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Answer :
To wait for the amount of Au-198 to fall to 0.75 mg when Gold-198 is used to treat liver cancer and has half-life is 2.7 days if ingest 3.75 mg of Au-198 would wait 6.26 days.
Gold-198 has a half-life of 2.7 days, which means that after 2.7 days, half of the initial amount of gold-198 would decay. To find out how long it would take for the amount of gold-198 to fall to 0.75 mg, we can use the following formula:
Final amount = Initial amount × (1/2)^(number of half-lives)
Let's assume that the initial amount of gold-198 is 3.75 mg, and we want to find out how many half-lives it would take for the amount to fall to 0.75 mg. We can set up the equation as follows:
0.75 mg = 3.75 mg × (1/2)^(number of half-lives)
Dividing both sides by 3.75 mg, we get:
0.2 = (1/2)^(number of half-lives)
Taking the logarithm of both sides, we get:
log(0.2) = number of half-lives x log(1/2)
Solving for the number of half-lives, we get:
number of half-lives = log(0.2) / log(1/2)
Using a calculator, we get:
number of half-lives ≈ 2.32
Therefore, it would take approximately 2.32 x 2.7 days = 6.26 days for the amount of gold-198 to fall to 0.75 mg.
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