RIA is based on the principle of competitive binding. In this technique, competitive binding occurs between an unlabeled antigen and radiolabel antigen (radiolabel with 125I-$\gamma$ emitting, bind to a tyrosine of protein or 3H-β particle emitting) with the high-affinity antibody. Firstly antigen mix is labeled with known amount of antibody in that concentration, which is able to saturate the antigen binding site on antibody and through which we can calculate total count per minute (CPU) through beta or gamma counter, after that the amount of radiolabeled antigen is obtained which is required to saturate the known amount of antibody.
Now make a set up in which known amount of antibody (same as the previously used) is added in to tube and after that known amount of radiolabeled antigen along with unknown concentration of test samples of unlabeled is antigen added in increasingly larger amount and allow the competition between labeled and unlabeled antigen for available antigen binding site on antibody Because antibody is not able to discriminate between labelled and unlabeled antigen, as gradually the concentration of unlabeled antigen increase, this causes the displacement of labelled antigen and this decreases the amount of antibody bound radiolabeled antigen (this is called decrease in count per minute-CPM) during the presence of test sample. It is used to measure the amount of antigen present in the test sample.

Here we have the standard curve generated between the decrease in radioactivity and the known concentrations of unlabeled antigen. As their concentration increases during the experiment, this is called as standards and we put the decrease in amount of radioactivity value or decrease in count per minute (CPU) value in our experiment by adding unlabeled sample containing antigen on that graph and by plotting this value on standard graph we get the concentration of antigen in unlabeled sample. We can take the standard graph previously present but generally, standards run simultaneously with experiment and their generated graph is used to determine the value of anti in the unknown sample.
RIA was developed by Yalow and Berson in 1960 and Yalow got Noble prize for this in 1977, they assayed concentration of insulin in blood plasma. RIA is used in the detection of the level of hormone, drug serum protein and vitamins and can detect 0.001 micrograms in one millilitre or less than that.
Secondary anti-isotype antiserum is used to precipitate the Ag-Ab complex, as a result, bound antigen gets separated from the free antigen in RIA. Staphylococcus aureus has a protein named protein A, which has a high affinity towards IgG, If IgG is present in Ag-Ab complex than mixing of this complex with formalin-killed S. aureus result in precipitation of this complex and removal of Ag-Ab complex either two method provide the free radiolabel antigen in supernatant , then minus the value of the supernatant containing radiolabeled antigen from the total, provide the value of antibody bound radiolabel antigen.
In solid-phase RIAs separation of Ag-Ab complex is easier. In some cases, the antibody also adheres on sepharose beads through covalent crosslinking. In this case by centrifugation of beads and then washing separately the beads bound radiolabeled antigen. The antibody can be also immobilized on polystyrene or polyvinylchloride wells. In this case amount of supernatant containing free radiolabeled Antigen is governed by a radiation counter. The antibody is also immobilized on 96-well microtiter plate, for determining the particular antigen in the various sample, it is a well-suited method, eg., hepatitis B.