Examine the model of half-life in radioactive decay and make quantitative predictions about the activity or amount of a radioactive sample

The rate of decay of an radioactive isotope is measured by its half life.

Half life : It is the time required for radioactive isotope to reduce to half of its initial value.

  • It has been found that the rate at which radioactive isotopes decay , is directly proportional to the number of atoms present. The rate can be expressed as :
    • (where wavelength is the decay constant , with units¬†s-1 )
  • This equation can be integrated to give the following result :
    • where,
      • No is the number of atoms present at time t = 0
      • Nt is the number of atoms present at time t
  • Using the definition of half life , we can find
    • is when the number of atoms are half the original amount, i.e.
    • Thus ,
    • rearranging we get ,decay constant
    • Thus if we can measure the half life, we can calculate the decay constant.

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