Final answer:
To calculate the time it takes for 60.0 g of iodine-131 to reduce to 3.75 g, we determine the number of half-lives that equals approximately 4 (using the half-life formula). Multiplying this by the half-life of 8 days, we find it takes about 32 days.
Step-by-step explanation:
The question asks how much time will pass before 60.0 g of radioactive iodine-131 is reduced to 3.75 g, given that the half-life of iodine-131 is 8 days. To solve this, we need to use the concept of half-lives, which is the period it takes for a substance undergoing decay to decrease by half. Since the question provides us with the initial and final masses, we can calculate the number of half-lives that have passed, and then determine the total time. The formula for the number of half-lives (n) can be given as:
n = log(final mass / initial mass) / log(0.5)
Plugging in the values:
n = log(3.75 / 60.0) / log(0.5) = 3.99 or approximately 4 half-lives
Since one half-life is 8 days, the total time (t) is:
t = number of half-lives × half-life duration
t = 4 × 8 days
t = 32 days
Therefore, it takes approximately 32 days for 60.0 g of iodine-131 to be reduced to 3.75 g.