Analyse and apply Einstein’s description of the equivalence of energy and mass and relate this to the nuclear reactions that occur in stars

From the Universe to the Atom > Origins of the Elements >

Einstein’s equation states that if m amount of mass was completely converted to energy, the total amount of energy released would be E = mc2

  • In fusion reactions, the final products have a lighter total mass than the total mass of original products.
  • This is called the mass defect , denoted bydelta m
  • The energy released can be calculated asdelta emc2
  • The earliest understanding of what provides energy in the stars came when Cecilia Payne , using spectroscopy discovered that Sun is composed mostly of Hydrogen .
  • The extreme heat in the sun due to change of gravitational potential energy to thermal energy, releases the electrons from the atoms and creates a ball of plasma , ionised hydrogen and helium nuclei.
  • One possible nuclear reaction could provide energy to the stars was the proton-neutron fusion.
    • proton-neutron fusion
    • The deuteron formed has less mass than the original proton and neutron .
    • This mass defect is converted to energy, according to the equation delta emc2.
    • The energy released with every fusion is about 2.2 MeV
    • But this reaction cannot be the major source of energy as there aren’t enough neutrons in the stars to sustain the reaction.
  • Since majority of the element in the stars are Hydrogen atoms, proton-proton fusion is likely the major cause of energy release.
    • Although proton-proton electrostatic repulsion is very strong, the extreme conditions in stars help the protons overcome this force and get close enough for strong nuclear force to act.
    • As they fuse the to form deuterium, the electrostatic repulsion doesn’t play a part anymore as one of the protons change into a neutron.
      • proton-neutron fusion
      • The energy released comes from the difference in mass of the original products from the final products, according to the equation :delta emc2
      • The positron gets annihilated by an electron :positron gets annihilated by an electron
    • The deuterium then further fuses with another proton to form Helium
      • deuterium then further fuses with another proton to form Helium
    • Depending on the condition of the star (temperature and pressure) , the Hemay fuse to form He through various intermediary steps.
 
 

Extract from Physics Stage 6 Syllabus © 2017 NSW Education Standards Authority (NESA)