Imagine a beaker with radioactive NaI solid at bottom. Carefully pour saturated solution of non-radioactive NaI over the solid.
It's important that the solution is saturated. That means that the solution is holding the maximum amount of NaI it can at that temperature.
Allow to sit for several hours.
Remove solution and filter to get solid out.
Solution found to be radioactive. Accounting for radioactive decay, the solution inceases in radioactivity until reaching a constant level.
There are two reactions happening and they are the reverse of each other:
1) Solid NaI is dissolving.
2) Dissolved NaI (as Na+ and I¯ ions) is being converted to the solid state.
The result over time is that radioactive NaI moves into the solution and non-radioactive NaI moves into the solid state. As the radioactive NaI moves into solution, the radioactivity increases until it reaches a certain, constant level.
At that point, the rate of NaI dissolving exactly equals that of NaI solidfying. An equilibrium between the two reactions has been established.