Radioactive Decay

What is Radioactive Decay?

• Radioactivity is a random and spontaneous process.
  • This means that radioactivity cannot be controlled and occurs without a cause.
• For a sample of a radioactive isotope that decays into a stable isotope, the number of decays per unit time (activity) decreases over time.
  • The activity, A, of a radioactive source is the total number of nuclei decaying every second.
  • The unit for activity is the becquerel, Bq, where 1 Bq equals 1 decay per second.

Half Life

• The decay of radioisotopes can be used to measure the material's age.
  • The half-life of an atom is the time taken for half of the radioisotopes in a sample to decay.

• Because the amount of original radioisotopes decreases by half every time, there is a consistent pattern we can use for formulae:

Experimental Determination of Half-Life

• In principle, the half-life of any radionuclide can be determined from a graph of the count-rate, activity or number of undecayed nuclei against time.
  • Although it is often easier to work with count rate or activity.

Practical Uses of Radionuclides

• Radioactive substances have a wide range of uses including:
  • Diagnosis of illness
  • Cancer treatment
  • Food preservation
  • Sterilization of medical equipment
  • Determining the age of rocks
  • Locating faults in metal structures, such as pipes
  • Carbon dating (using radioactive carbon isotopes)
  • Determining thicknesses
  • Smoke detectors

Radioactive Decay Law

• The number of radioisotopes that will decay clearly depends on the number of radioisotopes present at that point in time:

• Thus activity, or the number of decays per unit time, can be calculated using:

• The greater the decay constant, the greater the activity of the sample.
• The activity depends on the number of undecayed nuclei remaining in the sample.
• The minus sign indicates that the number of nuclei remaining decreases with time.

• Several additional formulae can be used to show the relationship of activity, the number of remaining nuclei and count rate.
  • These all use the constant e, or Euler's number.

Decay Constant and Half-Life

• We can relate the formula for half life and the formula for the decay constant to find their relationship.

Experimental Determination of Half Life

• For radioisotopes with relatively short half lives, we can create graphs using the radioactive decay laws by rearranging the formulas.

• The gradient of this graph should be the decay constant, which we can use to find the half-life of a substance.
• For radioisotopes with relatively long half-lives the count rate does not change during the course of an experiment, as some can take billions of years to decay!
  • Therefore we cannot use the count-rate equation.
  • Instead:

Sources

https://en.wikipedia.org/wiki/List_of_radioactive_nuclides_by_half-life#1030_seconds_(quettaseconds)