Nuclear Physics

• Rutherford scattering


  • Demonstrated the existence of a nucleus
  • Disproved Thomson's plum pudding model
• Thomson's plum pudding model

  Atom made up of a sphere of positive charge, with small areas of negative charge evenly distributed throughout
• Nuclear model


  New model for the atom after the plum pudding model was disproved
• Rutherford's apparatus


  1. Alpha source and gold foil in an evacuated chamber covered in a fluorescent coating

  2. Microscope to observe the path of the alpha particles
• If the plum pudding model was true, the expected results would be that the positively charged alpha particles would be deflected by a very small amount when passing through the foil
• Rutherford scattering results


  • Most alpha particles passed straight through the foil with no deflection
  • A small amount of particles were deflected by a large angle
  • Very few particles were deflected back by more than 90°
• From the results it was concluded that the atom has a small, dense, positively charged nucleus at its centre
• Types of radiation


  • Alpha (α)
  • Beta (β)
  • Gamma (γ)
• Alpha (α) radiation


  • Range in air: 2 - 10 cm
  • Highly ionising
  • Deflected by electric and magnetic fields
  • Absorbed by paper
• Beta (β) radiation


  • Range in air: Around 1 m
  • Weakly ionising
  • Deflected by electric and magnetic fields
  • Absorbed by aluminium foil (around 3 mm)
• Gamma (γ) radiation


  • Infinite range: follows inverse square law
  • Very weakly ionising
  • Not deflected by electric and magnetic fields
  • Absorbed by several metres of concrete or several inches of lead
• Identifying radiation types


  1. Measure background count

  2. Measure count rate with source

  3. Place paper between source and GM tube, if count rate decreases significantly then alpha radiation

  4. Repeat with aluminium foil and lead block, if count rate decreases significantly then beta and gamma radiation respectively

  
• Gamma radiation can be used to monitor the thickness of certain materials while they are being produced
• Gamma radiation can be used in medicine as a detector, to sterilise surgical equipment, and in radiation therapy
• Inverse square law


  Intensity of gamma radiation follows the formula I = k/x^2, where I is intensity, k is a constant, and x is distance from source
• Investigating inverse square law

  1. Measure count rate of gamma source at different distances from GM tube

  2. Adjust for background radiation

  3. Plot graph of corrected count against 1/x^2 to verify inverse square law
• Alpha radiation is highly ionising and can be incredibly dangerous if inhaled or ingested
• Beta particles and gamma radiation can also cause damage to body tissue with prolonged exposure
• Safety measures for handling radioactive sources

  • Use long handled tongs to move the source
  • Store the source in a lead-lined container when not in use
  • Keep the source as far away as possible from yourself and others
  • Never point the source towards others
• Background radiation


  Radiation around us constantly, must be measured and subtracted to find corrected count rate of a source
• Sources of background radiation

  • Radon gas
  • Artificial sources from nuclear weapons testing and nuclear meltdowns
  • Cosmic rays
  • Rocks containing naturally occurring radioactive isotopes
• Radioactive decay


  Random process with a constant decay probability (decay constant λ)

  
• Half-life (T1/2)


  Time taken for the number of nuclei to halve
• Measuring half-life


  1. Plot graph of number of nuclei against time and measure time taken to halve

  2. Plot graph of ln(N0) against time, modulus of gradient is decay constant, use formula T1/2 = ln(2)/λ
• Activity


  Number of nuclei that decay per second, proportional to number of nuclei (A = λN)
• Decay constant can only be used to model decay when there is a large number of nuclei in the sample

  
• Uses of radioactive nuclei based on half-life

  • Dating of objects using long half-life nuclei like carbon-14
  • Medical diagnosis using short half-life nuclei like technetium-99m

  
• Activity


  Easier to measure than the number of nuclei, often used to find the half-life of a sample
• Decay constant


  Can be used to model the decay of nuclei only when there is a large number of nuclei in a sample, as it models the number of nuclei decayed by statistical means

  
• Ways radioactive nuclei can be used

  • Dating of objects (e.g. carbon-14 with half-life of 5730 years used to date organic objects)
  • Medical diagnosis (e.g. Technetium-99m with half-life of 6 hours used as radioactive tracer)

  
• Technetium-99m


  • Pure gamma emitter
  • Half life of 6 hours, short enough to limit exposure but long enough for tests
  • Can be easily prepared on site

  
• The activity and half-life of radioactive nuclei will affect the way they must be stored, for example nuclei with an extremely long half-life will have to be suitably stored, for example in steel casks underground, to prevent these nuclei from damaging the environment and the people that may be living around them hundred of years into the future

  
• Strong nuclear force


  Holds nuclei together
• Electromagnetic force


  Causes protons to experience a force of repulsion
• Reasons a nucleus might become unstable

  • Too many neutrons (decays through beta-minus emission)
  • Too many protons (decays through beta-plus emission or electron capture)
  • Too many nucleons (decays through alpha emission)
  • Too much energy (decays through gamma emission)
• Nuclei may decay through several types of emission before finally becoming stable
• As the number of neutrons and protons in a nucleus increases beyond around 20 of each


  The electromagnetic force of repulsion becomes larger than the strong nuclear force keeping the nucleus together, and so more neutrons are needed to increase the distance between protons in order to decrease the magnitude of the electromagnetic force to keep the nucleus stable
• Energy level diagram


  Shows the differences in energy of particles in a nuclear decay

  
• Energy level diagrams


  • Alpha decay
  • Beta-minus decay forming Technetium-99m

  
• Distance of closest approach

  The point at which a charged particle fired at a nucleus stops and has no kinetic energy, its electrical potential energy is equal to its initial kinetic energy due to conservation of energy