Answer :
The percent activity of the sample of rhenium-186 remaining after 4 half-lives is 6.25%, calculated by halving the activity four times.
The percent activity of the rhenium-186 remaining after 4 half-lives is 6.25%.
Here's how we can find it:
Half-life: We don't have the specific half-life of rhenium-186 provided in the question. However, the concept applies regardless of the actual half-life value.
Number of half-lives: We are given that 4 half-lives have passed.
Activity remaining: The fraction of the original activity remaining after n half-lives can be calculated using the formula:
Fraction remaining = (1/2)^n
where n is the number of half-lives.
Calculate the fraction remaining: In this case, n = 4:
Fraction remaining = (1/2)^4 = 1/16
Convert to percentage: Multiply the fraction remaining by 100 to express it as a percentage:
Percent remaining = (1/16) x 100% = 6.25%
Therefore, after 4 half-lives, only 6.25% of the original activity of the rhenium-186 sample remains.
