The half-life of cobalt-60 is 5 years. How old is a sample of cobalt-60 if only one-eighth of the original sample is still cobalt-60?
A. 5 years
B. 10 years
C. 15 years
D. 20 years
To solve this problem, we can set up the equation:
(original sample) * (1/2)^(number of half-lives) = (final amount of sample)
We are given that only one-eighth of the original sample is still cobalt-60. Therefore:
(original sample) * (1/2)^(number of half-lives) = (1/8)(original sample)
We can cancel out the (original sample) from both sides of the equation to get:
(1/2)^(number of half-lives) = 1/8
To solve for the number of half-lives, we can take the logarithm of both sides of the equation:
log(base 1/2)(1/2)^(number of half-lives) = log(base 1/2)(1/8)
(number of half-lives) = log(base 1/2)(1/8) / log(base 1/2)(1/2)
(number of half-lives) = 3 / 1
(number of half-lives) = 3
According to the equation we set up, each half-life represents 5 years. Therefore, the sample is (3 x 5) = 15 years old.
Therefore, the answer is C. 15 years.