Physical, Biological & Effective Half Life (AQA A Level Physics)

• In a medical context, multiple half-life definitions must be considered
  • The radionuclides introduced have a half-life, but the radiopharmaceuticals (molecules with radionuclides attached) are also removed from the body by natural processes over time 
• The physical half-life of a radioisotope is defined as

The time taken for the number of radioactive nuclei to halve

• This is the same as the half-life of a radioactive nuclide, which is a constant quantity for a given nuclide

• The biological half-life of a substance is defined as:

The time taken for the concentration of a substance in the body to decrease by half

• This accounts for the processes of removing drugs from the system through excretion and respiration
  • This depends on many factors, such as the health and metabolism of the patient

• Effective half-life  is the combined half-life of physical and biological half-life
  • This accounts for radioactive processes and biological excretion

• Effective half-life is given by the equation:

• Effective half-life  is always shorter than the shortest half-life out of  and 

• If the physical half-life is short, the effective half-life is even shorter
  • This is because the body is also excreting the chemical to which the radionuclide is attached

• If the biological half-life is short, the effective half-life is even shorter
  • This is because the radionuclide is also decaying while the body is excreting the radiopharmaceutical at this fast rate