Understandable Earth Science

Radioactive decay is a process that is well understood and has been studied by physicists (and earth scientists) for over 100 years.  Nowadays radioactivity is used for a wide range of things, including power generation, specialist medical investigations and even making your smoke alarm work (don’t worry – smoke alarms are not dangerous!).

First, some definitions.

An atom is a basic unit of matter and consists of a nucleus of protons and neutrons surrounded by a cloud of electrons. Protons and neutrons both have mass. Protons have a positive charge and eletrons have a negative charge. The number of protons in the atom (the atomic number) defines what the element is (e.g. helium -He, carbon –C, argon – Ar, potassium – K, calcium – Ca, uranium – U….etc…).

Isotopes are atoms of a given element with different masses. They have different masses because they have different numbers of neutrons. For example, the element carbon (C ) has 6 protons but it can have 6, 7 or 8 neutrons, meaning that an atom of C could have a mass of 12, 13 or 14. We refer to different isotopes of an element by writing the mass in superscript in front of the element symbol – e.g. ¹²C, ¹³C, ¹⁴C.

Element Carbon Carbon Carbon Argon Potassium
Number of protons 6 6 6 18 19
Number of electrons 6 6 6 18 19
Number of neutrons 6 7 8 22 21
Total mass 12 13 14 40 40
Isotope ¹²C ¹³C ¹⁴C ⁴⁰Ar ⁴⁰K

Not all isotopes are stable – if there are too many or too few neutrons in a nucleus it can start to fall apart and / or change. Protons can change into neutrons and vice-versa, which involves the release of electrons or gamma-radiation, or sometimes neutrons are expelled from the nucleus to change the mass of the atom. When the number of protons in an atom changes, the atom becomes a different element. For example, the isotope of potassium ⁴⁰K (19 protons, 21 neutrons) radioactively decays to the isotope of argon ⁴⁰Ar (18 protons, 22 neutrons) by capturing an extra electron and converting a proton to a neutron. We call the original radioactive material (⁴⁰K) the parent isotope and the new material (⁴⁰Ar) the daughter isotope.

Radioactivity can be used as a kind of clock, because radioactive decay happens at a precise rate. Each radioactive isotope has a specific probability of decaying in a certain amount of time.  We can use that probability to predict how many parent isotopes will decay to daughter isotopes in a given time period. Or, turning that around, we can measure how many parent and daughter isotopes we have in a sample and use that to calculate how old the sample is.

radio-atoms2-r

The picture above gives a simplified explanation of how radiometric dating works. Parent isotopes are red circles and daughter isotopes are blue. We start off at time zero (t=0 mins) with 20 atoms of the parent isotope.  In this system, the radioactive parent isotope has a 50% chance of radioactively decaying within 10 minutes. That means that after 10 minutes (t=10 mins), 50% of the parent atoms have decayed and changed into the daughter isotope. That means that, at t=10 minutes, our sample now contains 10 atoms of parent and 10 atoms of daughter. 10 minutes later (t=20 mins) 50% of the atoms of parent isotope at t=10 mins (there were 10 atoms left) have decayed, adding an extra 5 daughter isotopes; at t=20 minutes there are 5 parent isotopes and 15 daughter isotopes.

Notice that the number of radioactive decays (parent changing to daughter) is not a set number for a given time period – there were 10 decays in the first 10 minutes, and only 5 decays in the next 10 minutes. The rate of radioactive decay is proportional to the amount of parent isotope, so the more parent isotopes you have, the greater the rate of change from parent to daughter. This means that radioactive decay is an exponential process.

This is shown in the next diagram which shows a sketch graph plotting the number of parent (red) and daughter (blue) isotopes over time.

radiograph-rgb

An atom of the parent isotope always produces an atom of the daughter isotope when it decays, so you can see that the curve for the number of parent atoms is just the mirror image of the daughter isotope curve.

Where the parent and daughter isotope curves cross is the point in time where the number of parent and daughter atoms are equal. This means that half of the original parent isotopes have now decayed. We call this time-interval the half-life of the isotope system. So in the example I described above, the half life is 10 minutes, because that is how long it takes for half of the parent isotopes to decay.

To be able to date rocks using this theory, we need to know:

  • how many atoms of parent and atoms of daughter isotope were present at the event we want to date (t=0),
  • how many atoms of parent and atoms of daughter isotope are present now
  • the rate of radioactive decay (for calculations we use the decay constant, which can be calculated from the half-life).

In the next blog I will show you how this is used in a dating technique called K-Ar dating.

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Comments on: "How old is that rock? Part 1: Radioactivity" (2)

  1. Heh, I was able to read through the post while understanding everything (and I’m as far from earth science as one can be, though I find it fascinating!). Just from curiosity, in reality… it is an approximation to exponential right? Just an exponential behavior. I mean it must reach a point where you have 0 parent isotopes, no? Can you still calculate the age from that scenario? Cheers!

  2. There are a couple of issues here. You are right, you can’t have half an atom decaying, so there will be a point when you run out of parent isotopes completely. In this situation, all you can say is that the age is older than can be measured by that isotope system. So, for instance, you can’t use radiocarbon dating to date material older than about 50 thousand years, because all of the radioactive ¹⁴C has decayed away.

    In reality, “0 parent isotopes” is the same as the detection limits of the technique being used to measure the sample – i.e. the smallest amount of material we can measure. This is where scientific and technological advances can extend the age-range of a particular isotope system; as technology improves, we can detect and measure much lower concentrations of parent and daughter isotopes, which makes it possible to date older and younger rocks. For example, 25 years ago, the upper limit for radiocarbon dating was about 40 thousand years, but technological improvements have added an extra 10 thousand years onto the age range.

    But running out of a parent isotope isn’t always bad news. Quite lot of “extinct radionuclides” have been identified – these are isotopes that have completely decayed away, and the main way we can tell that they ever existed is because there is a higher than expected concentration of the daughter isotope. They are particularly useful for tracing nuclear activity by humans, and for understanding very old processes, like formation of the solar-system. The first extinct isotope to be identified was an isotope of iodine – ¹²⁹I – this is produced by humans in nuclear reactors and from nuclear weapons, and in nature from supernovas. It decays to an isotope of the noble gas xenon – ¹²⁹Xe – with a half-life of ~16 million years. But a lot of meteorites contain a large amount of ¹²⁹Xe, which means they must have originally contained a lot of ¹²⁹I. This tells us that the meteorites must have formed quite soon after a supernova to be able to take in ¹²⁹I.

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