Answer :
To account for the decay over 12 days, at least 96 grams of mercury-197 should be ordered to ensure 6 grams remain for the study, considering its 3-day half-life.
To solve this, we need to determine how much of the mercury-197 will decay over the 12-day shipment period. Mercury-197 has a half-life of 3 days. This means that every 3 days, half of the mercury-197 will decay.
Let's start by finding the number of half-lives in the 12-day period:
Number of half-lives = Total time / Half-life
Number of half-lives = 12 days / 3 days = 4 half-lives
After 4 half-lives, the remaining quantity of the original mercury-197 can be calculated using the formula:
Remaining quantity = Initial quantity *[tex](1/2)^N^u^m^b^e^r^ o^f^ h^a^l^f^-^l^i^v^e^s[/tex]
To find out the initial quantity (let’s call it X) needed for 6.0 grams after 4 half-lives:
6.0 grams = X *[tex](1/2)^4[/tex]
6.0 grams = X * 1/16
X = 6.0 grams * 16
X = 96 grams
Thus, the minimum mass of mercury-197 that needs to be ordered is 96 grams.
