It is impossible to predict when a given atom will decay, but given a large number of similar atoms, the decay rate on average is predictable.
This predictable decay is called the half-life of the parent atom, the time it takes for one half of all of the parent atoms to transform into the daughter.
When the number of neutrons is not in balance with the protons then the atom of that particular element is said to be unstable.
In nature, all elements have atoms with varying numbers of neutrons in their nucleus.
These differing atoms are called isotopes and they are represented by the sum of protons and neutrons in the nucleus. Carbon has 6 protons in its nucleus, but the number of neutrons its nucleus can host range from 6 to 8.
We thus have three different isotopes of carbon: Carbon-12 with 6 protons and 6 neutrons in the nucleus, Carbon-13 with 6 protons and 7 neutrons in the nucleus, Carbon-14 with 6 protons and 8 neutrons in the nucleus.
Both carbon-12 and carbon-13 are stable, but carbon-14 is unstable, which means that there are too many neutrons in the nucleus. As a result, carbon-14 decays by changing one proton into a neutron and becoming a different element, nitrogen-14 (with 7 protons and 7 neutrons in the nucleus).
So, you can use the radioactive elements to measure the age of rocks and minerals. Their useful range is from about 1/10 their half-life (the time it takes for half of the radioactive element/isotope-- the parent, to convert into a non-radioactive element/isotope-- the daughter) to 10 times their half-life. You can use this to measure the age of a rock from about 128 million years to more than 10 billion years (the Solar System is 4.56 billion years old).
While not a chemical test, the presence of carbon in a sample (like a meteorite) can be found by vaporizing the sample and passing it through a mass spectrometer.
This is also a way to get at the abundance of the various isotopes of carbon.
Earth) and what could happen to Earth in an extreme case, etc.
From Wikipedia, radioactive decay is the process in which an unstable atomic nucleus spontaneously loses energy by emitting ionizing particles and radiation.