The idea behind this first article came from a discussion I had with a friend a few months ago.

‘How do you know the age of the Earth? I heard ¹⁴C gives only very recent ages.’

His statement was partly true, but overall it had some fake-news-flavour. Indeed ¹⁴C is unsuitable for that purpose, but other chronological tools are available. I will explain in a further article how we came to know the age of our planet, but right now let’s talk about ¹⁴C, arguably the most popular dating method. 

The scientific approach to get the age of something (such as, the Solar System - or swords and bones) is called radiometric dating. Assuming you might care about that, to understand the general issue and the carbon case, you should have the patience to get an idea about some key terms:

Isotope comes from Greek and means ‘same place’, meaning they occupy the same position on the periodic table (= have the same number of protons / atomic number / Z). As it’s obvious that each position in the periodic table belongs to a particular chemical element (in other words Z is sufficient to describe an element), then you would get that isotopes are versions of the same element.

The difference comes from the different number of neutrons which are bound together with the same Z protons in the atomic nucleus. Note that identical Z also means they have the same chemical properties.

We classify isotopes as either stable or radioactive. Stable means an equilibrium between nuclear internal forces in such a way that protons and neutrons are perfectly bound together inside the nucleus. Radioactive means that the excess neutron(s) affect the balance of these forces in such a way that the atom tries to adjust to a more stable nuclear configuration. This adjustment is not as easy as getting rid of the excess neutrons, but happens in many ways (I shall avoid presenting them, I want you to finish the article).

The funny thing is that actually the number of protons (Z) is modified, thus a daughter nuclide (different element) is being created as a result of a parent suffering a radioactive decay. The process can be imagined as reducing the energy expenses of your house (nucleus) after somebody leaves (emitting radiation).

You cannot predict when a particular atom will decay (as theorised from quantum mechanics). It’s a  process and deals with probabilities being applied to large populations of atoms. Imagine that the stats say that each year a different house from your neighbourhood is getting robbed. You don’t know if it’s your turn this year, but you know that it’s going to happen. That’s how it works with the radioactive atoms – we don’t know which one will decay, but we know how much time will take until the last one does.

Scientists developed some tools to predict the decrease in radioactive nuclide population. A key parameter is the decay constant, λ (lambda), which is the probability of decay per unit of time. Because in order to get that involves some derivatives, it’s way easier to deal with a related parameter called half-life (T1/2). Apart from the popular first person shooter of the 2000’s, half-life means the time taken for half of radioactive atoms to decay. After a half-life, the initial radionuclide population will be represented by 50% unradiogenic daughter nuclides and 50% radioactive parent nuclides. And so on.