Final answer:
The symbol M in the formula represents the final mass of radioactive iodine-131 after a number of half-lives have passed, with M₀ representing the initial mass. The half-life of iodine-131 is 8.1 days, which is the time required for half of the radioactive iodine-131 to decay. This concept is used to calculate the amount of radioactive material remaining after any given period.
Step-by-step explanation:
The remaining mass of radioactive iodine-131 after a certain number of half-lives can be represented by the formula M = M₀(1/2)n, where M denotes the final mass of the radioactive material, and M₀ denotes the initial mass. The variable n represents the number of half-lives that have passed.
For iodine-131, which has a half-life of 8.1 days, we can calculate the remaining mass after any given time. For example, if n equals 5, this would mean that 5 half-lives have passed. If we started with 50.0 mg of iodine-131, after 5 half-lives we would have 50.0 mg × (1/2)5 remaining.
The half-life of a radioactive substance is the time it takes for half of the atoms to decay. In the example of iodine-131 with a half-life of 8.1 days, if you begin with a certain amount of the substance, after 8.1 days, you would have half of that initial amount. After another 8.1 days (a total of 16.2 days), you'd have a quarter of the original amount, and so on.