Isotope dilution analysis is a technique to increase the precision and accuracy of chemical analysis. First, a known amount of an isotope is added to the sample. For example, to determine the amount of lead in a sample, a known amount of Pb-204, one of the isotopes of lead, can be added. The natural abundance of lead isotopes is 204 (1.8%), 206 (22.1%), 207 (24.2%), and 208 (52.1%). The isotopic composition of the sample will be slightly changed. Then, by measuring each isotope, the amount of lead in the original sample can be calculated. In a typical gas chromatography analysis, isotopic dilution can decrease the error of injection from 5% to 1%. It can also be used in mass spectrometry (commonly referred to as isotopic dilution mass spectrometry or IDMS), in which the isotopic ratio can be determined with precision typically better than 0.25%.[1]
A slightly different form of isotopic dilution can be used for determining the composition of a radioactive sample. An additional amount of the radioactive isotope in the sample is added and the change in radioactivity is measured. The amount of the isotope in the original sample can then be calculated. To determine the concentration x g (unknown) substance, y g of radioactive substance is added with Si as the initial activity. After homogenization, small sample of the substance has to monitor for the activity. By law of conservation of activity, the mixture (x + y) with show the specific conserved activity Sf (final activity). Therefore,
y * Si = (x + y) * Sf
now, x = y * (Si - Sf)/Sf thus, the concentration or quantity of the unknown substance can be calculated using the above equation.