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

Physical, Biological & Effective Half Life

• 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 $T_P$ 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 $T_B$ 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 process 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 $T_E$ 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:

$\frac{1}{T_E}=\frac{1}{T_P}+\frac{1}{T_B}$

• Effective half-life $T_E$ is always shorter than the shortest half-life out of $T_P$ and $T_B$

• 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