Question

The radioactivity due to carbon-14 measured in a piece of a wood from an ancient site was found to produce 20 counts per minute from a given sample, whereas the same amount of carbon from a piece of living wood produced 160 counts per minute. The half-life of carbon-14, a beta emitter, is 5730 y. The age of the artifact is closest to

Answer 1

Answer:

The answer is "17200 years".

Explanation:

Given:

$A = 20 \ \frac{counts}{minute}\\\\A_{o} = 160\ \frac{counts}{minute}$

Let the half-life of carbon-14, is beta emitter, is $T = 5730\ years$

Constant decay $\ w = \frac{0.693}{ T}$

$= 1.209 \times 10^{-4} \ \frac{1}{year}$

The artifact age $t= ?$

$A = A_{o} e^{-wt} \\\\e^{-wt} = \frac{A}{A_{o}}\\\\-wt = \ln \frac{A}{A_{o}}\\\\= -2.079\\\\t = 1.7199 \times 10^{4} \ years\\\\\sim \ 17200\ years$