[Lewis Thomson (OP)]

Paul wishes to know the answer to this question.

"An atom of carbon starts life alone, gets into a fish which dies and then the carbon is absorbed into seaweed, which ends up around a shoreline tree root and the carbon atom gets into the tree. The tree is cut down and used for a railway sleeper, and then sold to a cabinet maker who uses it to build a chair. The chair is thrown out on an Egyptian rubbish heap and years later some archaeologist finds the remnants (sorry swap railway sleeper for something appropriate for the time) and carbon dates it. How? Is he/she dating it back to the fish or the tree or the chair?"

Place your thoughts in the comments below to help him out...

[Origin]

The date from Carbon-14 dating in your scenario would be from the time the tree was alive.  The overwhelming majority of the carbon would come from respiration during the life of the tree.  Therefore the carbon dating would give the date as the time when the tree died.  If the Egyptian chair made from that tree was owned by a family and their descendant for 3,000 years (some fine chair I'd say) and then dug up by archeologist they could easily come to the incorrect conclusion that the house where the chair was found was 3,000 years older than it really was. 

[evan_au]

The date from Carbon-14 dating in your scenario would be from the time the tree was alive.

I would push the origin back slightly further to a cosmic ray striking a Nitrogen atom in the atmosphere, forming an atom of Carbon 14.
- Carbon-14 is slightly radioactive, with a half life of 5730 years
- This (slightly) radioactive carbon atom in the atmosphere is then absorbed by the tree, and built into the growth ring for that year.
- With a mass spectrometer, it is possible to measure the ratio of C14 to the "normal" C12; this ratio halves every 5730 years.
https://en.wikipedia.org/wiki/Radiocarbon_dating

An interesting recent development is the use of mass spectrometry to date samples from individual tree-rings, providing a high-resolution calibration curve of C14 production in the atmosphere. This allows researchers to date particular tree-rings to a specific year that had a big burst of C14 production (eg due to a solar storm). This allowed researchers to state that Vikings had chopped down a tree in Canada in the year 1021 (+/- 1 year), based on dating wood chips.
- Ironically, these researchers had easy access to Viking wood chips, because the archaeologists regard them as rubbish!
https://the-past.com/news/vikings-in-canada/