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

The answer is "17200 years".

Step-by-step explanation:

Given:

`A = 20 \ (counts)/(minute)\\\\A_(o) = 160\ (counts)/(minute)`

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

Constant decay
`\ w = (0.693)/( T)`

`= 1.209 * 10^(-4) \ (1)/(year)\\`

The artifact age
`t= ?`

`A = A_(o) e^(-wt) \\\\e^(-wt) = (A)/(A_(o))\\\\-wt = \ln (A)/(A_(o))\\\\= -2.079\\\\t = 1.7199 * 10^(4) \ years\\\\\sim \ 17200\ years\\`