Carbon-14, which is present in all living tissue, radioactively decays via a first-order process. A one-gram sample of wood taken from a living tree gives a rate for carbon-14 decay of 13.6 counts per minute. If the half-life for carbon-14 is 5720 years, how old is a wood sample that gives a rate for carbon-14 decay of 7.9 counts per minute? A. 5.3 x 102 yr. B. 7.6 x 102 yr. C. 1.1 x 103 yr. D. 9.5 x 103 yr.

The question is incorrect, the correct question is;

Carbon-14, which is present in all living tissue, radioactively decays via a first-order process. A one-gram sample of wood taken from a living tree gives a rate for carbon-14 decay of 13.6 counts per minute. If the half-life for carbon-14 is 5720 years, how old is a wood sample that gives a rate for carbon-14 decay of 11.9 counts per minute?

C. 1.1 x 103 yr

Explanation:

A = count rate of the wood sample

Ao= count rate of a living tissue

t1/2= half life of C-14

t = time taken

From;

0.693/t1/2 = 2.303/t log Ao/A

0.693/5720 = 2.303/t log (13.6/11.9)

1.2 * 10^-4 = 2.303/t * 0.05799

1.2 * 10^-4 = 0.1336/t

t = 0.1336/1.2 * 10^-4

t = 1.1 x 103 yr

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