Mercury-197 is used for kidney scans and has a half-life of 3 days. if the amount of mercury-197 needed for a study is 1.0 grams and the time allowed for shipment is 15 days, how much mercury-197 will need to be ordered.
That is five half-lives
amount needed=1*2^5=32 grams
To determine the amount of mercury-197 that needs to be ordered, we need to calculate the amount that will remain after 15 days, taking into consideration its half-life of 3 days.
The general formula to calculate the remaining amount of a substance after a certain time can be given by:
Remaining amount = Initial amount * (1/2)^(time elapsed / half-life)
In this case:
Initial amount = 1.0 grams
Time elapsed = 15 days
Half-life = 3 days
Substituting the values into the formula:
Remaining amount = 1.0 grams * (1/2)^(15 / 3)
To simplify the calculation, we can break down the exponent:
Remaining amount = 1.0 grams * (1/2)^5
Now, we can calculate:
Remaining amount = 1.0 grams * (1/32)
Remaining amount = 0.03125 grams
Therefore, in order to have 1.0 grams of mercury-197 available after 15 days, you will need to order approximately 32 grams of mercury-197.
To answer this question, we need to consider the half-life of mercury-197 and the time allowed for shipment.
The half-life of mercury-197 is 3 days, which means that every 3 days, the amount of mercury-197 is reduced by half.
Now, we need to find out how many times the half-life of mercury-197 fits into the given 15-day shipment time. We can do this by dividing 15 by 3:
15 days / 3 days = 5 half-lives
Since each half-life reduces the amount of mercury-197 by half, we need to determine how much mercury-197 is needed after 5 half-lives.
1.0 gram / (2^5) = 1.0 / 32 = 0.03125 grams
So, after 5 half-lives, we would need approximately 0.03125 grams of mercury-197 for the study.
Therefore, to ensure that we have enough mercury-197 for the study, we need to order at least 0.03125 grams of mercury-197.