Carbon-14 has a half-life of 5730 years. A sample of wood has been recovered by an archaeologist. The sample is sent to a laboratory, where it is determined that the activity of the sample is 0.137 Bq/g. By comparing this activity with the activity of living organic matter, 0.230 Bq/g, the scientist determines how old the wood sample is, or more precisely, when the tree that the sample came from died. How old is the sample of wood

Answer: 4282.928 = 4283 years

Explanation:

Data given;

Carbon 14 half life = 5740

No (initial radiation) = 0.230 Bq/g

Nf (final radiation) = 0.137 Bq/g

First we find the decimal fraction of the remaining half life of the carbon 14

k = No / Nf

k = (0.137 / 0.230) = 0.595652

So to find how many half-life has elapsed, we say

(1/2) ^n = k

(1/2) ^n = 0.595652

Therefore

n log 0.5 = log 0.595652

n = (log 0.595652) / (log 0.5)

n = 0.747457

To get the elapsed time or how old the sample is;

We say

Carbon 14 half-life * n

5730 yrs * 0.747457

= 4282.928

= 4283 years.

So the sample of the wood is 4283 years old.