Chapter 26- Nuclear physics

• Einstein's energy equation $E=$$mc^2$ has two interpretations ;

  • mass is a form of energy
  • Energy has mass
• Einstein's mass-energy equation can be used to calculate the energy release from nuclear decay using the difference in masses of the parent and daughter nuclei
• Positrons are the antiparticles of electrons so when they meet, they annihilate each other and their entire mass is transformed into energy in the form of two identical gamma photons
• In pair production, a single photon vanishes and its energy creates a particle and a corresponding antiparticle
• In particle accelerators very energetic protons are smashed together and their kinetic energy is transformed into matter. The total rest mass of the particles after the collision is greater than that before.
• The mass defect of a nucleus is defined as the difference between the mass of the completely separated nucleons and the mass of the nucleus
• The binding energy of a nucleus is defined as the minimum energy required to completely separate a nucleus into its constituent protons and neutrons
• Binding energy can be calculated using Einstein's mass-energy equation


  Binding energy of a nucleus = mass defect of nucleus x $c^2$
• To compare how easy it is to break up nuclei, the average binding energy per nucleon of nuclei is compared. The greater the binding energy per nucleon, the more tightly bound the nucleons are within the nucleus, so the more stable a nucleus is.
• Induced fission is nuclear fission occurring when a nucleus becomes unstable on absorbing another particle such as a neutron
• Uranium-235 absorbs a thermal nucleon and then becomes a highly unstable uranium-236 nucleus which splits in less than a microsecond. This produces 2 daughter nuclei and three fast neutrons.
• The total mass of the particles after fission is always less than the total mass of the particles before the reaction as the difference is equal to the energy released in the reaction. The energy released is a combination of kinetic energy of the particles produced and the energy of the photons and neutrinos emitted
• Fission is a chain reaction. The three fast neutrons can be slowed down to thermal neutrons which can be absorbed by more U-235 nuclei to form U-236 which decays and continues the chain reaction. The number of neutrons increases exponentially.
• A thermal neutron is a neutron in a fission reactor with mean kinetic energy similar to the thermal energy of particles in the reactor cores.
• Within a nuclear reactor, fuel rods are spaced evenly within a steel-concrete vessel known as the reactor core. A coolant is used to remove thermal energy produced from the fission reaction and the fuel rods are surrounded by the moderator and control rods can be moved in and out of the core

  
• Fuel rods in a fission reactor contain enriched uranium, mainly uranium-238 with 2-3% of uranium-235
• The role of the moderator in a fission reactor is to slow down the fast neutrons. In many reactors the moderator is also the coolant e.g. water
• Control rods in a fission reactor are made of a material whose nuclei readily absorb neutrons (most commonly boron or cadmium) with their purpose to stop the exponential increase of the number of thermal neutrons. Their position can be adjusted to ensure only one neutron survives per fission reaction
• Nuclear fission reactors produce radioactive waste such as plutonium-239 which is toxic as well as radioactive and has a high half-life. This radioactive waste cannot be disposed if normally. Instead they must be buried in geologically stable and safe locations that are marked for future generations
• Nuclear fusion is the process in which small nuclei are combined to make larger nuclei, producing a enormous amount of energy.
• The only way to fuse nuclei, is to bring them close together so that the short-range nuclear force can attract them into a larger nucleus. However the repulsive electrostatic force between the nuclei is enormous so high temperatures must be used to ensure the nuclei have energy great enough to overcome the force
• There are no fusion reactors yet as it requires vast amounts of energy to maintain the high temperatures required for the fusion reaction to occour