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?

Question

A. 5 years

B. 10 years

C. 15 years

D. 20 years

Answer 1

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.