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.
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