The half life of a certain radioactive element is 1,250 years. what percent of the atoms remain after 7,500 years?

Question

A. 25%
B. 1.5625%
C. 6.25%
D. 50%

Answer 1

The formula for calculating the percent of atoms remaining after a certain number of half-lives is:

Percent remaining = (1/2)^(number of half-lives) * 100%

In this case, since the half-life of the element is 1,250 years, we can calculate the number of half-lives that have passed in 7,500 years:

Number of half-lives = (total time) / (half-life) = 7500 / 1250 = 6

Now, we can substitute this value into the formula to find the percentage remaining:

Percent remaining = (1/2)^(6) * 100%

Percent remaining = (1/64) * 100% = 1.5625%

Therefore, the answer is B. 1.5625%.