# Math in carbon dating

But what's interesting is that a small fraction of carbon-14 forms, and then this carbon-14 can then also combine with oxygen to form carbon dioxide.

And then you can use that rate to actually determine how long ago that thing must've died. It would be a pretty reasonable estimate to say, well, that thing must be 5,730 years old.

The exponential decay formula is given by: $$m(t) = m_0 e^$$ where $\displaystyle r = \frac$, $h$ = half-life of Carbon-14 = 30$years,$m_0$is of the initial mass of the radioactive substance. So, we have:$\displaystyle r = \frac = \frac = 0.000121$The mass ratio of Carbon-14 to Carbon-12 is$\displaystyle m_0 = \frac\$ (just look this up).

And we talk about the word isotope in the chemistry playlist. But this number up here can change depending on the number of neutrons you have. And every now and then-- and let's just be clear-- this isn't like a typical reaction. So instead of seven protons we now have six protons. And a proton that's just flying around, you could call that hydrogen 1. If it doesn't gain an electron, it's just a hydrogen ion, a positive ion, either way, or a hydrogen nucleus. And so this carbon-14, it's constantly being formed. I've just explained a mechanism where some of our body, even though carbon-12 is the most common isotope, some of our body, while we're living, gets made up of this carbon-14 thing.

So carbon by definition has six protons, but the typical isotope, the most common isotope of carbon is carbon-12. And then that carbon dioxide gets absorbed into the rest of the atmosphere, into our oceans. When people talk about carbon fixation, they're really talking about using mainly light energy from the sun to take gaseous carbon and turn it into actual kind of organic tissue.