverse beta decay proton emits positron and becomes neutron, decreasing atomic number
• Can be stopped by sheet of aluminum
• Involves emission of antineutrinos (with e^-) or neutrinos (with e⁺) also

Gamma radiation

• Most penetrating, will penetrate several centimeters of lead
• High energy photon emitted when nucleons move into lower energy state
• Often occurs as a result of alpha or beta emission

Nuclear Decay

• In many cases decay of parent nucleus produces unstable daughter nucleus
• Decay process continues until stable daughter nucleus is produced
• Often involves many steps called a decay series

Writing Nuclear Reactions

• Write chemical symbol with mass number and atomic number of parent nucleus
• On right side of arrow, leave a space for the daughter element and write the symbol for the type of emission occurring
• alpha:
• beta:
• neutron:
• Mass and charge are conserved quantities so totals on left side of equation must equal totals on right of equation for both the mass numbers and the atomic numbers
• Calculate atomic number of daughter and look up its symbol on periodic table
• Calculate mass number of daughter

Half-Life

• Decay constant for a material indicates rate of decay
• Half-life is the time for � of a sample to decay; after 2 half-lives, � of sample remains; after 3, 1/8 remains
• Half-lives range from less than a second to billions of years

Nuclear Fission

• Heavy nucleus splits into two smaller nuclei
• Energy is released due to higher binding energy per nucleon (and so less mass) in smaller nuclei
• Often started by absorption of a neutron by large nucleus making it unstable
• U-235 and Pu-239 are usual fission fuels for reactors and atomic bombs
• Fission products include two smaller elements, high energy photons, and 2 or 3 more neutrons
• Neutrons then can be absorbed by other nuclei creating chain reaction
• Need a minimum amount of fuel for sustained reaction called critical mass

Nuclear Fusion

• Two light nuclei combine to form heavier nucleus
• Product has higher binding energy (less mass) so energy is released
• Fusion occurs in stars and hydrogen bombs (thermonuclear)
• Stars fuse protons (hydrogen) and helium atoms
• Fusion fuel on earth usually deuterium (heavy hydrogen)
• For fusion to occur, electrostatic repulsion forces must be overcome so nuclei can collide
• Extremely high temperatures and pressures needed
• Sustained, cost-effective fusion reaction has not been achieved
• Would be better then fission because:
  • products are not radioactive
  • fuel is cheap and plentiful
  • no danger from critical mass