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Answer :
Final answer:
After 3 half-lives of gold -198 , approximately 12.5 mg of gold-198 will remain.
Explanation:
The half-life of gold-198 is 2.7 days.
After each half-life, the amount of gold-198 remaining is halved.
After 3 half-lives, the amount of gold-198 remaining will be one-eighth of the original amount.
So, to calculate the mass of gold-198 remaining after 3 half-lives:
- Calculate the number of half-lives: 3 half-lives = 3 x 2.7 days = 8.1 days
- Calculate the fraction remaining: 1/2 x 1/2 x 1/2 = 1/8
- Calculate the mass remaining: 1/8 x 100.0 mg = 12.5 mg
Approximately 12.5 mg of gold-198 will remain after 3 half-lives.
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