A piece of fossilized wood has a carbon-14 radioactivity that is 1/4 that of new wood.The half-life of carbon-14 is 5730 years.How old is the cloth?

Question

Quizplus · Accepted Answer

Since the carbon-14 radioactivity of the fossilized wood is 1/4 that of new wood, it means that 3 half-lives (1/2 x 1/2 x 1/2 = 1/8) have passed, since after each half-life, only half of the remaining carbon-14 is left. Therefore, we can set up the equation:

1/4 = (1/2)^3

Simplifying this equation gives:

1/4 = 1/8
8 = 4 x 2^(t/5730)

Where t is the age of the fossilized wood in years. Solving for t gives:

t/5730 = log2(8/4)
t/5730 = 1
t = 5730 years x 2 = 11,460 years

Thus, the best choice is B.

A Piece of Fossilized Wood Has a Carbon-14 Radioactivity That