# How exactly Radiocarbon dating Works?

So how exactly does Carbon Dating work ?

$$^{14}$$C is produced from $$^{14}$$N in the atmosphere. Since there is considerable amount of Nitrogen in the atmosphere,we can have quantifiable amount of $$^{14}$$C in the atmosphere, the ratio of $$^{14}$$C to $$^{12}$$C is $$1:10^{12}$$.

An average human weights $$80\,\rm kg$$, $$18\%$$ of our body is Carbon ,that's $$14.4\,\rm kg$$ ,so every time we are breathing we have $$6.194×10^{26}$$ Carbon atoms with us and around $$7×10^{14}$$ $$^{14}$$C atoms.

When the human body dies, the $$^{14}$$C atoms stop getting replenished and the number of atoms starts to get reduced.

So its rate of decay is $$0.0001209424$$ per year.

Now how do we proceed with finding the life time.

Scientists supposedly burn a piece of the adtifact to find the CO$$_2$$. I don't get this part .

• You extract carbon from a sample, ionize it, accelerate it, magnetically separate it, and count the two masses to get a ratio. See for example pelletron.com/products/… Apr 6, 2022 at 16:29
• Where does the information about burning the sample to obtain $CO2_$ come from? Apr 6, 2022 at 17:13
• Apr 6, 2022 at 17:54
• @MisterMak - burning the material to form a gas leaves much of the non-carbon stuff as solids. Now one either feeds the ion source with the gas, or can readily remove the other main gas component, water. Apr 6, 2022 at 18:03
• WP. Apr 6, 2022 at 19:44

...the $$^{14}\text{C}$$ atoms stop getting replenished and the number of atoms starts to get reduced...

It's not the number of $$^{14}\text{C}$$ atoms that matters, it's the ratio of $$^{14}\text{C}$$ to $$^{12}\text{C}$$. That ratio remains constant throughout the organism's life, but then it starts to change after the organism dies and stops exchanging carbon with its environment.

Scientists supposedly burn a piece of the artifact to find the CO2. I don't get this part.

Presumably you are talking about an artifact that was made from plant or animal tissue (wood, leather, sinews, grass, etc.)

An archaeologist can analyze the $$\text{CO}_2$$ from the burning with a mass spectrometer to measure the $$^{14}\text{C}$$ to $$^{12}\text{C}$$ ratio, and thereby determine approximately how long ago the wood or leather or whatever was harvested.

P.S., Depending on what equipment is available in the mass spec lab, it may be possible to liberate carbon from the sample by other means than burning.

• Ok I understand that the ratio gets changed ,but how does this help with our cause ?My ratio was 1:$10^{12}$ at the beginning ,now it's changed ,I don't understand how this piece of info helps us Apr 7, 2022 at 2:39
• @HarryCase, Maybe I did not understand what you are asking. Are you asking for the exact mathematical formula that maps the isotope ratio to a number of years? I don't know that off the top of my head. With a bit of work, I could derive a naive version from the ratio in air and from the half-life of $^{14}\text{C}$, which I would look up using Google. But, it turns out, the naive version can be pretty far from the mark. There apparently are multiple reasons why. You can read the Wikipedia Article to get a sense of it. Apr 7, 2022 at 13:09
• yeah I was asking how the mass ratio helps us with finding the age of the artifact Apr 7, 2022 at 14:55