Calculations involving effective halflifeThe biological halflife can be defined as the time taken for half of the available radioactive material to be removed from the body by natural processes. This assumes no new material is arriving. It is due to the metabolic turnover of the molecule the radioactive tracer atom has been attached to. This will vary from one person to another and from one organ to another, thereby making accurate estimates of biological halflife very difficult to make. It follows that effective halflife also has a larger than desirable error margin also. Let l_{B} be the fraction of the radioisotope removed per second by biological processes Let l_{p} be the fraction of the radioisotope removed per second by radioactive decay. Let l_{E} be the fraction of the radioisotope removed per second by both physical and biological processes. Then l_{E} = l_{B} + l_{P } Let T_{B} be the biological halflife Let T_{p} be the physical halflife. Let T_{E} be the effective halflife. Now l_{E }= ln2/T_{E} l_{P }= ln2/T_{P} and l_{B }= ln2/T_{B} So it follows that ln2/T_{E }= ln2/T_{P }+ ln2/T_{B} and 1/T_{E }= 1/T_{P }+ 1/T_{B} (Note the similarity of this equation to the resistances in parallel one. This is because just as current flow has two routes through the potential drop when resistances are in parallel so the radioactive isotopes have 'two routes' out of the body… biological or by physical radioactive decay). Try this calculation The human serum, albumin can be labelled with atoms of the radioactive isotope iodine 131. This has a physical half life of 8 days and a biological halflife of 21 days. Find the effective halflife. 
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