nuclear physics

• Attendance


  Code - i655jc
• You will learn about
• Topics to be learned

  • How to identify a nucleus
  • Nuclear stability
  • Binding energy
  • The Liquid drop model of the nucleus

  
• Background reading Chp42 S2
• We have seen from the work done by Rutherford that an atom comprises a nucleus located at its centre, surrounded by a cloud of electrons that are distributed in space according to their energy and angular momentum, which are defined by the electron's quantum numbers

  
• Now we will consider the nucleus
• Nuclide


  Contains neutrons and protons
• Designation of a particular nucleus

  Z

  AX

  where X is the chemical symbol for the element, A is the atomic mass number, and Z is atomic number which give the number of protons

  
• A = Z + N, where N is the number of neutrons

  
• Isotopes


  Atoms with the same number of protons but different atomic mass numbers and hence different numbers of neutrons

  
• Isotopes of hydrogen


  • 1

  1H, 1

  2H, 1

  3H

  hydrogen, deuterium and tritium
• Nuclides with an excess number of protons or neutrons tend to be unstable and will decay to other nuclides
• Nuclear radius


  Approximately 1.2 A^(1/3) fm
• The volume is proportional to the atomic mass number A, the number of nucleons

  
• All nuclei have the same density, and all the nucleons are closely spaced in a sphere of radius R

  
• Identification of atomic mass


  Accelerate isotope of charge q through potential difference ΔV

  Isotope experiences Lorentz force in magnetic field B

  Measure position on target to determine mass

  
• The radius of the orbit is proportional to the square root of the mass of the isotope
• Bainbridge spectrometer


  Singly charged ions injected

  Velocity selected by balancing deflection due to magnetic and electric fields

  Radius of path determined
• Given the size of the nucleus there should be a very large Coulomb repulsion between the protons

  
• The strong nuclear force overcomes this electrostatic repulsion
• The strong nuclear force is charge-independent, binding neutron to neutron, proton to neutron, proton to proton
• Experimentation shows that for distances less than 0.4 fm there is a strong repulsive component that prevents nucleons from getting too close
• For low atomic number Z the number of neutrons and protons in a nucleus are equal, but as Z increases the electrostatic repulsion between protons increases, requiring more neutrons to ensure the nuclear force overcomes the electrostatic force

  
• Atomic Mass Unit (u)


  1/12 the mass of the atom carbon-12

  
• 1u = 931.494 MeV/c^2
• Binding energy


  The reduction in mass of a nucleus compared to the sum of the masses of its nucleons, due to the energy used to bind the nucleus

  
• Calculating binding energy


  BE = Z*mH + N*mn - mX*c^2

  
• The binding energy is not an energy that resides in the nucleus, it is the difference in mass energy between the nucleus and the individual nucleons

  
• The binding energy per nucleon is not proportional to A as expected from the number of nucleon interactions, but follows a more complex relationship

  
• Liquid drop model


  Bohr's model of the nucleus as a liquid drop, with nucleons free to vibrate and undergo frequent collisions

  
• Liquid drop model of binding energy

  Eb = C1*A - C2*A^(2/3) - C3*Z*(Z-1)/A^(1/3) - C4*(N-Z)^2/A
• The 4 contributions to the liquid drop model are: volume effect, surface effect, Coulomb repulsion effect, and symmetry effect