A radioactive isotope will decay in the laboratory with a half life (the time taken for half of the isotope to decay) characteristic of the isotope. When a radioactive source enters the human body, the amount of radioactive substance present at any time depends on both the half life of the isotope and the biological half life – the body is removing substances constantly by excretion, exhalation and sweating. The biological half life measures the time taken for the amount of substance in the body to halve DUE TO BIOLOGICAL PROCESSES.
The effective half life is the time taken for the amount of radioactive substance in the body to halve. The effective half life obviously depends on both the half life of the isotope and the rate at which the body rids itself of the isotope, and is shorter than either.
If the biological half – life is given by
the radioactive half – life is given by
and the effective half – life is given by
then
Alternatively, using
so that
and 
the amount of the isotope present in the body is given by