The half-life of a certain radioactive element is 1,250 years. What percent of the atoms remain 7,500 years?
a
50%
b
1.5625%
c
6.25%
d
25%
The percent of atoms remaining after a certain period of time can be determined by the formula:
Remaining atoms = (1/2)^(time / half-life) * 100
In this case, the time is 7,500 years and the half-life is 1,250 years. Plugging these values into the formula:
Remaining atoms = (1/2)^(7500 / 1250) * 100
Simplifying the exponent:
Remaining atoms = (1/2)^6 * 100
Calculating the exponent:
Remaining atoms = (1/64) * 100
Simplifying the fraction:
Remaining atoms = 1.5625%
Therefore, the correct answer is b) 1.5625%.