Final answer:
The decay of iodine-131 can be calculated using an exponential decay equation and the decay constant. By rearranging this equation, we can solve for the time it takes for 90% of the substance to decay, given an initial concentration and a decay constant of 0.138 d−¹.
Step-by-step explanation:
Understanding the decay of radioisotopes requires the use of exponential decay equations and half-life concepts. The decay of radioactive material is an exponential process, which means that the amount of a radioactive substance decreases by a fixed percentage over equal time periods. The half-life is the amount of time it takes for half of the original substance to decay. This is expressed mathematically in a decay equation using the decay constant (k).
For iodine-131, with a given decay constant of 0.138 d−¹, to calculate how long it will take for 90% to decay, we would use the equation:
amount remaining = initial amount × e−kt
If we start with a 0.500 M solution, we want to find the time when the solution is reduced to 0.050 M (10% remaining). By rearranging the decay equation and solving for t, we can find the number of days it will take for this level of decay to occur.