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Answer :
Final answer:
After 256.4 hours, approximately 0.3125 ng of mercury-197 will remain based on its half-life of 64.1 hours.
Explanation:
The half-life of mercury-197 is 64.1 hours. To determine how much will remain after 256.4 hours, we can divide the total time by the half-life to find the number of half-life periods that have passed. In this case, 256.4 hours divided by 64.1 hours gives us approximately 4 half-life periods.
Each half-life period reduces the amount of mercury-197 by half. So, if a patient is given 5.0 ng of mercury-197, after 4 half-life periods, only one-sixteenth (1/2^4) of the original amount will remain.
Therefore, after 256.4 hours, approximately 0.3125 ng (5.0 ng divided by 16) of mercury-197 will remain.
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